Response of near-inertial energy to a supercritical tropical cyclone and jet in the South China Sea: modelling study

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 20
Near-inertial oscillations (NIOs), whose frequencies are close to the local inertial frequency, 21 contain around half of the observed internal wave kinetic energy in the ocean (Simmons and 22 Alford, 2012). NIOs also greatly affect the kinetic energy budget in the deeper ocean as they 23 propagate downward from the surface and enhance the mixing by increasing vertical shear (Gill, 24 1984;Gregg et al., 1986;Ferrari and Wunsch, 2009;Alford et al., 2016). 25 Tropical cyclones (TCs), with the rapid change of wind stress, provide an important 26 generation mechanism for the NIOs. Observational studies related to a single storm or tropical 27 cyclone (Price, 1981; Shay and Elsberry, 1987;D'Asaro et al., 1995) showed that the NIOs related 28 to TCs can be a factor 2-3 larger than the background NIOs and last for more than 5 inertial periods 29 5 In this study, we apply a well-validated numerical model with specific China Sea 66 configurations to examine the response of KEni to a large TC and background jet over the sloping 67 topography in the SCS. A description of Typhoon Neoguri and the details of the numerical model 68 implementation are given in Section 2. In Section 3, the general characteristic response of the near-69 inertial current and the energy fluxes during the TC forced stage and their later relaxation stage as 70 TC moved away from the concerned region are presented. Following Section 3, the KEni equation 71 is used to identify the dynamic processes of the vertical viscous dissipation, pressure work, and 72 7 10 m Blended Sea Winds released by the National Oceanic and Atmospheric Administration 110 (https://www.ncdc.noaa.gov/oa/rsad/air-sea/seawinds.htm). The dynamic configuration and 111 numerical implementation of the CMOMS system are described in detail in Gan et al. (2016aGan et al. ( , 112 2016b. 113 We have thoroughly validated the CMOMS by comparing simulated results with those 114 obtained from various measurements and findings in previous studies. In particular, we have 115 validated the extrinsic forcing of time-dependent, three-dimensional current system in the tropical 116 NPO, transports through the straits around the periphery of the SCS, and corresponding intrinsic 117 responses of circulation, hydrography and water masses in the SCS (Gan et al., 2016a). We have 118 also validated the circulation of CMOMS by providing a consistent physics between the intrinsic 119 responses of the circulation and extrinsic forcing of flow exchange with adjacent oceans (Gan et 120 al., 2016b). The model is also validated with available ARGO temperature profiles (not shown), 121 observed sea surface temperature (SST) and currents from a time-series current meter mooring 122 during Neoguri, as described below. 123 Three-dimensional, hourly-mean dynamic, and thermodynamic variables from April 10 to , (2) 176 where ui and vi are the eastward and northward inertial currents at 10 m in the mixed layer, A and 177 ϕ are the amplitude and phase of the rotary currents, respectively. Subscripts represent the 178 clockwise (cw) and counter-clockwise (ccw) rotating direction, and f is the local Coriolis 179 coefficient. To obtain the amplitude and phase, we performed harmonic analysis daily with each 180 segment over one inertial period (IP). Then the rotary amplitude and phase were calculated 181 following previous studies (Mooers, 1973, Qi et al., 1995, Jordi and Wang, 2008. 182 The time evolution of the daily rotary currents during the FS and RS in the surface layer 183 varied spatially and was related to the intensity and translation speed of the TC. On April 15 during 184 PS, Neoguri affected mainly the region south of 13°N, with a relatively fast translation speed (Uh 185 > 3C1, Fig. 1b) and weaker intensity (Vmax~35 m s -1 ). In most areas, cw rotary currents were strong 186 (Acw >0.1 m s -1 ) yet decayed quickly after 3 days (<2 IP) (Fig. 5a), while the magnitudes of ccw 187 currents were very small (Fig. 5b). After April 18, Neoguri moved into the region between 14°N 188 and 18°N, where it intensified more than 40% but moved slower with Uh~2C1. Both the cw and 189 ccw currents possessed larger intensities than in the southern region. The induced cw currents 190 displayed an obvious rightward bias, where the enhanced inertial currents extended to ~350 km to 191 the right of the track and to ~<150 km to the left of the track. This extension of horizontal scale 192 was related to the region with wind stress |τ|>0.25 Pa in Neoguri. 193 The maxima of the ccw component were located to the left of the TC's path where the wind 194 vector (Fig. 6) rotated in the same direction as the ocean currents presented in Fig. 5 Besides the intensity and duration, we also looked at the frequency shift (δω=ω-f) and the 202 horizontal scale of the NIOs. The frequency shift from the local inertial frequency was estimated 203 from the temporal evolution of the phase of the rotary current: δω=-∂ϕ/∂t. In the FS, the maximum 204 frequency shift occurred near the jet (112°E to 115°E, 15°N to 16°N), where δω≈0.08f 205 (∆ϕ≈π/4,∆t=3 days, f=4×10 -5 s -1 at 16°N). The horizontal scale was estimated from the spatial 206 variation of the rotary current by calculating the horizontal wave number in the meridional 207 direction as ky=∂ϕ/∂y. The largest wave number 3.1 10 rad m -1 was also found near the 208 jet. 209

