Chinese Journal of Oceanology and Limnology   2015, Vol. 33 Issue(5): 1265-1278     PDF       
http://dx.doi.org/10.1007/s00343-015-4254-z
Shanghai University
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Article Information

YANG Bing (杨兵), HOU Yijun (侯一筠), HU Po (胡珀)
Observed near-inertial waves in the wake of Typhoon Hagupit in the northern South China Sea
Chinese Journal of Oceanology and Limnology, 2015, 33(5): 1265-1278
http://dx.doi.org/10.1007/s00343-015-4254-z

Article History

Received Sep. 28, 2014
accepted in principle 2015-01-03;
accepted for publication Feb. 25, 2015
Observed near-inertial waves in the wake of Typhoon Hagupit in the northern South China Sea
YANG Bing (杨兵)1,2,3, HOU Yijun (侯一筠)1,2 , HU Po (胡珀)1,2       
1 Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China;
2 Key Laboratory of Chinese Academy of Sciences for Ocean Circulation and Waves, Institute of Oceanology, Qingdao 266071, China;
3 University of Chinese Academy of Sciences, Beijing 100049, China
ABSTRACT:Energetic near-inertial internal waves (NIWs) were observed on the continental slope of the northern South China Sea in September 2008.Characteristics of the observed near-inertial waves were examined based on current data recorded by a moored acoustic Doppler current profiler.Results of a simple slab model indicated that the NIWs were generated by the surface winds of Typhoon Hagupit.Following Hagupit's passage, the wave field was dominated by baroclinic NIWs.The near-inertial currents were surface-intensified with a maximum of 0.52 m/s but still reached 0.1 m/s at the depth of 210 m.Moreover, the near-inertial currents were clockwise-polarized and slightly elliptical.A depth-leading phase of the nearinertial currents was evident, which indicated downward energy propagation.However, the rotary vertical wavenumber spectra suggested that upward energy propagation also existed, which was consistent previous theoretical study.The frequency of the NIWs, modified by the positive background vorticity, was 0.714 2 cycles per day, which was 0.02 f0 higher than the local inertial frequency (f0).The near-inertial kinetic energy evolved exponentially and had an e-folding timescale of about 3 days.The vertical phase and group velocity were estimated to be 10 and 2.1 m/h, respectively, corresponding to a vertical wavelength of 340 m.The NIWs were dominated by the second mode with a variance contribution of >50%, followed by the third mode, while the first mode was insignificant.
Keywords: near-inertial internal waves     South China Sea     Typhoon Hagupit    
1 INTRODUCTION

Near-inertial internal waves(NIWs)are commonplace features of the oceans. The frequency spectra of most ocean current records tend to display an energetic peak around the local inertial frequency f0(=2 Ω sin φ, where Ω and φ denote the angular velocity of the earth’s rotation and latitude, respectively). The predominant generation mechanism for NIWs is thought to be wind forcing at the ocean surface(Pollard and Millard, 1970; D'Asaro, 1985; Alford, 2001). Rapidly translating winds impart momentum into the surface mixed layer(SML), leading to an ageostrophic flow that subsequently adjusts and radiates NIWs(Rossby, 1937; Gill, 1984; D'Asaro, 1995; Moehlis and Smith, 2001)that contribute to ocean mixing(Munk and Wunsch, 1998).

NIWs generated by storms have been examined in many previous studies(Price, 1983; Shay and Elsberry, 1987; Cuypers et al., 2013). In the wake of storms, the difference between the frequency ω and local inertial frequency of the generated NIWs depends on the horizontal wavenumber(k, l)of the disturbance left behind by storms, which can be determined according to the following formula(Garrett, 2001):

where cz is the eigenvalue associated with the n -th vertical mode and LR is the baroclinic Rossby radius of deformation. Because the spatial scale of the NIWs is much larger than LR, the frequency of the NIWs shifts slightly above the local inertial frequency, i.e., the so-called blue shift, which has been verifi ed by previous studies(Fu, 1981; Price, 1983; Shay et al., 1990). However, red shift also occurs when the NIWs are modified by negative background vorticity(Kunze, 1985). Moreover, NIWs excited by storms are characterized by lower order baroclinic modes(Geisler, 1970) and downward energy propagation(Pollard, 1980; Brooks, 1983).

