We used a well-validated three-dimensional ocean model to investigate the
process of energetic response of near-inertial oscillations (NIOs) to a
tropical cyclone (TC) and strong background jet in the South China Sea
(SCS). We found that the NIO and near-inertial kinetic energy (KEni) varied
distinctly during different stages of the TC forcing, and the horizontal and
vertical transport of KEni was largely modulated by the velocity and
vorticity of the jet. The KEni reached its peak value within ∼1/2 the inertial period after the initial TC forcing stage in the upper
layer, decayed quickly by 1/2 in the next 2 d, and further
decreased at a slower rate during the relaxation stage of the TC forcing.
Analyses of the KEni balance indicate that the weakened KEni in the upper
layer during the forcing stage was mainly attributed to the downward KEni
transport due to pressure work through the vertical displacement of
isopycnal surfaces, while upward KEni advection from depths also contributed
to the weakening in the TC-induced upwelling region. In contrast, during the
relaxation stage as the TC moved away, the effect of vertical advection on KEni
reduction was negligible and the KEni was chiefly removed by the outward
propagation of inertial-gravity waves, horizontal advection, and viscous
dissipation. Both the outward wave propagation and horizontal advection by
the jet provided the KEni source in the far field. During both stages, the
negative geostrophic vorticity south of the jet facilitated the vertical
propagation of inertial-gravity waves.
Introduction
Near-inertial oscillations (NIOs), whose frequencies are close to the local
inertial frequency, contain around half of the observed internal wave
kinetic energy in the ocean (Simmons and Alford, 2012). NIOs also greatly
affect the kinetic energy budget in the deeper ocean as they propagate
downward from the surface and enhance the mixing by increasing vertical
shear (Gill, 1984; Gregg et al., 1986; Ferrari and Wunsch, 2009; Alford et
al., 2016).
Tropical cyclones (TCs), with the rapid change of wind stress, provide an
important generation mechanism for the NIOs. Observational studies related
to a single storm or tropical cyclone (Price, 1981; Shay and Elsberry, 1987;
D'Asaro et al., 1995) showed that the NIOs related to TCs can be a factor
2–3 larger than the background NIOs and last for more than five inertial
periods (IPs). Using a hurricane–ocean coupled model, Liu et al. (2008)
estimated that the energy input of tropical cyclones into the near-inertial
currents was about 0.03 TW, about 10 % of the total wind-induced
near-inertial energy (Watanabe and Hibiya, 2002; Alford, 2003). The input of
wind energy to the near-inertial band is also controlled by the translation
speed of the TC (Uh) (Geisler, 1970; Price, 1981). In fact, the NIOs
are largely variable during the forcing and relaxation stage of the TC
forcing related to the intensity and translation speed of the TC. The
variation is determined not only by the different magnitude of the input of wind
energy but also by the different dynamic conditions that regulate the
near-inertial kinetic energy (KEni) transport during these stages. The
variable response of NIOs during different stages of TC forcing is critical
for understanding the process and physics of NIOs.
Once generated, the characteristics of NIOs, in terms of the decay timescale, propagation direction, and propagation speed are influenced by
various mechanisms. In linear wave theory, the β effect leads to
equatorward propagation of the NIOs, and their decay timescale is reduced
because of the vertical propagation into deeper ocean (Gill, 1984; D'Asaro,
1989; Garrett, 2001). Background flow fields also have great influence on
the evolution of NIOs. The influence of background vorticity on NIOs has
been observed by Weller (1982) and Kunze and Sanford (1984) and proven
analytically by Kunze (1985), Young and Jelloul (1997), and Danioux et
al. (2015). A numerical study using a primitive equation model with a
turbulent mesoscale eddy field and uniform wind forcing came to a similar
conclusion (Danioux et al., 2008). Non-linear interactions also provide a
mechanism for increasing the vertical wave number and thus for larger vertical
shear and dissipation and reduced decay time (Davies and Xing, 2002; Zedler,
2009). In addition to modifying the characteristics of the inertial-gravity
waves, nonlinear advection related to a front can transport NIOs away from
the storm track and to higher latitudes (Zhai et al., 2004). Recent
observations and numerical studies in the Gulf Stream, Kuroshio, and Japan Sea
revealed the role of vertical circulation on the generation and radiation of
near-inertial energy (Whitt and Thomas, 2013; Nagai et al., 2015; Rocha et
al., 2018; Thomas, 2019).
The South China Sea (SCS) is a region with frequent tropical cyclone
occurrence: ∼10 each year (Wang et al., 2007). Observations
(Sun et al., 2011a, b; Xu et al., 2013) and numerical studies (Chu et al.,
2000) indicated that these TC events are sources for near-inertial energy
bursts. Additionally, the SCS circulation contains abundant energetic flow
(e.g. Qu, 2000; Gan et al., 2006; Gan et al., 2016a) and mesoscale features,
such as a strong coastal jet off the Vietnamese coast (e.g. Gan and Qu,
2008) and eddies (e.g. Chen et al., 2012). The distribution and evolution of
the TC-induced NIOs are susceptible to the influence of these background
currents. (Sun et al., 2011a, b). However, the estimate of
the total contribution of a TC to the KEni in the SCS is difficult to obtain
from observations or linear wave theory due to sparse spatial observations
and the non-homogenous nature of SCS circulation.
