1. Introduction
Topographic Rossby waves (TRWs) are induced by cross-isobathic motion as water columns are stretched and compressed over sloping topography under the conservation of potential vorticity. With periods ranging from several days to hundreds of days (Rhines 1970), they always propagate with shallower water to their right in the Northern Hemisphere (Gill 1982). Previous studies have revealed that the generation of TRWs in the Gulf of Mexico is mainly associated with the Loop Current (Vukovich et al. 1979; Oey 1996; Oey and Lee 2002). Small-scale disturbances of the meanders provide the necessary linkage for energy transfer from the Loop Current and Loop Current eddies to TRWs, via potential vorticity adjustment to the changing depth of the bottom or interface (Hamilton 1990; Oey and Lee 2002). In the Gulf of Mexico, TRWs contribute significantly to the low-frequency current variance at depths greater than 1000 m (Hamilton 1990, 2007; Oey and Lee 2002). The Gulf Stream region along the continental slope of the U.S. East Coast is also an area of TRW activity, generated by the deep meandering Gulf Stream and warm core rings (Thompson and Luyten 1976; Thompson 1977; Hogg 1981, 1988; Louis et al. 1982; Smith and Petrie 1982; Johns and Watts 1986; Pickart and Watts 1990). In addition to the TRWs in the Gulf of Mexico and Gulf Stream, a recent study in the South China Sea reported that the amplitude of TRW velocities is about one order larger than the time-averaged velocity (Shu et al. 2016).
In the northern South China Sea (NSCS), complex topography and active eddies favor the generation of TRWs. There are three groups of islands on the continental slope (the Dongsha, Zhongsha, and Xisha Islands) in the NSCS, which contribute to the complex topography (Fig. 1). The Kuroshio intrusion through the Luzon Strait varies on multiple time scales (Nan et al. 2013, 2015) and sheds many mesoscale eddies (Yuan et al. 2007; Nan et al. 2011; Zu et al. 2013). Recently, Shu et al. (2016) reported persistent and energetic TRWs with periods of 9–14 days around the Xisha Islands in the western NSCS.
Topography of the northern South China Sea. Red stars indicate mooring stations (A1 and A2). The blue triangle indicates the Dongsha Islands. The dashed square indicates the Xisha waters. The shading is bathymetry and the white lines are isobaths.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
The Kuroshio intrusion separates at the Dongsha Islands in the eastern NSCS, with one branch flowing northward toward the Taiwan Strait or back to the northern Luzon Strait, and another flowing southwestward where it merges with the slope current (Wang et al. 2013a). The mesoscale eddies are deformed as they interact with the complex topography around the Dongsha Islands (Yang et al. 2016). The significant baroclinic feature induced by the joint effect of the Kuroshio intrusion and topography can also trigger strong cross-slope flows (Wang et al. 2010, 2013b, 2015). Based on the similar dynamic environment to the Gulf of Mexico, we hypothesize that there may be TRWs near the Dongsha Islands in the NSCS, which might originate from the upper-ocean flow variability.
Although Shu et al. (2016) reported the period of TRWs around the Xisha Islands in the western NSCS, the propagation and energy source of TRWs in the NSCS remain unknown due to a lack of observations. As measurements have become more extensive in recent years, some current observations can be used to focus on TRWs in the NSCS. In particular, data have been acquired recently from three long-period deep mooring stations aligned from east to west along the NSCS continental slope, and they allow us to explore propagation features and track the energy source of the TRWs.
The remainder of this paper is organized as follows. Section 2 describes the data, methods, and ray-tracing model that will be used in later sections. Section 3 describes the spectral and correlation analysis of the observations. Ray tracing yields information on various wave properties along the rays in section 4. Sources of TRW energy are discussed in section 5. Finally, conclusions are given in section 6.