The South China Sea(SCS), which comprises a large NE-SW-oriented abyssal basin, is the largest semi-enclosed marginal sea in the western tropical Pacifi c Ocean(Liu et al., 2008). The SCS is infl uenced by tropical cyclones generated both locally and over the western Pacifi c Ocean(Wang et al., 2007). However, most studies of internal waves in the northern SCS have focused on internal tides(Lee et al., 2012; Ma et al., 2013; Xu et al., 2013) and the associated nonlinear internal solutions(Alford et al., 2010; Guo and Chen, 2014).

Relatively few studies have considered windgenerated NIWs. Using the Princeton Ocean Model, Chu et al.(2000)verifi ed that energetic NIWs existed in the wake of Typhoon Ernie. Wang et al.(2008)reported that after the passage of Typhoon Damrey, energy injected into the ocean was mainly in the nearinertial band . Sun et al.(2011a)reported that mesoscale eddies induced the blue shift of NIWs, and that energy was transferred from the diurnal tide band to the near-inertial band by parametric subharmonic instability mechanism. Sun et al.(2011b)also reported that a 2% red shift of the NIWs could be attributed to the Doppler shift and /or shear flow modulation. Subsequently, Sun et al.(2012)investigated the oceanic response to Typhoon Faith and found that near-inertial signals were also remarkable in the temperature and salinity fi elds. Chen et al.(2013)found that large near-inertial kinetic energy(NIKE)events were related to storms and eddies, and that the NIKE in the subsurface layer exhibited obvious seasonality with larger values in the autumn. Yang and Hou(2014)reported the existence of NIWs dominated by the second baroclinic mode with horizontal wavelength of 420 km and vertical phase(group)velocity of 9.7(2.9)m/h in the wake of Typhoon Nesat in 2011.

In situ observations of NIWs generated by typhoons in the northern SCS are relatively scant. In September 2008, Typhoon Hagupit passed over a mooring that provided data for the study of NIWs in the northern SCS. The mooring was deployed as part of the SCS internal wave experiment undertaken by the Institute of Oceanology, Chinese Academy of Sciences. Based on those in situ observations, the objective of this study was to investigate the characteristics of the observed NIWs.

The remainder of this paper is organized as follows. Section 2 provides details of Typhoon Hagupit and the in situ observations. The data processing methods are presented in Section 3. Section 4 presents the results and the discussions and conclusions are offered in Section 5.

2 TYPHOON HYGUPIT AND IN SITU OBSERVATIONS2.1 Typhoon Hagupit

Typhoon Hagupit was the 14th typhoon of the 2008 western Pacifi c typhoon season. According to the Japan Meteorological Agency(JMA), Hagupit formed as a tropical depression on September 17 over the western Pacifi c Ocean. Later on September 19, it was upgraded to a tropical storm; it intensifi ed into a severe tropical storm on September 20 and then into a typhoon on September 21. Hagupit entered the SCS through the Luzon Strait on September 22 and then moved northwestward(Fig. 1). On September 24, Hagupit struck Guangdong Province, moved inl and , and then dissipated 2 days later.

Fig. 1 Topography of the northern South China Sea based on the ETOPO-1 dataset (Amante and Eakins, 2009), location of the mooring (the black star), and track of Typhoon Hagupit (solid line)Six-hourly positions of Hagupit are denoted by dots (typhoon) and squares (severe tropical storm) with maximum wind speeds denoted in parentheses. Category of tropical cyclone intensity scale corresponds to the criterion of the Japan Meteorological Agency.

After Hagupit entered the SCS, it moved northwestward with a translation speed of about 8.0 m/s, estimated from its six-hourly positions, and its center passed over the mooring(the black star in Fig. 1)at around 15:00 local time(LT)on September 23, 2008. The mooring station was under the infl uence of the strong winds associated with Hagupit from September 23 to 24. According to Gill(1982), if the translation speed of storms exceeds the phase velocity of internal gravity waves, the baroclinic response of the ocean has a wave-like solution, i.e., the generation of internal inertia-gravity waves.