In this study, we apply a well-validated numerical model with specific China
Sea configurations to examine the response of KEni to a large TC and
background jet over the sloping topography in the SCS. A description of
Typhoon Neoguri and the details of the numerical model implementation are
given in Sect. 2. In Sect. 3, the general characteristic response of the
near-inertial current and the energy fluxes during the TC forced stage and
their later relaxation stage as TC moved away from the concerned region are
presented. Following Sect. 3, the KEni equation is used to identify the
dynamic processes of the vertical viscous dissipation, pressure work, and
nonlinearity during different phases of the NIOs.
Typhoon Neoguri (2008) and the ocean modelTyphoon Neoguri (2008)
Typhoon Neoguri formed east of the Philippines and entered the SCS on 15 April. It first moved west–northwest with an average translation speed of 5.8 m s-1 before it slowed down to 1.6 m s-1 on 16 April, based on the
Joint Typhoon Warning Center (JTWC) best track data, (Fig. 1). On 17 April,
Neoguri sped up to 3.8 m s-1, turned more northward, and developed into
a typhoon with a maximum wind speed of 51 m s-1 and an MSLP (minimum sea
level pressure) of 948 hPa, at 18:00 UTC on 17 April near the Xisha Islands. The
Neoguri was a supercritical typhoon travelling with a translation speed
greater than the first baroclinic wave speed. After skirting Hainan Island
on 18 April, Neoguri moved northward, weakened to a tropical storm, and
further dissipated as it moved farther inland. The NIO burst induced by
Neoguri was shown by the clockwise (Acw) and counter-clockwise
(Accw) rotary current amplitudes (m s-1), from a current meter
mooring at Wenchang station, to the east of Hainan Island (Fig. 1c).
(a) Track of Typhoon Neoguri (2008) from JTWC; blue square
represents Wenchang where there were ADCP observations; (b) translation
speed (Uh; unit: m s-1) and the first baroclinic wave speed
(C1; unit: m s-1) along the TC track; (c) clockwise (Acw) and
counter-clockwise (Accw) rotary current amplitude (m s-1) from
current measurement at Wenchang. TS: tropical storm; STS: strong tropical
storm.
Ocean model
We use the China Sea Multi-scale Ocean Modeling System (CMOMS) (Gan et al.,
2016a, b) in this study. CMOMS is based on the Regional
Ocean Modeling System (ROMS) (Shchepetkin and McWilliams, 2005), and the
model domain covers the northwest Pacific Ocean (NPO) and the entire China
Seas (Bohai, Yellow Sea, East China Sea, and SCS) from approximately
0.95∘ N, 99∘ E in the southwest corner to the northeast corner of
the Sea of Japan. The horizontal size of this grid array decreases gradually
from ∼10 km in the southern part to ∼7 km in
the northern part of the domain. Vertically, we adopted a 30-level stretched
generalized terrain-following coordinates.
The model was forced with 6-hourly actual wind speeds of typhoon Neoguri
obtained from the Cross-Calibrated Multi-Platform (CCMP) dataset, with a
horizontal resolution of 0.25∘ (Atlas et al., 2011; http://data.remss.com/ccmp/v02.0/Y2008/, last access: 16 September 2020). Wind stress is
calculated based on the bulk formulation by Fairall et al. (2003). The daily
mean air temperature, atmospheric pressure, rainfall or evaporation, radiation,
and other meteorological variables from 15 to 18 April 2008 from the
NCEP/NCAR Reanalysis 1 were used to derive the atmospheric heat and fresh
water fluxes. External forcing of depth-integrated velocities (U,V),
depth-dependent velocities (u,v), temperature, T, and salinity, S, at the lateral
boundaries were obtained from the Ocean General Circulation Model for the
Earth Simulator (OFES) (Sasaki et al., 2008). Open boundary conditions from
Gan and Allen (2005) were applied at the open boundaries.
The model was spun up from 1 January 2005 with winter initial fields
(temperature and salinity) obtained from the last 3-year mean fields of
a 25-year run that is initialized with the World Ocean Atlas (2005) (WOA05;
Locarnini et al., 2006; Antonov et al., 2006) data and forced by wind
stress derived from climatological (averaged from 1988 to 2013) monthly
Reanalysis of 10 m Blended Sea Winds released by the National Oceanic and
Atmospheric Administration (https://www.ncei.noaa.gov/thredds/catalog/uv/monthly/catalog.html, last access: 16 September 2020). The dynamic
configuration and numerical implementation of the CMOMS system are described
in detail in Gan et al. (2016a, b).
We have thoroughly validated the CMOMS by comparing simulated results with
those obtained from various measurements and findings in previous studies.
In particular, we have validated the extrinsic forcing of a time-dependent,
three-dimensional current system in the tropical NPO, transports through the
straits around the periphery of the SCS, and corresponding intrinsic
responses of circulation, hydrography, and water masses in the SCS (Gan et
al., 2016a). We have also validated the circulation of CMOMS by providing consistent physics between the intrinsic responses of the circulation and
extrinsic forcing of flow exchange with adjacent oceans (Gan et al., 2016b).
The model is also validated with available Argo (https://data-argo.ifremer.fr/geo/pacific_ocean/, last access: 16 September 2020) temperature profiles (not
shown), observed sea surface temperature (SST), and currents from a
time series current meter mooring during Neoguri, as described below.
Three-dimensional, hourly-mean dynamic, and thermodynamic variables from
10 April to 10 May 2008 were used to examine the near-inertial oscillations
in this study. Because the inertial period (IP) in the SCS is larger than 32 h (near 22∘ N), the error induced by the hourly model output
is <3 %.