Response in the upper layer 211
We focused on the area between 110-115°E and 13-19°N (box in Fig. 5a), defined as the 212 forced region, where the strongest NIO was produced during FS of Neoguri. We calculated the 213 wind-induced near-inertial energy flux (or the wind work) using ⃑ • ⃑ , where ⃑ is the band-passed 214 near-inertial wind stress and ⃑ is the near-inertial current at the surface (Silverthorne and Toole, 215 2009). A 4 th order elliptic band-pass filter (Morozov and Velarde, 2008) was applied to obtain 216 near-inertial motion with a band ranging from 0.8f to 1.2f, where f is the local Coriolis coefficient. 217 The time series of domain-averaged ⃑ • ⃑ over the forced region reveals that significant energy 218 input took place during the FS, with the peak value about 68×10 -3 W m -2 on April 17 (Fig. 7). 219 Under this large wind energy input, the area-averaged depth-integrated KEni (or AKEni hereafter) 220 in the upper layer (0-30 m) increased significantly from its pre-storm value to a maximum ~1500 221 layer based on domain mean stratification and current (vorticity) vertical structure. Despite the 223 continuous positive wind energy flux, the AKEni in the upper layer plateaued, indicating that a 224 large amount of the wind energy was either propagating out of the forced region or was lost to the 225 lower layers due to entrainment. The detailed mechanisms are discussed in the following sections. 226 After the peak of FS, the wind work decreased significantly with small negative value around the 227 end of the FS. The AKEni decreased to one half of its peak value within 2 days (decrease rate was 228 about 7×10 -3 W m -2 ). After that, the wind work was almost negligible, and the decrease rate of 229 AKEni became smaller (~0.8×10 -3 W m -2 ). 230

Response at depths 231
During the FS, the AKEni in the upper 200 m constituted ~90% of the total AKEni in the 232 whole water column, while the AKEni between 30-200 m alone accounted for ~30-50% (Fig. 7b).

Vertical propagation of near-inertial energy 255
It is clear that the distribution of the KEni was mainly controlled by the propagation of 256 near-inertial wave energy both horizontally and vertically as well as by the background jet. In order 257 to understand the KEni distribution in the deeper water inside the forced region and in the far field, 258 we selected four different locations, marked as A1, A2, C1, and C2 in Fig. 8

South of the jet at station A1 266
The time series of the band-passed inertial velocity ui as a function of depth shows that there was 267 an upward phase propagation, in which ui, in the layers below 100 m was leading the upper 50 m  Consistent with the case of (ω0-feff)/feff <0.1 in Kunze (1985), the background vorticity in our case 292 accounted for more than 90% of the modification of the magnitude of the wave dispersion property. 293 Meanwhile, the KEni in the layer below 200 m did not increase notably, suggesting that other 294 mechanisms besides vertical propagation of the near-inertial gravity wave might have been 295 important in the evolution of KEni in water deeper than 200 m. 296