2.2 In situ observations

Measurements of the horizontal velocity were obtained using a 150-kHz up-looking Teledyne RD Instruments acoustic Doppler current profile(ADCP)with a precision of 5×10-3 m/s. The mooring station, located at 20°29.6′N, 115°30.2′E, was positioned on the continental slope of the northern SCS with a local water depth of 405 m. The ADCP could detect horizontal velocity from 22 to 210 m with a temporal sampling interval of 1 h and a vertical bin size of 4 m. The 9-month current record(September 14, 2008 to June 16, 2009)covered the period of the passage of Hagupit. The local inertial frequency(f0)was 0.700 2 cycles per day(cpd)corresponding to a period of 34.28 h.

The horizontal velocity used here was decomposed into zonal and meridional components and the depthmean velocity calculated. By subtracting the resultant depth-mean velocity from the original record, we were able to estimate the baroclinic velocity. Spectral analysis of the depth-mean velocity revealed that near-inertial signals were not evident. Thus, in the presented analysis, we focus on baroclinic velocity. Estimates of the near-inertial velocity(u, v)were derived by applying a type-II Chebyshev band -pass filter 0.85–1.15 f0(similar to Byun et al.(2010))to the original record. The Chebyshev filter is characterized by steep roll-off from the pass-band to the stop-band that ensures the response is sharp enough to exclude other signals. In practice, to avoid introducing phase distortion, the designed filter is applied twice, i.e., in both forward and backward directions.

As in situ wind velocity observations were unavailable, we resorted to the product of the European Centre for Medium-Range Weather Forecasts(ECWMF), using the 10-m zonal and meridional wind components from the ERA-Interim dataset(http://apps.ecmwf.int/datasets/data/interim_ full_daily/). The wind product has time resolution of 6 h and spatial resolution of 1/8°. Moreover, the daily HYCOM+NCODA Global 1/12° Analysis data(http:// coastwatch.pfeg.noaa.gov/erddap/griddap/hycom_ GLB a008_tdyx.html)were adopted to substitute for the hydrography(similar to Chen et al.(2013)). Then, vertical profiles of the background buoyancy frequency were calculated according to Fofonoff and Millard(1983), which were interpolated vertically into 2-m intervals using the cubic spline interpolation method. The resultant buoyancy frequency was used to normalize the vertical profile of the horizontal velocity when the rotary vertical wavenumber spectra were estimated(see Section 3.1) and to solve the vertical normal mode equation(see Section 3.5). Allsatellite merged absolute dynamic topography from the Archiving, Validation, and Interpretation of Satellite Oceanographic dataset(http://www.aviso. altimetry.fr/en/data.html)were used to calculate the background vorticity. The absolute dynamic topography data have a time resolution of 1 day and spatial resolution of 1/4°.

3 METHOD3.1 Spectra

Power spectra of the baroclinic velocity were estimated using the method developed by Welch(1967). To illustrate the vertical variation of the spectra clearly, the spectra were rescaled to decibel(dB)according to

where ps and p denote the power spectra density in dB and m2 /(s2∙cpd), respectively, and pr represents the reference power spectral density. Herein, the minimum value of the estimated spectra was assigned to pr ; hence, the minimum power spectral density in dB was 0.

The rotary spectra of the baroclinic velocity were estimated to investigate the rotary feature of the observed currents. The horizontal velocity vectors can be written as u(ω)+iv(ω), corresponding to the angular frequency ω(Gonella, 1972)

where T is the duration of the record. It can be divided into two parts based on the positive and negative rotating components, i.e., where u- and u+ are the clockwise and anticlockwise components, respectively. The spectra of the clockwise and anticlockwise rotating components are: where S(S+)is the clockwise(anticlockwise)spectrum and the angled brackets represent the average over all pieces. S(S+)indicates the signifi cance of the clockwise(anticlockwise)rotating horizontal currents.

The rotary vertical wavenumber spectra were estimated to examine the direction of vertical energy propagation. According to Leaman and Sanford(1975), the vertical distribution of the horizontal velocity vectors can be written as u(m)+iv(m), corresponding to the vertical wavenumber m,

where D is the water depth. It can be divided into two parts based on the positive and negative wavenumbers, where u and u+ are the clockwise and anticlockwise rotating with depth components, respectively. The spectra of the clockwise and anticlockwise rotating components are: where Cm(Am)is the clockwise(anticlockwise)rotary spectrum, the angled brackets denote that the parameters within them are averaged, and stars denote the complex conjugate. Cm(Am)indicates how “intensively” the wave energy is propagating downward(upward) and the energy propagation direction is indicated by CmAm(Liu et al., 2011). Positive (negative) CmAm indicates that the energy propagates downward (upward). As a preprocessing step, the vertical averages and time averages of the horizontal velocity were removed (Silverthorne and Toole, 2009),the horizontal velocity was then scaled based on the Wentzel-Kramers-Brillouin approximation(Leaman and Sanford, 1975).