Model resultCharacteristic response to the TC
The evolution of the response to the TC in the ocean with the existence of a
coastal jet in the SCS is presented according to different stages of the TC
forcing. During the pre-storm stage (PS), before Neoguri entered the SCS on
14 April, the wind stress was relatively weak (<0.1 Pa). A
prominent jet current separated from the Vietnamese coast flowing
northeastward near 16∘ N (Fig. 2a) and characterized the
circulation in the western part of the SCS. The jet resulted from the
(summer) monsoon-driven strong coastal current over narrow shelf topography
off Vietnam and it persisted as a distinct circulation feature in the SCS
during summer. The northward-flowing coastal current separated from the
coast and overshot northeastward into the SCS basin as it encountered the
coastal promontory in central Vietnam (Gan and Qu, 2008).
Daily mean KE (J m-3, colour contour) and current vectors
(arrows) at 10 m (a) on 14 April of the pre-storm stage (PS), (b) on 18 April
during the strongest wind forcing of the forced stage (FS), (c) on 20 April
after the end of the FS, and (d) on 30 April during the relaxation stage
(RS). The grey contours are the 200, 500, and 1000 m isobaths. The
magenta line represents TC track. Yellow triangle on 18 April represents the
TC location. The TC was located beyond the plotting domain during the other
3 d, as shown in Fig. 1a. The velocity magnitudes <0.2 m s-1 are not shown in the vectors.
The jet formed negative (positive) geostrophic vorticity (ζg) to
the south (north), with the minimum (maximum) Rossby number (ζgf-1) <-0.2 (>0.2) near 15.8∘ N
(16.8∘ N). During the forced stage (FS; Fig. 2b) between 15 and 19 April, the SCS was under the direct influence of Neoguri, the wind
forcing became significantly stronger (>0.1 Pa), the kinetic energy (KE) near the
surface (10 m) intensified significantly (>500 J m-3) to
the east of the TC, and the coastal jet was suppressed by southward flow.
Meanwhile, a strong local divergence and upwelling formed at the surface and
generated a strong cooling (∼1.5∘C) belt along the
TC path that lasted for more than a week. The cooling zone radiated hundreds
of kilometres away from the core of the TC. These features were well captured
by the TC-induced temperature difference between 19 and 14 April from both
simulated (Fig. 3a) and observed SST (Fig. 3b)
(https://podaac-opendap.jpl.nasa.gov/opendap/allData/ghrsst/data/GDS2/L4/GLOB/JPL/MUR/v4.1/, last access: 16 September 2020). After the end of
the FS on 20 April (Fig. 2c), the jet returned to its pre-storm intensity
and shifted slightly northward (Fig. 2c) when the TC centre approached the
coast (Fig. 1a). Afterwards, during the relaxation stage (RS) after 20 April
(Fig. 2d), the wind forcing from the TC decreased to <0.05 Pa.
ΔSST (19 April–14 April) from (a) model results and
(b) GHRSST JPL MUR satellite products. The pink curve indicates to the
trajectory of the TC Neoguri.
The rotary spectrum shows that the near-inertial response of surface currents to
the TC occurred near the local inertial frequency (f=0.028 cph, cycles per hour) at Wenchang station (19.6∘ N, 112∘ E) during the model
simulation period (10 April–5 May) (Fig. 4). The clockwise rotary spectra
are calculated by
Scw=1/8(Puu+Pvv-2Quv),
where Puu, Pvv, and Quv are auto and quadrature spectra,
respectively (Gonella, 1972). This simulated result is highly consistent
with the observations in the lower-frequency band. We found that the
correlation coefficients of near-inertial band-passed velocity between acoustic Doppler current profiler (ADCP) and model simulation at Wenchang station were 0.62 and 0.57 for the east–west
(u) and north–south (v) component, respectively, which indicated that the
model captured reasonably well the NIOs under the influence of the
background circulation of the SCS. There inevitably existed model–observation discrepancies, such as differences in velocity magnitude
(∼0.06 m s-1) at near-inertial band and rotary spectra
at the higher frequency (Fig. 4). The discrepancies could have been caused
by many factors, such as the lack of mesoscale and sub-mesoscale processes
in the atmospheric forcing field, the linear interpolation process of the
atmospheric forcing (Jing et al., 2015), and not resolving the oceanic
subscale processes by the current model resolution. However, these
discrepancies will not undermine the discussion about the process and
mechanism of near-inertial energy response to the TC and jet in this study.
Rotary spectra of clockwise component (upper 10 m) at Wenchang
(19.6∘ N, 112∘ E) from model simulations (red) and
observations (blue).
Near-inertial response in the upper ocean
We adopted the complex demodulation method successfully used in previous NIO
studies (Gonella, 1972; Brink, 1989; Qi et al., 1995) to extract the
inertial current signal. The simulated horizontal currents
(uh) were analysed for inertial currents
(ui). The inertial currents contain clockwise (cw) and
counter-clockwise (ccw) rotating components:
ui+ivi=Acwe-i(ϕcw+ft)+Accwei(ϕccw+ft),
where ui and vi are the eastward and northward inertial currents
at 10 m in the mixed layer (ML) and A and ϕ are the amplitude and phase of the
rotary currents, respectively. Subscripts represent the clockwise (cw) and
counter-clockwise (ccw) rotating direction, and f is the local Coriolis
coefficient. To obtain the amplitude and phase, we performed harmonic
analysis daily with each segment over one inertial period (IP). Then the
rotary amplitude and phase were calculated following previous studies
(Mooers, 1973; Qi et al., 1995; Jordi and Wang, 2008).
