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

Abstract. 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 stream 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 stream. The KEni reached its peak value within ~one-half the inertial period after the initial TC forcing stage in the upper layer, decayed quickly by one-half in the next two days, and further decreased in 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 surface, while the upward KEni advection from depths also contributed to the weakening in the TC-induced upwelling region. In contrast, during the relaxation stage as 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 stream provided the KEni source in the far-field. During both stages, the negative geostrophic vorticity south of the jet stream 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 Meanwhile, a strong local divergence and upwelling formed in the surface and generated a strong 140 cooling (~1.5°C) belt along the TC path that lasted for more than a week. The cooling zone radiated 141 hundreds of kilometer away from the core of the TC. These features were well captured by the 142 TC-induced temperature difference between April 19 and 14 from both simulated (Fig. 3a) and 143 observed SST (Fig. 3b) (http://podaac.jpl.nasa.gov/dataset/JPL-L4UHfnd-GLOB-MUR). After 144 the end of the FS on April 20 (Fig. 2c), the jet returned to its pre-storm intensity and shifted slightly 145 northward ( Fig. 2c) when the TC center approached the coast (Fig. 1a). Afterwards, during the 146 relaxation stage (RS) after April 20 (Fig. 2d), the wind forcing from the TC decreased to <0.05 Pa. 147 have been caused by many reasons, such as the lack of mesoscale and sub-mesoscale processes in 156 the atmospheric forcing field, and not resolving the oceanic subscale processes due to the limitation 157 of current model resolution. 158

Near-inertial response in the upper ocean 159
We adopted the complex demodulation method successfully used in previous NIO studies 160 (Gonella, 1972;Brink, 1989;Qi et al., 1995) to extract the inertial current signal. The simulated 161 horizontal currents (�⃑ ℎ ) were analyzed for inertial currents (�⃑ ). The inertial currents contain 162 clockwise (cw) and counter-clockwise (ccw) rotating components: 163 where ui and vi are the eastward and northward inertial currents at 10 m in the mixed layer, A and 165 ϕ are the amplitude and phase of the rotary currents, respectively. Subscripts represent the 166 clockwise (cw) and counter-clockwise (ccw) rotating direction, and f is the local Coriolis 167 coefficient. To obtain the amplitude and phase, we performed harmonic analysis daily with each 168 segment over one inertial period (IP). Then the rotary amplitude and phase were calculated 169 following previous studies (Mooers, 1973, Qi et al., 1995, Jordi and Wang, 2008. 170 The time evolution of the daily rotary currents during the FS and RS in the surface layer 171 varied spatially and was related to the intensity and translation speed of the TC. On April 15 during 172 PS, Neoguri affected mainly the region south of 13°N, with a relatively fast translation speed (Uh 173 > 3C1, Fig. 1b) and weaker intensity (Vmax~35 m s -1 ). In most areas, cw rotary currents were strong 174 (Acw >0.1 m s -1 ) yet decayed quickly after 3 days (<2 IP) (Fig. 5a), while the magnitudes of ccw 175 currents were very small (Fig. 5b). After April 18, Neoguri moved into the region between 14°N 176 and 18°N, where it intensified more than 40% but moved slower with Uh~2C1. Both the cw and 177 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 179 the right of the track and to ~<150 km to the left of the track. This extension of horizontal scale 180 was related to the region with wind stress |τ|>0.25 Pa in Neoguri.

Response in the upper layer 199
We focused on the area between 110-115°E and 13-19°N (box in Fig. 5a), defined as the 200 forced region, where the strongest NIO was produced during FS of Neoguri. We calculated the 201 wind-induced near-inertial energy flux (or the wind work) using ⃑ • �⃑ , where ⃑ is the band-passed 202 near-inertial wind stress and �⃑ is the near-inertial current at the surface (Silverthorne and Toole, 203 2009). A 4 th order elliptic band-pass filter (Morozov and Velarde, 2008) was applied to obtain 204 near-inertial motion with a band ranging from 0.8f to 1.2f, where f is the local Coriolis coefficient. 205 The time series of domain-averaged ⃑ • �⃑ over the forced region reveals that significant energy 206 input took place during the FS, with the peak value about 68×10 -3 W m -2 on April 17 (Fig. 7). 207 Under this large wind energy input, the area-averaged depth-integrated KEni (or AKEni hereafter) 208 in the upper layer (0-30 m) increased significantly from its pre-storm value to a maximum ~1500 209 J m -2 during the FS, with an increase rate of about 16×10 -3 W m -2 (Fig. 7a). Despite the continuous 210 positive wind energy flux, the AKEni in the upper layer plateaued, indicating that a large amount 211 of the wind energy was either propagating out the forced region or was lost to the lower layers due 212 to entrainment. The detailed mechanisms are discussed in the following sections. After the peak 213 of FS, the wind work decreased significantly with small negative value around the end of the FS. 214 The AKEni decreased to one half of its peak value within 2 days (decrease rate was about 7×10 -3 215 W m -2 ). After that, the wind work was almost negligible, and the decrease rate of AKEni became 216 smaller (~0.8×10 -3 W m -2 ). 217