3.2 The slab model

Slab mixed-layer models have been used widely and successfully to explain the generation of nearinertial currents in the SML by wind stress(Pollard and Millard, 1970; Gill, 1984; D'Asaro, 1985; Zervakis and Levine, 1995; Alford, 2001). Here, we used the slab model to investigate the relation between the surface wind forcing and near-inertial currents in the SML. Such models assume that the horizontal momentum imparted by the wind is distributed quickly and evenly in the vertical direction within the SML, and that it has no horizontal gradients(Mackinnon and Gregg, 2005). The evolution of the mixed-layer horizontal velocities is given by:

where ${{\vec{\tau }}_{x}}{{\vec{\tau }}_{y}}$ are the wind stress components, ρ(=1 024 kg/3)is water density, H is the depth of the SML, and r is a damping coeffi cient that represents energy loss to unresolved processes(D'Asaro, 1985). Wind stress was evaluated according to where ρa is the air density, Cd is the drag coeffi cient, and U10 and ${{\vec{u}}_{10}}$ are the magnitude and vector of the 10-m wind. The drag coeffi cient was calculated according to the formulation recommended by Oey et al.(2006), which applies to both medium and strong winds.

3.3 Least square fi tting

As the frequency resolution of the estimated spectra was too low to resolve the peak frequency of the observed NIWs, we resorted to an alternative method, i.e., the near-inertial velocity was fitted to the following equation(Sun et al., 2011b):

where V(t)is the near-inertial velocity, fi is the trial frequency, v0, v1, and θ are parameters to be fitted, and R(t)is the residual. In practice, we tried values of fi from 0.9 f0 to 1.1 f0 with an increment of 10 -4 f0 . Finally, the resultant fi corresponding to the minimum residual was chosen as the frequency of the NIWs.

4 RESULT4.1 Current spectra

Vertical profiles of the current spectra are characterized by three powerful stripes i.e., the nearinertial, diurnal, and semi-diurnal, indicating the existence of the NIWs, and diurnal and semi-diurnal internal tides, respectively(Fig. 2a). Among these, the near-inertial stripe is the most energetic. Moreover, the power of the NIWs is concentrated in the upper ocean(above 50 m) and attenuated toward the deeper ocean, whereas that of the internal tides has no signifi cant variation throughout the vertical profile, suggesting the spatial intermittence of the observed NIWs. The surface-intensifi ed power suggests that the observed NIWs were excited by surface wind forcing.

Fig. 2 Depth-frequency plot of (a) the rescaled current spectra; (b) current spectra at depths of 30, 110, and 190 m; and (c) depth-averaged rotary current spectraThe local inertial frequency ( f0 ) is denoted by the full vertical line.

The detailed power spectra of the baroclinic velocity in the SML(30 m), mid-column(110 m), and deeper ocean(190 m)are shown in Fig. 2b. In the SML, the power of the near-inertial peak overwhelms that of the diurnal and semi-diurnal tidal peaks by a factor of four. However, in the deeper ocean, the power of the near-inertial peak is comparable with that of the semi-diurnal peak and lower than that of the diurnal peak. The rotary spectra(Fig. 2c)indicate that the currents were dominated by clockwise rotating components. In the near-inertial band , the power density of the clockwise rotating component overwhelms that of the anticlockwise component by a factor of 100.

One common feature of these three spectra is that the peak frequency of the near-inertial band is shifted above the local inertial frequency. As can be seen in Fig. 2a and 2b, the near-inertial peak is clearly blueshifted in the SML, while it shows a broad band characteristic in the mid-column. In the deeper ocean, the near-inertial peak shows an increasing trend(Fig. 2a), which might result from the downward and equatorward propagation of the NIWs(Qi et al., 1995). According to Fig. 2a, the peak frequency of the near-inertial band has a depth-mean value of approximately 1.04 f0 .