The time evolution of the daily rotary currents during the FS and RS in the
surface layer varied spatially and was related to the intensity and
translation speed of the TC. On 15 April during PS, Neoguri mainly affected the region south of 13∘ N, with a relatively fast translation
speed (Uh>3C1, Fig. 1b) and weaker intensity
(Vmax∼35 m s-1). In most areas, cw rotary currents
were strong (Acw>0.1 m s-1), yet decayed quickly after
3 d (less than two IPs; Fig. 5a), while the magnitudes of ccw currents were
very small (Fig. 5b). After 18 April, Neoguri moved into the region between
14 and 18∘ N, where it intensified more than 40 %
but moved slower with Uh∼2C1. Both the cw and ccw
currents possessed larger intensities than in the southern region. The
induced cw currents displayed an obvious rightward bias, where the enhanced
inertial currents extended to ∼350 km to the right of the
track and to ∼<150 km to the left of the track. This
extension of horizontal scale was related to the region with a wind stress
|τ|>0.25 Pa in Neoguri.
Time series, represented by colour bar, of daily (a) clockwise and
(b) counter-clockwise rotary current vectors from 14 to 30 April during
different stages of the TC forcing, signifying the response of the current
to the local wind rotation. For the clockwise (counter-clockwise) component,
only currents with a magnitude larger than 0.2 (0.05) m s-1 are shown.
The black box represents the forced region.
The maxima of the ccw component were located to the left of the TC's path
where the wind vector (Fig. 6) rotated in the same direction as the ocean
currents presented in Fig. 5. The connection between the right (left) bias
of the cw (ccw) currents with the rotation direction of the wind vector is
in agreement with the explanation of Price (1981). Two to three IPs (>6 d) after the direct forcing, the cw currents remained significant
(>0.2 m s-1) in an area extending from 110 to
116∘ E. In contrast, the ccw components dissipated quickly, within
∼1 d after the wind forcing stopped. This short duration of
the forced inertial motion is in agreement with previous studies (Jordi and
Wang, 2008).
Time series of 6-hourly wind stress vectors during the forced-stage
(FS) from 15 to 20 April.
Besides the intensity and duration, we also looked at the frequency shift
(δω=ω-f) and the horizontal scale of the NIOs. The frequency shift from the local inertial frequency was estimated from the
temporal evolution of the phase of the rotary current: δω=-∂ϕ/∂t. In the FS, the maximum frequency shift occurred near the jet (15
to 16∘ N, 112 to 115∘ E), where δω≈0.08f (Δϕ≈π/4, Δt=3 d, f=4×10-5 s-1 at 16∘ N). The horizontal scale was estimated from the
spatial variation in the rotary current by calculating the horizontal wave
number in the meridional direction as ky=∂ϕ/∂y. The largest wave number ky≈3.1×10-5 rad m-1 was also found near the jet.
Characteristic near-inertial energyResponse in the upper layer
We focused on the area between 110–115∘ E and 13–19∘ N
(box in Fig. 5a), defined as the forced region, where the strongest NIO was
produced during the FS of Neoguri. We calculated the wind-induced near-inertial
energy flux (or the wind work) using
τi⋅ui, where
τi is the band-passed near-inertial wind stress and
ui is the near-inertial current at the surface (Silverthorne and
Toole, 2009). A fourth-order elliptic band-pass filter (Morozov and
Velarde, 2008) was applied to obtain near-inertial motion with a band
ranging from 0.8 f to 1.2 f, where f is the local Coriolis coefficient. The
time series of domain-averaged
τi⋅ui over the forced region reveals that significant energy input took
place during the FS, with the peak value about 68×10-3 W m-2 on 17 April (Fig. 7). Under this large wind energy input, the
area-averaged depth-integrated KEni (or AKEni hereafter) in the upper layer (0–30 m) increased significantly from its pre-storm value to a maximum
∼1500 J m-2 during the FS, with an increase rate of
about 16×10-3 W m-2 (Fig. 7a). We set 0–30 m as an upper
layer based on domain mean stratification and current (vorticity) vertical
structure. Despite the continuous positive wind energy flux, the AKEni in the
upper layer plateaued, indicating that a large amount of the wind energy was
either propagating out of the forced region or was lost to the lower layers
due to entrainment. The detailed mechanisms are discussed in the following
sections. After the peak of FS, the wind work decreased significantly with
a small negative value around the end of the FS. The AKEni decreased to one half of
its peak value within 2 d (decrease rate was about 7×10-3 W m-2). After that, the wind work was almost negligible, and the
decrease rate of AKEni became smaller (∼0.8×10-3 W m-2).
Time series of (a) the area-averaged wind energy flux into the
near-inertial band (unit: 10-3 W m-2) and (b) depth-integrated
KEni (J m-2) in the forced region for different layers.