2. Data and ray-tracing model
a. Data
Two mooring stations (A1 east of the Dongsha Islands and A2 to the west) were located on the NSCS continental slope (Fig. 1) from 20 September 2014 to 15 September 2015 (station A2 was only maintained until 18 May 2015), approximately along the 2200-m isobath (Table 1). Sampling time intervals were 1 h at both stations. At station A1, velocity profiles were acquired by acoustic Doppler current profilers (ADCPs) over the upper 890 m, and velocities by Aanderaa recording current meters (RCMs) near the bottom. There were upward- and downward-looking ADCPs of 75 kHz at A1, which were generally deployed at ~380 and 410 m, respectively. The velocity profiles from the ADCPs have been projected onto a vertical coordinate between 0 and 890 m with a resolution of 8 m. Any velocity larger than 3 times the standard deviation of its layer (range from 0.9 to 0.32 m s−1) is defined as an invalid value. The percentage of valid values was only 73.0% above 50 m, so values above 50 m have been removed. At station A2, velocity profiles were acquired by ADCPs over the upper 690 m, and a time series of velocity by RCM near the bottom. A 75-kHz upward-looking ADCP was deployed at ~420 m and a 150-kHz upward-looking ADCP was deployed at ~690 m. For the same reasons as at station A1, the velocities above 50 m have been removed. These upper ADCP velocity profiles have been used to analyze the cross-slope flow induced by a mesoscale eddy (Wang et al. 2018). Using the threshold of three standard deviations, the percentages of valid RCM velocities were 99.6% and 99.5% at stations A1 and A2, respectively. Short gaps caused by invalid data were subsequently filled by linear interpolation. In the study, a 48-h low-pass filter has been applied to all the data (hereafter raw data) to remove the tides and inertial oscillations. The velocity was then projected onto directions orthogonal and parallel to the topography, where positive values indicate the onshore and eastward directions, respectively.
Moorings, instruments, and deployment periods.
To identify and track eddies, daily merged sea surface height anomalies (SSHA) at 0.25° resolution from the French Archiving, Validation, and Interpretation of Satellite Oceanographic Data (AVISO; Ducet et al. 2000) are used. Mesoscale eddies are identified using an eddy detection scheme based on the geometry of the velocity vectors (Nencioli et al. 2010). An eddy center is defined as the position of minimum speed that the relative velocity vectors (relative to the time-averaged velocity) rotate around. The period of mesoscale eddy influence at each mooring station is defined as when the local surface relative vorticity is larger than half its standard deviation, and the results are consistent with the period identified by Wang et al. (2018).
The bathymetry is prescribed by ETOPO2 (Marks and Smith 2006). The climatological temperature and salinity fields are from the World Ocean Atlas 2001 (WOA01; Boyer et al. 2005), at 0.25° × 0.25° spatial resolution.
b. Topographic Rossby wave dispersion relation
In the NSCS continental slope region, N is ~1.0 × 10−3 s−1, f is ~5 × 10−5 s−1, |∇h| ~ 0.02 [∇h = (hx, hy)], and the water depths at the stations are ~2500 m. Thus, the topographic beta effect dominates the planetary beta effect (βTopo = f|∇h|/h = 4 × 10−10 m−1 s−1 ≫ β = 2 × 10−11 m−1 s−1) and the β term can be dropped in Eq. (1). For the wavelengths (2π/K) < 300 km, NhK/f ≈ O(1) or larger is a good approximation (where K2 = k2 + l2), which means from Eqs. (1) and (2) that tanh(λdh) = tanh(NhK/f) ≈ 1. The dispersion relation [Eqs. (1) and (2)] can then be simplified to ω = N|∇h| sin(θ), where θ is the clockwise angle that the wavenumber vector makes with the direction of the topographic gradient (i.e., ∇h/|∇h|). When the wavenumber points downslope (i.e., upslope group velocity), 0 < θ < π/2, and when the wavenumber points upslope (i.e., downslope group velocity), π/2< θ < π (Oey and Lee 2002).
c. Ray-tracing model
3. Deep-flow variability
a. Spectral analysis
To examine the dominant periods at these mooring stations, the power spectra of the velocity records were calculated (Fig. 2). The most significant phenomenon is that a spectral peak occurred near 14.5 days at both stations. The ~14.5-day oscillation has been shown to be associated with TRWs in Xisha waters (Shu et al. 2016); however, its generation and propagation have not been investigated.
Power spectra of the observed bottom velocity. (a) Cross-slope flow at station A1; (b) along-slope flow at station A1; (c) cross-slope flow at station A2; (d) along-slope flow at station A2. The dashed gray lines represent the 95% significance level (CL95) based on a Student’s t test.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
To see the contribution of this ~14.5-day oscillation to the velocity field, 10–20-day bandpassed and raw data are shown in Fig. 3. The amplitude and phase of the bandpassed series generally follow those of the raw series. The ratio of the standard deviations of the bandpassed and raw data [i.e., (standard deviation of 10–20-day bandpassed)/(standard deviation of raw data)] is then calculated to assess the contribution of the ~14.5-day oscillation. The standard deviation ratio of cross-slope flow is 48.1% (43.9% for along-slope flow) at station A1 (Figs. 3a,b). The standard deviation ratio is 53.6% for cross-slope flow (54.4% for along-slope flow) at station A2 (Figs. 3c,d). That is to say, this ~14.5-day oscillation accounts for about half the total bottom fluctuations at these two stations.