4.2 Near-inertial currents

The near-inertial currents vary signifi cantly along the vertical direction with two prominent areas located in the SML and the mid-column(Fig. 3). The maximum near-inertial velocities of the SML and the mid-column are 0.52 and 0.36 m/s, respectively. Meanwhile, the zonal velocity is slightly larger than the meridional velocity, indicating elliptical particle motions, and the maximum zonal and meridional velocities in the SML were 0.52 and 0.48 m/s, respectively. Upward propagation of phase is evident, especially below 60 m, indicating downward energy propagation. Moreover, upward phase propagation becomes more evident as the NIWs evolve, especially after September 24, denoting that the energy imparted into the SML by the wind was redistributed vertically by the NIWs. Based on the slope of the contours, it was established that it took about 0.8 days for the upward phase to propagate 188 m and thus, the upward phase velocity was estimated as 10 m/h. Although the near-inertial currents are surfaceintensifi ed, their vertical range reaches 210 m, where the vertical range is defi ned as the maximum depth of the horizontal velocity of 0.1 m/s.

Fig. 3 Depth-time plots of (a) the zonal and (b) meridional near-inertial currents from September 22 to October 4, 2008Solid (dashed) contours starting at 0.1 (-0.1) m/s, denote positive (negative) values, and the interval between adjacent contours is 0.1 m/s.

Based on the wind product of the ECWMF, windgenerated currents in the SML were simulated using the aforementioned slab model. Herein, the depth of the SML was set to 40 m; determined as the depth above which the vertical shear of the near-inertial currents was lower than 0.01/s(see Fig. 7). Model results showed that r =0.1/day yielded a good match between the simulated and observed currents(Fig. 4). The results of the slab model and the downward energy propagation verifi ed that the near-inertial currents in the SML were excited by the strong winds of Hagupit, during only a short period, which radiated energy into the ocean interior in the form of NIWs(Gill, 1984). It is noteworthy that the wind amplitude of the ECWMF product was smaller than that of Hagupit reported by the JMA. Consequently, the simulated currents would be larger if the real values of the wind were applied. The discrepancy was due to the simple linear parameterization of the dissipative processes at the base of the mixed layer in the slab model, which can overestimate the work done by the wind(Plueddemann and Farrar, 2006).

Fig. 4 (a) surface wind stress calculated from ECWMF 10-m wind data; (b) comparison of the observed (solid blue line) and simulated (dashed red line) zonal near-inertial currents in the surface mixed layer, (c) same as (b) but for meridional near-inertial currents
4.3 Near-inertial kinetic energy(NIKE)

The NIKE at each level was calculated according to :

where ρ0 =1 024 kg/m3 is the reference density. The NIKE was averaged over one local inertial period to characterize the mean energy of the observed NIWs(Zheng et al., 2006).

A vertical profile of the calculated NIKE is shown in Fig. 5a. As with the near-inertial currents, the NIKE is concentrated above 50 m with a maximum value of 65 J/m3 . Another extremum is apparent at the depth of around 100 m with a maximum value of 32 J/m3 . These two energetic regions exhibited a downward propagation trend and the vertical group velocity was estimated as 2.1 m/h, which is close to the values of 2.5 m/h estimated by Brooks(1983) and 2.9 m/h estimated by Yang and Hou(2014).

Fig. 5 Depth-time (a) plot and (b) time series of one local inertial period averaged near-inertial kinetic energy

Figure 5b shows the detailed evolution of the NIKE in the SML(30 m), mid-column(110 m), and deeper ocean(190 m), as well as the depth-averaged NIKE. It is evident that the NIKE of the SML is several times larger than that of the mid-column and deeper ocean. Moreover, the NIKE increases and is attenuated exponentially; thus, we used an e -folding timescale to denote the persistence time of the observed NIWs. The e -folding timescale is defi ned as the time interval between moments when the NIKE reaches its maximum and 1/ e of its maximum. The estimated e - folding timescale was about 3 days based on the time series of the NIKE at 30 and 110 m.