Response at depths
During the FS, the AKEni in the upper 200 m constituted ∼90 % of
the total AKEni in the whole water column, while the AKEni between 30 and 200 m alone
accounted for ∼30–50 % (Fig. 7b). The AKEni in this
mid-layer had a temporal evolution different from that in the near-surface
layer. It reached its maximum on 20 April, around 1.5 d later,
and was more than 70 % of the peak value of the AKEni in the upper layer
(∼1700 J m-2). Compared to the upper-layer AKEni, the
mid-layer AKEni during FS increased slightly more slowly (∼4×10-3 W m-2), while from 20 April to 5 May during RS
it decreased much more slowly (∼0.61×10-3 W m-2), and the AKEni became greater than that in the upper layer at the end of
FS. The AKEni below 200 m was much smaller but increased continuously from 17 to 29 April, with a rate of about 0.62×10-3 W m-2, which
was comparable to the AKEni rate of decrease in the 30–200 m layer. The AKEni in this
deep layer became greater than that in the upper layer after 25 April and
that in the layer 30–200 m after 29 April; the deep layer reached its
maximum value ∼10 d after the ending of the FS.
Spatially, two relatively large KEni patches below the upper layer were located
to the north and south of ∼16∘ N (Fig. 8a). Their
horizontal scales, influenced by near-inertial waves, were much smaller
compared with those in the upper layer. The region with relatively large
KEni in the layer between 30 and 200 m was located near the jet currents, with
stronger value during FS than during RS (Fig. 8a, b). These results suggest
that the KEni in this layer might have been determined by both vertical
propagation of the near-inertial gravity wave and horizontal advection of
KEni of the background current. Similar horizontal distribution also
occurred below 200 m (Fig. 8c, d). In contrast to the layer above, the
relatively large value during RS on 30 April indicated a downward
propagation of KEni into the deeper layer. Around the saddle zone west of
the Xisha Islands, a relatively large KEni below 200 m aligned with the 1000 m isobath and might reflect a topographic effect on the near-inertial wave.
Daily averaged KEni (KJ m-2) of layers (a, b) 30–200 m and
(c, d)<200 m on (a, c) 20 April during FS and (b, d) 30 April during
RS. The thick red arrows show the location of the jet (Fig. 2), while the
blue curved arrows indicate regions with relative vorticity ζ<0 and
the orange curved arrows indicate regions with ζ>0. Stations A1 and A2
are on the right side of the TC track at the northern (A2) and southern (A1)
sides of the jet, respectively. Stations C1 and C2 are corresponding
stations in the far field. Station B is located in the upstream area of the jet.
Vertical propagation of near-inertial energy
It is clear that the distribution of the KEni was mainly controlled by the
propagation of near-inertial wave energy both horizontally and vertically as
well as by the background jet. In order to understand the KEni distribution
in the deeper water inside the forced region and in the far field, we
selected four different locations, marked as A1, A2, C1, and C2 in Fig. 8a–d, for the analysis of the KEni evolution during the FS and RS. Among
them, A1 (15.7∘ N, 113∘ E) and A2 (16.9∘ N, 112.5∘ E) are on the right side of the TC track, inside the forced
region and situated about 200 km apart from each other at the northern (A2)
and southern (A1) sides of the jet, respectively. C1 (16.9∘ N, 114.9∘ E) and C2 (18∘ N, 114.9∘ E) are the
corresponding stations in the far field where relatively strong KEni
intensification occurred.
Forced region (stations A1 and A2)South of the jet at station A1
The time series of the band-passed inertial velocity ui as a function
of depth shows that there was an upward phase propagation, in which ui,
in the layers below 100 m was leading the upper 50 m (Fig. 9a). Accompanying
this phase propagation was a downward propagation of surface KEni, which was
represented by the lowering of the ui maxima as a typical Poincaré
wave (Kundu and Cohen, 2008). There were two phases of vertical energy
propagation: (1) during FS, there was a rapid extension of the large ui
maxima to below 100 m from 17 to 20 April, and (2) during RS, the centre of
the large ui value descended from ∼100 to 280 m from
25 April to 5 May. The vertical propagation velocity, Cgz, estimated
from this downward transport, was ∼17 m d-1.
Time series of (a, b)ui (m s-1), (c, d) KEni (J m-2), and (e, f) rotary spectra (cw component) at locations A1 (a, c, e)
and A2 (b, d, f).
During the first phase, the KEni in the top 30 m and in the 30–200 m layer
shared a similar rate of increase on 17 April, indicating that the
enhancement of KEni at 30–200 m was related to the entrainment between the
upper and deep layer (Fig. 9c). While the KEni in the upper 30 m decreased
quickly from 18 April, it kept increasing at depths from 30 to 200 m,
suggesting that other contributing mechanisms existed besides the
entrainment. The KEni below 200 m also experienced notable intensification,
with a smaller rate of increase than that found in the 30–200 m layer (Fig. 9c). Because the viscous effect is small in the deeper water, this
enhancement of the KEni was most likely associated with the propagation of
an inertial-gravity wave.
During the second phase, the KEni in the 30–200 m layer decreased
significantly at station A1, indicating the existence of either downward or
horizontal energy transport. From the linearized inertial-gravity wave
equation under the influence of background vorticity, Cgz can be
obtained by Morozov and Velarde (2008):
Cgz=ω2-feff2ωm,
where ω≈1.08f is the frequency with maximum Scw at 200 m (Fig. 9e); feff=f+ζg/2 is the effective Coriolis
coefficient; and ζg/f=-0.1 at A1. m is the vertical wave
number that we chose to be the first baroclinic mode under a two-layer
approximation based on the stratification (blue line in Fig. 10a). From Eq. (2), Cgz was about 19.1 m d-1, which was in the same range as
the modelled Cgz. Consistent with the case of (ω0-feff)/feff<0.1 in Kunze (1985), the background
vorticity in our case accounted for more than 90 % of the modification of
the magnitude of the wave dispersion property. Meanwhile, the KEni in the
layer below 200 m did not increase notably, suggesting that other mechanisms
besides vertical propagation of the near-inertial gravity wave might have
been important in the evolution of KEni in water deeper than 200 m.