Response at depths 218
During the FS, the AKEni in the upper 200 m constituted ~90% of the total AKEni in the 219 whole water column, while the AKEni between 30-200 m alone accounted for ~30-50% (Fig. 7b). 220 The KENI in this mid-layer had a temporal evolution different from that in the upper layer. It 221 reached its maximum on April 20, around one and a half days later, and was more than 80% of the

Vertical propagation of near-inertial energy 242
It is clear that the distribution of the KEni was mainly controlled by the propagation of 243 near-inertial wave energy both horizontally and vertically as well as by the background jet stream. 244 In order to understand the KEni distribution in the deeper water inside the forced region and in the 245 far field, we selected four different locations, marked as A1, A2, C1, and C2 in Fig. 8  At location A2, strong ui was mainly trapped in the water above 100 m, and below 100 m 284 ui <10 cm s -1 . It returned to its pre-storm magnitude after 5 IPs (Fig. 9b). The local upwelling 285 related to the positive background vorticity and to the associated strong surface divergence might 286 have caused the smaller vertical scale of ui at A2 (Fig. 4b). The KEni was generally smaller than 287 that at A1, and relatively large energy was found only in the ML (Fig. 9d). Cgz at A2, estimated 288 from Eq. (3), was 1.2 m day -1 (feff =1.065f, ω≈1.1f , f=4.2×10 -5 s -1 , and m=2π/30 m), which was 289 about one tenth of that at A1. This is consistent with the lack of a distinct pattern of vertical 290 propagation of NIOs at this station, as shown in the band-passed ui (Fig. 9b), and the presence 291 (absence) of a near-inertial peak of Scw at 10 m (200 m) (Fig. 9f). 292

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 294 KEni (Fig. 11c,d) in the upper layer were smaller than those at those stations in the forced region 295 due to the weaker TC influence. Only a small downward propagation was discerned during the FS 296 ( Fig. 11a,b). However, notable intensification of the KEni occurred in the layers below the upper 297 layer after April 23. At C1, the Scw at 10 m had a small red shift, while the Scw at 200 and 500 m 298 displayed blue shifts with peaks near 1.07f (Fig. 11e). The difference between Scw in the upper 299 layer and in the layers below implies another source of KEni other than local inertial-gravity wave 300 vertical propagation. 301 At C2, downward energy propagation appeared after April 23, reaching 100 m from the 302 surface within 7 days, giving Cgz =14.3 m day -1 (Fig. 11b). Unlike C1, the intensification was 303 mainly in the 30-200 m layer. The Scw at both 10 m and 200 m had a broad energy band near the 304 local f (Fig. 12f). Because ζg/f = 0.12 and feff = 1.06f, Cgz estimated from Eq. (3) had an upward 305 propagation, which cannot explain the downward propagation here. The linearized wave theory, 306 with the consideration of Doppler drift due to background currents, does not seem to be valid in 307 this location. We will discuss this issue in the next section. 308 where AKEni is the area-averaged depth-integrated near-inertial energy; �⃑ and �⃑ ℎ are the near 316 inertial velocity vector and horizontal velocity, respectively; p is pressure; ρ0 is the reference 317 density; ∇ ℎ is the horizontal gradient operator; w is the vertical velocity; is the viscosity 318 coefficient; and the angle bracket represents band-passed filtering on the near-inertial band. The 319