According to Fig. 6a, following the passage of Hagupit, positive CmAm(red stripes)dominated, especially in the smaller wavenumber band (<0.01 cpm), which indicates downward energy propagation. From September 21 to 29, both downward and upward energy propagation existed but occurred in different wavenumber band s, i.e., <0.01 cpm and 0.01–0.02 cpm, respectively. However, upward energy propagation was much smaller than downward, i.e., <1/5 of the downward propagation. The observed upward energy propagation verifi es the theoretical results of Gill(1984), who indicated that both upward and downward energy propagation exists after the passage of storms. However, downward energy propagation at a reduced rate took over the two aforementioned wavenumber band s after September 29. Overall, following the passage of Hagupit, downward energy propagation dominated, especially in the smaller wavenumber band corresponding to lower modes, while upward energy propagation also existed in the early stages, which was prominent in the larger wavenumber band corresponding to higher modes. The different patterns of vertical energy propagation associated with different wavenumbers denote the multi-modal characteristics of the observed NIWs. The timeaveraged rotary vertical wavenumber spectra show downward energy propagation in the wavenumber band < 0.02 cpm(Fig. 6b).

Fig. 6 (a) time-wavenumber plot of CmAm ; (b) plot of rotary vertical wavenumber spectra averaged from September 21 to October 3The units of the vertical wavenumber are cycles per meter (cpm).

Vertical shear of the near-inertial currents is variable along the vertical profile with a prominent area between depths of 40 and 70 m where the maximum shear was 0.019/s(Fig. 7). Strong vertical shear indicates active momentum transfer between the SML and ocean interior. Upward phase propagation of the near-inertial currents is prominent directly below this area(see Fig. 3), which indicates downward energy propagation. Moreover, the SML is directly above this area where near-inertial currents are driven by surface wind stress. In summary, the near-inertial currents in the SML, driven by Hagupit, forced downwardpropagating NIWs at the base of the SML, i.e., the area with strong shear acted as a momentum transfer zone that radiated NIWs into the ocean interior.

Fig. 7 Depth-time plot of vertical shear of (a) the zonal and (b) meridional near-inertial currents corresponding to upward z -axisSolid (dashed) contours starting at 0.005 (-0.005)/s with an interval of 0.005/s, denote positive (negative) values.
4.4 Blue shift

The frequency of the observed NIWs varies with depth(Fig. 8a). Above 50 m, the average frequency is about 1.03 f0, whereas from 70 to 110 m it is about 1.01 f0 . Moreover, the frequency increases with depth below 150 m, which is also evident in Fig. 2a. The depth-averaged frequency is about 1.02 f0, i.e., a blue shift of 0.02 f0 . With the vertical phase velocity of 10 m/h, as mentioned earlier, the corresponding vertical wavelength is about 340 m. The phase of the NIWs shows a signifi cant depth-leading trend, which indicates downward energy propagation(Fig. 8b). As it takes one period for the phase of a certain wave to change by 360°, the vertical phase velocity can be estimated based on the vertical profile of the phase. According to Fig. 9b, the phase of the meridional velocity varies 130° from 70 to 200 m; therefore, the vertical phase velocity is about 10 m/h, which is consistent with the former outcome.

Fig. 8 Vertical profi les of (a) frequency and (b) phase of the observed near-inertial currentsThe horizontal axis is normalized by the local inertial frequency in (a) and larger phase means leading in (b).

Fig. 9 Distribution of absolute dynamic topography (color) and geostrophic current (arrows) in the northern South China SeaThe mooring station is denoted by the bold plus sign.

Kunze(1985)explored the infl uence of the mean flow shear on NIWs by examining a wave-mean flow interaction model and found that the background flow vorticity would modify the frequency of the NIWs. If the background vorticity were small compared with the planetary vorticity, the frequency shift of the NIWs is

where feff is the effective Coriolis frequency and ζ is the vorticity of the mean flow(u0, v0). Herein, the absolute dynamic topography data of AVISO were adopted to calculate the background vorticity. The spatial distributions of the absolute dynamic topography and corresponding geostrophic current for every third day from September 20 to October 5 are shown in Fig. 9. The mooring station was in the northwest periphery of a cyclonic eddy that grew in intensity from September 20 to 29. Moreover, the vorticity of the geostrophic current was calculated and the spatially averaged vorticity in a 1°×1° area around the mooring station was adopted to represent the background vorticity. From Fig. 10, the background vorticity can be seen as negative on September 20, although it increases gradually to 0.046 f0 by September 25. After this, the background vorticity varies from 0.04 f0 to 0.06 f0 without any signifi cant increasing or decreasing trend. The temporally averaged effective Coriolis frequency from September 23 to October 5 is 1.022 f0, which is comparable with the aforementioned blue shift, indicating the contribution made by the background vorticity.