North of the jet at station A2 297
At location A2, strong ui was mainly trapped in the water above 100 m, and below 100 m 298 ui <10 cm s -1 . It returned to its pre-storm magnitude after 5 IPs (Fig. 9b). This constraining of 299 vertical propagation is likely associated with the vertical scale of the strong positive background 300 vorticity (Fig. 10b). The KEni was generally smaller than that at A1, and relatively large energy 301 was found only in the ML (Fig. 9d). Cgz at A2, estimated from Eq. (3), was 2.1 m day -1 (feff =1.08f, 302 ω≈1.1f , f=4.2×10 -5 s -1 , and m=2π/30 m), which was about one tenth of that at A1. This is consistent 303 with the lack of a distinct pattern of vertical propagation of NIOs at this station, as shown in the 304 band-passed ui (Fig. 9b), and the presence (absence) of a near-inertial peak of Scw at 10 m (200 m) 305 ( Fig. 9f).
layer and in the layers below implies another source of KEni other than local inertial-gravity wave 314 vertical propagation. 315 At C2, downward energy propagation appeared after April 23, reaching 100 m from the 316 surface within 7 days, giving Cgz =14.3 m day -1 (Fig. 11b). Unlike C1, the intensification was 317 mainly in the 30-200 m layer. The Scw at both 10 m and 200 m had a broad energy band near the 318 local f (Fig. 11f). Because ζg/f = -0.11 and feff = 1.06f, Cgz estimated from Eq. where KEni is the near-inertial energy; ⃑ and ⃑ are the near inertial velocity vector and horizontal 329 velocity, respectively; p is pressure; ρ0 is the reference density; ∇ is the horizontal gradient 330 operator; w is the vertical velocity; is the viscosity coefficient; and the angle bracket represents 331 band-passed filtering on the near-inertial band. The PRES term on the right side of equation 332 represents the pressure work on the KEni, which is associated with the inertial-gravity wave 333 propagation. NLh and NLv represent the horizontal and vertical divergence of energy flux that 334 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 336 advection of KEni contributed most of the NLh and was the main mechanism for transporting the 337 NIOs in the absence of baroclinic dispersion of inertial-gravity waves. It was also found to be more 338 important than the dispersive processes along the Gulf Stream or shelf-break jet. VVISC is the 339 vertical viscous effect. As before, we integrate this equation vertically in three layers: the upper 340 layer (0-30 m), the subsurface layer (30-200 m), and the deep layer (>200 m). In the following 341 sections, the AKEni budget is considered in entire forced region (Fig. 5) as well as at the specific 342 stations along the jet.  (Table 1). This suggests that, during the FS, the main role of the 360 pressure work was to transport the KEni from the upper layer to the deep layers, and <15% of the 361 KEni was horizontally propagated outside the forced region. 362 During the RS, the VVISC was relatively small in the upper layer and it accounted for one 363 third of the AKEni removal in the layers below (Table 1) In the upper layer, NLh advected the KEni from the source region; NLh had positive and 374 negative values on the eastern and western sides of the TC track, respectively (Fig. 13g). Similar 375 features, but with much weaker amplitude, were found in the layers below (Fig. 13h,i) upwelling around 16-17°N (Fig. 4b). As a result, the smaller KEni in the lower layer was advected 380 to the surface east of the Xiasha 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. 382 As a result, a positive NLh center located around the area with the strongest negative NLv, and a 383 negative NLh center lay to the west of the positive maximum of NLh. During the RS, NLh became 384 negative for all layers and provided ~1/3 of the total KEni loss in the water column (-0.35×10 3 J 385 became a notable sink after April 21 and was accompanied by a positive NLh (Fig. 14d). This 405 suggests that the strong jet increased the AKEni through either advection or wave propagation due 406 to PRES as a result of jet-NIO interaction at this station. In the deeper layer, the PRES provided a 407 positive AKEni flux. From the spectral analysis, the wave at 500 m had a large blue shift of >0.15f 408 (Fig. 9f) that cannot be explained by the background vorticity alone. The wave likely originated 409 from the northern latitude. 410 In the far field at stations C1 and C2, where there was no direct wind forcing from the TC, 411 surface forcing (VVISC) was relatively small during the FS (Fig. 14g,j). Therefore, horizontal 412 transport of energy is needed to sustain the KEni intensification at these two locations (Fig. 11c,d). 413 At C1, which was on the southern side of the jet (Fig. 8) and had a negative background vorticity, 414 the PRES was the main source of AKEni in both subsurface and deep layers (Fig. 14h,i). The 415 existences of the blue shift near the local inertial frequency (Fig. 11e) and of the negative 416 background vorticity suggest the presence of a southward propagating near-inertial wave towards 417 C1 from northern region. Because C2 lies near the northeastward turning point of the jet (Fig. 8), 418 the nonlinear effect became significant in the 30-200 m layer where the jet was strongest (Fig.  419 14k). After the enhancement of AKEni in the subsurface layer, the PRES further transported the 420 KEni downwards and became the major source for the increase of AKEni in the deep layer after 421 April 27 (Fig. 14l). The northeast current advected the lower frequency NIO from the lower 422 latitude towards the higher latitude, C2, which explains the red shift of the NIO at this location 423 (Fig. 11f). During the TC relaxation stage, the loss of KEni in the forced region of the whole water 445 column were caused by the vertical viscous term, the pressure work, and horizontal advection 446 effects (Table 1) Table   Table 1. Time integrated KEni budget (unit: ×10 3 J m -2 ) during the FS and RS.