Time-averaged (a)N2 (s-2) and (b) low-passed (3 d)
vorticity from 15 April to 5 May at locations A1 (red) and A2 (blue).
North of the jet at station A2
At location A2, strong ui was mainly trapped in the water above 100 m,
and below 100 m ui<10 cm s-1. It returned to its
pre-storm magnitude after five IPs (Fig. 9b). This constraining of vertical
propagation is likely associated with the vertical scale of the strong
positive background vorticity (Fig. 10b). The KEni was generally smaller
than that at A1, and relatively large energy was found only in the ML (Fig. 9d). Cgz at A2, estimated from Eq. (2), was 2.1 m d-1 (feff=1.08f,ω≈1.1f,f=4.2×10-5 s-1, and m=2π/30 m), which was about 1/10th of that at A1. This is consistent with the lack of a distinct pattern
of vertical propagation of NIOs at this station, as shown in the band-passed
ui (Fig. 9b), and the presence (absence) of a near-inertial peak of
Scw at 10 m (200 m) (Fig. 9f).
Far-field region (stations C1 and C2)
C1 and C2 are located ∼400 km to the right of the forced
region. During the FS, ui (Fig. 11a, b) and KEni (Fig. 11c, d) in the
upper layer were smaller than those at those stations in the forced region
due to the weaker TC influence. Only a small downward propagation was
discerned during the FS (Fig. 11a, b). However, notable intensification of
the KEni occurred in the layers below the upper layer after 23 April. At C1,
the Scw at 10 m had a small red shift, while the Scw at 200 and
500 m displayed blue shifts with peaks near 1.07f (Fig. 11e). The difference
between Scw in the upper layer and in the layers below implies another
source of KEni other than local inertial-gravity wave vertical propagation.
As in Fig. 9, except for locations C1 (a, c, e) and C2 (b, d, f).
At C2, downward energy propagation appeared after 23 April, reaching 100 m
from the surface within 7 d, giving Cgz=14.3 m d-1 (Fig. 11b). Unlike C1, the intensification was mainly in the 30–200 m layer. The
Scw at both 10 m and 200 m had a broad energy band near the local f (Fig. 11f). Because ζg/f=-0.11 and feff=1.06f,
Cgz estimated from Eq. (2) had an upward propagation (Cgz=-5.4 m d-1), which cannot explain the downward propagation here.
The linearized wave theory, with the consideration of Doppler drift due to
background currents, does not seem to be valid in this location. We will
discuss this issue in the next section.
KEni Budget
We utilized the KEni equation to provide a further analysis of the source of
KEni in the water column. Because the horizontal component of near-inertial
kinetic energy is significantly larger than the vertical component (Hebert
and Moum, 1994), we used the horizontal component to represent the KEni. The
KEni budget can be obtained from the horizontal momentum equation:
∂KEni∂t︸RATE=-ui⋅∇hp︸PRES-ρ0ui⋅uh⋅∇huh︸NLh-ρ0ui⋅w∂uh∂z︸NLv-ρ0ui⋅∂∂zυ∂uh∂z︸VVISC,
where KEni is the near-inertial energy;
ui and
uh are the near-inertial velocity vector and horizontal velocity,
respectively; p is pressure; ρ0 is the reference density;
∇h is the horizontal gradient operator; w is the
vertical velocity; υ is the viscosity coefficient; and the angle
bracket represents band-passed filtering on the near-inertial band. The PRES
term on the right side of equation represents the pressure work on the
KEni, which is associated with the inertial-gravity wave propagation. NLh
and NLv represent the horizontal and vertical divergence of energy flux
that include the effects of (1) the advection of KEni due to background currents
and (2) the straining of the wave field due to the background shear currents.
Zhai et al. (2004) found that the geostrophic advection of KEni contributed most
of the NLh and was the main mechanism for transporting the NIOs in the
absence of baroclinic dispersion of inertial-gravity waves. It was also
found to be more important than the dispersive processes along the Gulf
Stream or shelf-break jet. VVISC is the vertical viscous effect. As before,
we integrate this equation vertically in three layers: the upper layer (0–30 m), the subsurface layer (30–200 m), and the deep layer (>200 m). In the following sections, the AKEni budget is considered in entire forced
region (Fig. 5) as well as at the specific stations along the jet.
Mean balance
Figure 12 shows the time series of the AKEni budget over the entire forced region
defined in Fig. 5. The time-averaged horizontal distributions of each term
are presented in Fig. 13. During the FS, the increase in AKEni in the upper layer
was mainly attributed to the wind energy input because the VVISC term was
1 order larger than the other terms, with a maximum of 30×10-3 W m-2 on 17 April (Fig. 12a). The time-integrated VVISC during
the FS was 2.15×103 J m-2 (Table 1). Stronger VVISC in
the upper 30 m occurred in the region between 14∘ N
and 18∘ N (Fig. 13a) along the TC track with a rightward bias,
similar to the distribution of current intensity (Fig. 5c). Like the wind
work during the FS (Fig. 7a), VVISC became negative after 19 April, indicating
the AKEni removal by negative wind work. The influence of VVISC extended to the
30–200 m layer and provided a positive energy flux (∼1×103 J m-2) in this layer (Figs. 12b, 13b). The effect
of VVISC in the deep layer was negligible (Fig. 12c).