Fig. 10 Time series of the background vorticity from September 20 to October 5The vertical axis is normalized by 10-2 f0 .
4.5 EOF and vertical mode

Empirical orthogonal function(EOF)analysis was used to find spatial patterns and the corresponding time series of the near-inertial currents. Herein, the EOF decomposition was performed to the nearinertial horizontal velocity. Vertical profiles of the fi rst two EOFs are shown in Fig. 11. The first EOF mode with one node at 60 m has a variance contribution of about 76%. However, the second EOF mode, which contributes only 16% to the total variance, has two nodes located at about 30 and 130 m. Higher EOF modes contribute less than 10% to the total variance and thus, they are not shown here.

Fig. 11 Vertical profi les of (a) the fi rst and (c) second EOF modes and (b and d) their corresponding time seriesBlue solid and red dotted lines represent the zonal and meridional velocity components, respectively, and the variance contributions are denoted in the legend.

The fi rst EOF mode was generated immediately following the passage of Hagupit and its maximum magnitude is shown at around September 26(Fig. 11b). However, the second EOF mode appears to lag the fi rst, reaching its maximum magnitude around September 27(Fig. 11d). Moreover, the fi rst EOF mode seems to strengthen and dissipate faster than the second. The faster dissipation of the fi rst EOF mode is probably due to the larger vertical energy propagation rate(see Fig. 6) and its larger horizontal phase velocity(Gill, 1984).

The motion of the ocean can be expressed as the sum of normal modes, each of which have a fi xed vertical structure and behave both in the horizontal dimension and in time in the same manner as a homogeneous fl uid with a free surface(Gill, 1982). The normal mode equation of the internal gravity wave is

where ϕn is the shape of the n-th baroclinic mode and N is the buoyancy frequency. The vertical displacement associated with the n -th mode is proportional to ϕn, while the horizontal velocity is proportional to d ϕn /d z . The boundary condition corresponding to a rigid surface and a fl at seafl oor is ϕ(0)= ϕ(-H)=0.

Equation 14 was solved numerically using a fi nite central difference scheme and adopting the timeaveraged(9/20–10/5)buoyancy frequency shown in Fig. 12a. The time-averaged buoyancy frequency is small near the surface and bottom, but has a maximum of about 2×10-2 /s at the depth of 70 m. In the neighborhood of the maxima, both the seawater temperature and salinity change rapidly(see the embedded picture in Fig. 12a). Moreover, the zonal and meridional near-inertial velocity can be written as the sum of the normal modes(Gill, 1984):

Fig. 12 Vertical profi les of (a) the buoyancy frequency and (b) fi rst three vertical modesThe time-averaged (9/20–10/5) seawater temperature and salinity are denoted in the insert in (a).

In practice, the near-inertial velocity was projected onto the fi rst three baroclinic modes. The resultant contributions of each mode to the total NIKE are 10.4%, 56.5%, and 24.1%, respectively, for the fi rst three modes. According to Fig. 12b, one obvious feature is that the vertical profile of the fi rst(second)EOF mode(see Fig. 11a, c)corresponds well with that of the second(third)vertical mode. Moreover, in terms of energy contribution, the fi rst(second)EOF mode and the second(third)vertical mode are the main contributors. The similarity of the vertical profiles and the ranking of the energy contribution between the fi rst(second)EOF mode and the second(third)vertical mode indicate that the fi rst(second)EOF mode corresponds to the second(third)vertical mode. In other words, the observed NIWs were dominated by the second mode, followed by the third mode. It is worth noting that the discrepancy in the energy contribution obtained from the two methods might result from the substitution of the real hydrography by the HYCOM dataset.

5 DISCUSSION AND CONCLUSION

In September 2008, Typhoon Hagupit passed over the northern SCS and induced energetic NIWs along its wake. The current record detected by a moored ADCP encompassed the passage of Hagupit, making it possible to examine the response induced in the upper ocean. Our results indicated that the dominant response of the ocean was baroclinic NIWs, the characteristics of which we carefully analyzed.