Time series of observed bottom velocity. (a) Cross-slope flow at station A1; (b) along-slope flow at station A1; (c) cross-slope flow at station A2; (d) along-slope flow at station A2. The black and gray lines are the 10–20-day bandpass-filtered and raw data, respectively. Ratio is the ratio between the standard deviation of 10–20-day bandpass-filtered data and standard deviation of raw data.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
Further, the velocity “flatness” was calculated to determine whether the observed 14.5-day peaks result from oscillatory (wave-like) or rotational (eddy-like) motion (Thompson 1977). To get the flatness at period of ~14.5 days, the records have been broken into overlapping 66-day segments with a 10-day shift over the length of the record, giving 30 (18) segments of the records at station A1 (A2). And the lag time was selected as one-third of each record segment length when calculating cross-spectrum. Based on the F-distribution, the 95% significance levels of the flatness of velocity at stations A1 and A2 are 0.54 and 0.44, respectively. The velocity flatness of our target ~14.5-day oscillation was significantly small (i.e., 0.40 and 0.32 at stations A1 and A2, respectively), which demonstrates that motion at this period tends to be dominated by waves (Thompson 1977). However, whether these ~14.5-day oscillations are TRWs needs further validation, that is, whether they satisfy the dispersion relation of TRWs.
b. Local wavenumbers
In theory, if the ~14.5-day oscillations are TRWs, the dispersion relation [Eqs. (1) and (2)] should be satisfied. That is, its wavenumber vector is perpendicular to the principal axis of the velocities (Thompson 1977). We calculated the variance ellipses of the 10–20-day bandpassed velocities at station A1 and A2. The major principal axes of the velocities are at a slight angle to the general trend of the isobaths for each station (Fig. 4), comparing the nine-point smoothed (~30-km spatial scale) topography and major principal axes at each station.
Principal axis variance ellipse of the 10–20-day bandpass-filtered bottom velocity with group velocity direction Cg and wavenumber vector K at observed stations. The black lines are isobaths. The directions of Cg and K are calculated from the simplified dispersion relation, i.e., ω = N|∇h| sin(θ).
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
Lags in the incidence of large kinetic energy of 10–20-day bandpassed bottom flow at stations A1 and A2 (Figs. 5a,b) indicate the direction of the bottom flow energy propagation (Figs. 5a,b). The burst of kinetic energy at station A2 significantly lagged that at station A1 (by ~17.6 days; Fig. 5c), which demonstrates that the kinetic energy propagates westward along the slope.
(a) Kinetic energy at station A1 (values larger than one standard deviation are shown); (b) as in (a), but for station A2; (c) coefficient of correlation between velocity at station A2 and that at station A1 as a function of lag. Bold solid lines indicate correlations exceeding the 95% confidence level based on a Student’s t test. A 10–20-day bandpass filter has been applied to all variables. The velocities in (c) have been projected onto the associated principal axis of the flow.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
The direction of the wavenumber vector can be calculated from the simplified dispersion relation mentioned in section 2b [i.e., ω = N|∇h| sin(θ)] in the NSCS continental slope region. Two roots of θ can be obtained, that is, one within (0, π/2) and the other within (π/2, π). The observations of westward propagation kinetic energy (Figs. 5a,b) and major principal axis of the velocity variance ellipse (Fig. 4) indicate the downslope group velocities. And then θ should be within (π/2, π). Based on the local parameters [ω = 5.02 × 10−6 s−1 (i.e., period = 14.5 days); N = 2.2 × 10−3 s−1, |∇h| = 0.027 at station A1, and N = 1.8 × 10−3 s−1, |∇h| = 0.026 at station A2], the angles θ at stations A1 and A2 are 175.15° and 173.84°, respectively. The angles between wavenumber vector and principal axis were further calculated as 77.5° and 79.4° at stations A1 and A2, respectively.
Therefore, the wavenumber vectors are almost perpendicular to the associated principal axis of velocities at stations A1 and A2. The slight differences in angle between them are possibly due to environmental uncertainty (i.e., N and topography have been averaged and smoothed). Given the above, the principal axes at stations A1 and A2 satisfy the theoretical TRW prediction (Thompson 1977; Hamilton 1990). This demonstrates that the ~14.5-day motions at these two stations are TRWs. Further, the directions of phase speed and group velocity of the ~14.5-day TRWs can be given at each station by theory (Fig. 4).
c. Correlation analysis
Theoretically, a packet of TRWs should traverse the continental slope, with group velocities parallel to the principal axis (Fig. 4). That is to say, coherent signals with appropriate lag should be seen at neighboring stations (Hamilton 1990).