Time series of area-averaged, depth-integrated KEni budget for (a)
0–30 m, (b) 30–200 m, and (c)>200 m in the forced region. Terms
represent (unit: ×10-3 W m-2) pressure work (PRES), vertical viscous effect (VVISC), horizontal non-linear
interaction (NLh), vertical non-linear interaction (NLv), and
changing rate of KEni (RATE). The vertical lines separate the pre-storm
stage, FS, and RS during the TC forcing.
Horizontal distribution of time-averaged (15 April–5 May)
depth-integrated KEni budget in different layers: 0–30 m (left column),
30–200 m (middle), and >200 m (right). The terms represented are
(unit: ×10-3 W m-2) (a–c) VVISC, (d–f) PRES, (g–i) NLh,
and (j–l) NLv.
Time integrated KEni budget (unit: ×103 J m-2)
during the FS and RS.
Shortly (∼1 d) after the large injection of KEni into the
upper layer during the FS, the PRES became significant (Fig. 12a, Table 1), and
its horizontal distribution resembled that of VVISC (Fig. 13a, d),
suggesting that PRES radiated the KEni out of the forced region. It provided a
negative KEni flux in the upper layer (-0.65×103 J m-2),
which was largely compensated for by the positive flux in deeper layers (Table 1). This suggests that, during the FS, the main role of the pressure work
was to transport the KEni from the upper layer to the deep layers, and
<15 % of the KEni was horizontally propagated outside the forced
region.
During the RS, the VVISC was relatively small in the upper layer and it accounted
for one-third of the AKEni removal in the layers below (Table 1). The PRES became a
major sink for AKEni in the ML (-0.85×103 J m-2) and
subsurface layer (-0.16×103 J m-2) but was the major
source in the water below 200 m. The AKEni loss due to the horizontal wave
propagation outside the forced region was ∼-0.42×103 J m-2, accounting for about 40 % of the total loss in the
whole water column.
Nonlinear advection terms had an important influence in the top 200 m but
made little contribution to the AKEni budget in the water below 200 m (Fig. 12, Table 1). The horizontal effects of NLh and NLv in these layers
were mainly limited to a smaller region, as compared to the VVISC and the
PRES; and their relatively large values occurred near the slope and the jet
(Fig. 13).
In the upper layer, NLh advected the KEni from the source region;
NLh had positive and negative values on the eastern and western sides
of the TC track, respectively (Fig. 13g). Similar features, but with much
weaker amplitude, were found in the layers below (Fig. 13h, i). During the
FS, in the 30–200 m layer, the domain-averaged NLh was positive
(0.21×103 J m-2), indicating a possible extraction of
the KEni from background flows. NLv was a strong energy sink in the
upper 200 m (∼0.64×103 J m-2). The TC
wind field generated a strong surface horizontal divergence and upwelling
around 16–17∘ N (Fig. 4b). As a result, the smaller KEni in the
lower layer was advected to the surface east of the Xisha Islands. This
lower KEni generated a negative gradient with ambient water and resulted in
the strong eastwards transport of KEni in the eastward jet current. As a
result, a positive NLh centre was located around the area with the
strongest negative NLv, and a negative NLh centre lay to the west
of the positive maximum of NLh. During the RS, NLh became
negative for all layers and provided ∼1/3 of the total KEni
loss in the water column (-0.35×103 J m-2), while
NLv over the whole water column was significantly reduced.
Role of the jet
We further show the distinct AKEni balance in the southern and northern sides of
the jet. During the FS, VVISC at A1 on the southern side of the jet was the
dominant AKEni source in both the upper layer and the 30–200 m layer (Fig. 14a, b), consistent with the large vertical scale on the southern side of the
jet due to local negative vorticity. The enhancement of near-inertial
currents in the upper layer and the concurrent current divergence resulted
in the vertical oscillation of isopycnals (pressure) below the upper layer
at this station. During this pumping process, the AKEni in the upper layer was
partly transported downward by the PRES and partly by the NLv. During the RS,
the PRES became the main factor in the AKEni budget. It changed from source to
sink in the 30–200 m layer because of less downward KEni flux from the
upper layer. In the deeper layer, the negative PRES indicated that there was a
near-inertial wave propagating away from this location. The positive AKEni flux
provided by NLh weakened the effect of the negative PRES.
Time series of KEni budget at locations: A1 (a–c), A2 (d–f), C1
(g–i), and C2 (j–l) in the following layers: 0–30 m (left column), 30–200 m (middle
column), and >200 m (right column).
Presented are (unit: ×10-3 W m-2) (a–c) VVISC,
(d–f) PRES, (g–i) NLh, and (j–l) NLv.
During the FS at A2 on the northern side of the jet, VVISC in the upper
layer (Fig. 14d) had slightly larger magnitude than that at A1. However, it
greatly decreased to 3×10-3 W m-2 below the ML (Fig. 14e), which suggested that the smaller vertical scale on the northern side
of the jet limited the deep penetration of the wind energy in this location.