KEni Budget
PRES term on the right side of equation represents the pressure work on the AKEni, which is 320 associated with the inertial-gravity wave propagation. NLh and NLv represent the horizontal and 321 vertical divergence of energy flux that include the effects of 1) the advection of AKEni due to 322 background currents and 2) the straining of the wave field due to the background shear currents.  the VVISC term was one order larger than the other terms, with a maximum of 30×10 -3 W m -2 on the wind work during the FS (Fig. 7a), VVISC became negative after April 19, indicating the AKEni 339 removal by negative wind work. The influence of VVISC extended to the 30-200 m layer, and 340 provided a positive energy flux (~1×10 3 J m -2 ) in this layer (Figs. 12b, 13b). The effect of VVISC 341 in the deep layer was negligible (Fig. 12c). 342 Shortly (~1 day) after the large injection of KEni into the upper layer during the FS, the 343 PRES became significant (Fig. 12a, Table 1) and its horizontal distribution resembled that of 344 VVISC (Fig. 13a, d), suggesting that PRES radiated the KEni out of the forced region. It provided 345 a negative KEni flux in the upper layer (-0.65×10 3 J m -2 ), which was largely compensated by the 346 positive flux in deeper layers (Table 1). This suggests that, during the FS, the main role of the 347 pressure work was to transport the KEni from the upper layer to the deep layers, and <15% of the 348 KEni was horizontally propagated outside the forced region. 349 During the RS, the VVISC was relatively small in the upper layer and it accounted for one 350 third of the AKEni removal in the layers below (Table 1). The PRES became a major sink for 351 AKEni in the ML (-0.85×10 3 J m -2 ) and subsurface layer (-0.16×10 3 J m -2 ), but was the major 352 source in the water below 200 m. The AKEni loss due to the horizontal wave propagation outside 353 the forced region was ~-0.42×10 3 J m -2 , accounting for about 40% of the total loss in the whole 354 water column. 355

Nonlinear advection terms had an important influence in the top 200 m but made little 356
contribution to the AKEni budget in the water below 200 m (Fig. 12, Table 1). The horizontal 357 effects of NLh and NLv in these layers were mainly limited to a smaller region, as compared to the In the upper layer, NLh advected the KEni from the source region; NLh had positive and 361 negative values on the eastern and western sides of the TC track, respectively (Fig. 13g). Similar 362 features, but with much weaker amplitude, were found in the layers below (Fig. 13h,i) During the FS at A2 on the northern side of the jet stream, VVISC in the upper layer (Fig.  386 14d) had slightly larger magnitude than that at A1. However, it greatly decreased to 3×10 -3 W m -2 387 below the ML (Fig. 14e), which suggested that the smaller vertical scale on the northern side of 388 the jet limited the deep penetration of the wind energy in this location. Compared to A1, the NLv 389 was much stronger in the upper layer, and about one half of the lost energy was compensated for 390 by the NLh. The PRES was negligible compared to that at A1 (Fig. 14d-f). During the RS, the PRES 391 in the ML became a notable sink after April 21 and was accompanied by a positive NLh (Fig. 14d). 392 This suggests that the strong jet increased the AJEni through either advection or wave propagation 393 due to PRES as a result of jet-NIO interaction at this station. In the deeper layer, the PRES provided 394 a positive AKEni flux. From the spectral analysis, the wave at 500 m had a large blue shift of 395 >0.15f (Fig. 9f) that cannot be explained by the background vorticity alone. The wave likely 396 originated from the northern latitude. 397 In the far field at stations C1 and C2, where there was no direct wind forcing from the TC, 398 surface forcing (VVISC) was relatively small during the FS (Fig. 14g,j). Therefore, horizontal 399 transport of energy is needed to sustain the KEni intensification at these two locations (Fig. 11c,d). 400 At C1, which was on the southern side of the jet stream (Fig. 8) and had a negative background 401 vorticity, the PRES was the main source of AKEni in both subsurface and deep layers (Fig. 14h,i). 402 The existences of the blue shift near the local inertial frequency (Fig. 11e) and of the negative 403 background vorticity suggest the presence of a southward propagating near-inertial wave towards 404 C1 from northern region. Because C2 lies near the northeastward turning point of the jet (Fig. 8), 405 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 407 KEni downwards and became the major source for the increase of AKEni in the deep layer after 408 April 27 (Fig. 14l). The northeast current advected the lower frequency NIO from the lower 409 latitude towards the higher latitude, C2, which explains the red shift of the NIO at this location 410 (Fig. 11f). 411

412
TCs force the ocean to form NIOs. The response of NIOs is largely associated with the 413 different forcing stages of the TCs and background flow. Due to spatiotemporally limited 414 measurements, our understanding of the process and mechanism that govern the NIO response is 415 mainly based on theories that are constrained by idealized assumptions. In this study, we utilize a 416 well-validated circulation model to investigate the characteristic response of KEni to a moderately 417 strong TC (Neoguri) with observed strong KEni and to a unique background circulation. 418 The near-inertial currents in the upper layer strengthened significantly during the TC forced 419 stage and displayed a clear rightward bias due to stronger wind forcing and the resonance between 420 the wind and the near-inertial currents. The distribution of near-inertial currents and the associated 421 rotary spectra showed that the propagation patterns of NIOs varied greatly from location to 422 location and were closely linked to the influences of the background jet. During the TC relaxation stage, the loss of KEni in the forced region of the whole water 432 column were caused by the vertical viscous term, the pressure work, and horizontal advection 433 effects (Table 1) Table   Table 1. Time integrated KEni budget (unit: ×103 J m-2) during the FS and RS.