The near-inertial currents were clockwise-polarized with two peak areas: one located in the SML and the other in the mid-column. The maximum near-inertial velocities in the SML and mid-column were 0.52 and 0.36 m/s, respectively. A simple slab model forced by the winds of Hagupit reproduced the observed nearinertial currents in the SML and indicated they were generated by Hagupit. The zonal velocity was slightly larger than the meridional velocity and their maximas were 0.52 and 0.48 m/s, respectively, which were much larger than the value of 0.4 m/s reported in Sun et al.(2011b, 2012). The inequality between the zonal and meridional velocities indicated elliptical particle motions and a shift of oscillation frequency from the local inertial frequency. Although the observed NIWs were surface-intensifi ed, their vertical range extended > 210 m, where the vertical range was defi ned as the maximum depth with a near-inertial velocity of 0.1 m/s.

Spectral analysis suggested that the spectral density of the near-inertial band was concentrated in the SML with a peak frequency slightly larger than the local inertial frequency. In the SML, the near-inertial peak overwhelmed that of the internal tides by a factor of four, whereas they were comparable in the deeper ocean. Meanwhile, the spectral density was dominated by the clockwise rotating component in the nearinertial band . The NIKE had two cores: one located in the SML and the other in the mid-column. The vertical shear of the near-inertial currents was concentrated between the two NIKE cores, i.e., from 40 to 70 m, which indicated active momentum transfer. Upward phase propagation of the NIWs was evident, indicating downward propagating NIWs below the area of strong shear. These characteristics suggested that the energy injected into the SML by Hagupit spread into the ocean interior via the NIWs, i.e., the NIWs played a crucial role in the energy redistribution of the ocean after the passage of Hagupit.

The depth-averaged frequency of the NIWs was 1.02 f0, which corresponds to a blue shift of 0.02 f 0 . This is smaller than the blue shift of 0.09 f0 in the central SCS reported by Sun et al.(2011a) and it differed from the red shift of 0.02 f0 that resulted from the shear flow in the northern coastal SCS reported by Sun et al.(2011b). Examination of the background vorticity based on the AVISO dataset suggested that it contributed to the blue shift. The vertical profiles of the phase showed a depth-leading trend based on which the vertical phase velocity and wavelength were estimated as 10 m/h and 340 m, respectively, which overwhelmed that of Chen et al.(2013; their Table 1). However, the upward propagation of NIKE also existed, especially in the larger vertical wavenumber band , which verifi ed the theoretical result that both upward and downward energy propagation exist in the wake of storms(Gill, 1984).

The NIKE had a core located in the SML and another in the mid-column with maximum values of 65 and 32 J/m3, respectively. Vertical propagation of kinetic energy was evident and the vertical group velocity was about 2.1 m/h, comparable with the values of 1.8 m/h estimated by Sun et al.(2011b) and 2.9 m/h obtained by Yang and Hou(2014). Based on the evolution of the NIKE, the observed NIWs had an e-folding time of 3 days, consistent with the fi nding that the decay timescale of NIKE is generally less than 5 days(Park et al., 2009). The small e-folding time was partially due to the positive background vorticity that radiated NIWs away instead of trapping them(Kunze, 1985; Lee and Niiler, 1998).

According to the EOF and normal mode analyses, the observed NIWs were dominated by the second baroclinic mode with a variance contribution >50% followed by the third mode. This was consistent with the fi nding of Chen et al.(2013), i.e., the higher mode(modes 2–4)NIWs contributed signifi cantly to the stronger NIKE in the deeper layer(see Fig. 9 of Chen et al.(2013)). Moreover, Yang and Hou(2014)also reported NIWs dominated by the second normal mode. The insignifi cance of the fi rst normal mode might be because of its larger horizontal scale, which requires larger-scale forcing that exceeds the horizontal scale of certain tropical cyclones. This case study of in situ observed NIWs has enriched the underst and ing of tropical-cyclone-generated NIWs in the SCS, and our results suggest that tropical-cyclone generated NIWs in the SCS are varied and modified by various parameters, i.e., the background vorticity, buoyancy frequency, and horizontal scale of the tropical cyclones.

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