Compared to A1, the NLv was much stronger in the upper layer, and about
one half of the lost energy was compensated for by the NLh. The PRES
was negligible compared to that at A1 (Fig. 14d–f). During the RS, the PRES
in the ML became a notable sink after 21 April and was accompanied by a
positive NLh (Fig. 14d). This suggests that the strong jet increased
the AKEni through either advection or wave propagation due to PRES as a result of
jet-NIO interaction at this station. In the deeper layer, the PRES provided
a positive AKEni flux. From the spectral analysis, the wave at 500 m had a large
blue shift of >0.15f (Fig. 9f) that cannot be explained by the
background vorticity alone. The wave likely originated from the northern
latitude.
In the far field at stations C1 and C2, where there was no direct wind
forcing from the TC, surface forcing (VVISC) was relatively small during the FS
(Fig. 14g, j). Therefore, horizontal transport of energy is needed to sustain
the KEni intensification at these two locations (Fig. 11c, d). At C1, which
was on the southern side of the jet (Fig. 8) and had a negative background
vorticity, the PRES was the main source of AKEni in both subsurface and deep
layers (Fig. 14h, i). The existences of the blue shift near the local
inertial frequency (Fig. 11e) and of the negative background vorticity
suggests the presence of a southward-propagating near-inertial wave towards
C1 from northern region. Because C2 lies near the northeastward turning
point of the jet (Fig. 8), the nonlinear effect became significant in the
30–200 m layer where the jet was strongest (Fig. 14k). After the enhancement
of AKEni in the subsurface layer, the PRES further transported the KEni downwards and
became the major source for the increase in AKEni in the deep layer after 27 April (Fig. 14l). The northeast current advected the lower-frequency NIO from
the lower latitude towards the higher latitude, C2, which explains the red
shift of the NIO at this location (Fig. 11f).
Summary
TCs force the ocean to form NIOs. The response of NIOs is largely associated
with the different forcing stages of the TCs and background flow. Due to
spatiotemporally limited measurements, our understanding of the process and
mechanism that govern the NIO response is mainly based on theories that are
constrained by idealized assumptions. In this study, we utilize a
well-validated circulation model to investigate the characteristic response
of KEni to a moderately strong TC (Neoguri) with observed strong KEni and to
a unique background circulation.
The near-inertial currents in the upper layer strengthened significantly
during the TC forced stage and displayed a clear rightward bias due to
stronger wind forcing and the resonance between the wind and the
near-inertial currents. The distribution of near-inertial currents and the
associated rotary spectra showed that the propagation patterns of NIOs
varied greatly from location to location and were closely linked to the
influences of the background jet.
We calculated the KEni balance to diagnose spatiotemporally varying
responses and processes of the near-inertial signals in terms of different
forcing stages of the TC. Results show that during the forcing period, the
vertical viscous term, which represents the wind work and entrainment at the
base of the upper layer, was the KEni source in the upper layer. Around 0.5 IP after the maximum TC forcing, the pressure work became the main KEni sink
in the upper layer, transporting KEni in the ML into the deeper layers
through inertial pumping. In the meantime upwelling, caused by the
TC-enhanced divergence, advected smaller KEni from deeper layers to weaken
the KEni in the upper layer.
During the TC relaxation stage, the loss of KEni in the forced region of the
whole water column was caused by the vertical viscous term, the pressure
work, and horizontal advection effects (Table 1). However, these effects
acted differently in different layers. The viscous effect mainly occurred
inside the water column but decreased to near zero in the upper layer after
the direct impact of Neoguri. The pressure work mainly transported the KEni
out of the forced region horizontally and out of the upper layer vertically.
It was strongest on the southern side of the jet, where the negative
background vorticity was located. The horizontal nonlinear effect also
contributed greatly to the KEni balance near the jet region. It acted as a
major sink of KEni by horizontally advecting the NIO away from the forced
region. For locations away from the forced region, both near-inertial wave
propagation and horizontal advection contributed to the intensification of
the KEni.
We examined the NIOs processes and underlying dynamics in response to
different stages of the TC in the semi-enclosed SCS under the influence of unique
and strong basin-wide circulation. Unlike a similar study in the SCS, this
study enriches our understanding of the spatiotemporal variability of
TC-induced NIOs and provides a useful physical guidance for future
process-oriented field experiments in the SCS as well as in other subtropical
marginal seas that are frequently affected by the TC.
Data availability
The data for this study are generated from the publicly distributed Regional Ocean Model System (ROMS, https://www.myroms.org/, last access: 16 September 2020) and are available from https://odmp.ust.hk/cmoms/ (CMOMS, 2020).
Author contributions
All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by HSK. The first draft of the papaer was written by HSK and all authors commented on previous versions of the paper. All authors read and approved the final paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This research was funded by the Key Research Project of the National Science
Foundation of China (41930539), the General Research Fund of Hong Kong
Research Grant Council (GRF16204915), and the Center for Ocean Research in Hong Kong and Macau (CORE), a joint research centre between QNLM and HKUST. The buoy data were
provided by Qi He from CNOOC Energy Technology & Services Limited, China.
We appreciate the editor's review and suggestions. We are also grateful for the
support of The National Supercomputing Center of Tianjin and Guangzhou.
Financial support
This research was supported by the Key Research
Project of the National Science Foundation of China (grant no. 41930539),
the General Research Fund of Hong Kong Research Grant Council
(grant no. GRF16204915), and the Center for Ocean Research (CORE) in Hong Kong and Macau.
Review statement
This paper was edited by John M. Huthnance and reviewed by two anonymous referees.
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