To extract the TRW signal, we project the velocity onto the associated principal axis of velocities, and then compute time-lagged correlations between the two stations (where the western station lags the eastern station). The most significant correlation between the A2 and A1 velocities occurs when A2 lags by ~279 h (i.e., ~11.6 days; Fig. 5c). The 11.6-day lag gives a direct estimate of the lower bound on the group velocity of 9 cm s−1 using the straight-line distance (~90 km) between these two stations (Hamilton 1990). Based on the simplified TRW dispersion relation, the group velocity |Cg| = N|∇h| ⋅ |cos(θ)|/|K| (where θ is still the clockwise angle K makes with ∇h; Oey and Lee 2002), and hence a 13-km average wavelength between stations A1 and A2 can be estimated using the average parameters along the straight line between these two stations.
4. TRW energy propagation identified by the ray-tracing model
Now that the ~14.5-day motions have been identified as TRWs, their energy source and propagation can be investigated. Ray-tracing models have been widely used to identify TRW energy sources and propagation (Pickart 1995; Oey and Lee 2002). In this section, we trace wave rays based on the TRW dispersion relation [Eqs. (1)–(4)] to yield information on various wave properties along the rays.
a. Environmental fields and initial conditions
Without loss of generality, we choose a wavelength of 30 km as the “benchmark” calculation in the ray-tracing model. The initial wavenumber pairs at stations A1 and A2 are set based on the principal axis of velocities. The initial wavenumber pairs are given as (−14.3 × 10−5, 15.3 × 10−5) and (−16.9 × 10−5, 12.3 × 10−5) at stations A1 and A2, respectively. The ray-tracing model is integrated for 50 days using a fourth-order Runge–Kutta method with adaptive time step (Press et al. 1992).
Topography h and Brunt–Väisälä frequency N are inputs of the ray-tracing model. Since the WKB approximation has been made, all the variables should vary slowly in space and time (Lighthill 1978). A 9-point smoothing filter has been applied to the topography (~30 km spatial scale, which is close to the selected wavelength), removing short-scale topographic irregularities but leaving the large-scale features intact (Fig. 6a).
(a) Gradient of topography |∇h| in the NSCS. (b) Distribution of the Brunt–Väisälä frequency N near the bottom (vertically averaged over the bottom 250 m). (c) Profiles of N at stations.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
Dropping the β term, the vertical trapping scale is
The time mean bottom velocities are u = −1.2 ± 1.5 cm s−1, υ = 0.2 ± 1.2 cm s−1 (where u is along-slope velocity and υ is cross-slope velocity) at station A1 and u = −0.1 ± 1.6 cm s−1, υ = 0.8 ± 1.3 cm s−1 at station A2. Calculation of the deep layer geostrophic flow based on climatologic data (Wang et al. 2011) also suggests that the amplitude of the near bottom velocity is much smaller than 1 cm s−1, especially in the NSCS. The time mean amplitude of the bottom velocity is much smaller than the estimated group velocities (~10 cm s−1), so the background time mean flow is not included in the ray-tracing model.
b. Results
The rays emanating from each station mainly follow the continental slope westward, but there is a downslope component of energy propagation (Fig. 7). Ray 1 takes about 6.2 days to travel from A1 to A2, which is substantially faster than the observations due to the larger “benchmark” wavelength used in this calculation (Fig. 8a). Based on |Cg| = N|∇h| ⋅ |cos(θ)|/|K|, the time from A1 to A2 is ~14.3 days for the wavelength of 13 km, which is close to the observations. Ray 2 reveals stronger refraction, as N and |∇h| decrease offshore (Figs. 6a,b). The estimated angle between wavenumber and topographic gradient will be shown later.
Wave rays (thick colored lines) traced using the TRW dispersion relation and wavenumber vectors (thin arrows).
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
Features of the simulated topographic Rossby waves along the ray paths in Fig. 7 for (left) Ray 1 and (right) Ray 2. (a),(e) Group velocity (cm s−1); (b),(f) wavelength (km); (c),(g) topographic gradient; and (d),(h) Brunt–Väisälä frequency (10−3 s−1).
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
Distribution of terms on the right-hand side of Eq. (5). (a) Contribution of N to wavenumber variability along rays [i.e., −sin(θ)|∇h|K ⋅ ∇(N)]. (b) Contribution of topography to wavenumber variability along rays [i.e., −sin(θ)NK ⋅ ∇(|∇h|)]. (c) Total contribution to wavenumber variability along rays [i.e., −sin(θ)K ⋅ ∇(N|∇h|)]. (d) Gradient of |∇h| along direction of rays. (e) Meridionally averaged −sin(θ)NK ⋅ ∇(|∇h|) and K⊥ ⋅ ∇(|∇h|), which have been normalized by their respective standard deviations. Here, K is the unit wavenumber vector based on the simplified dispersion relation [i.e., ω = N|∇h| sin(θ)] at each point and K⊥ is the unit vector perpendicular to K. In (c), red stars indicate mooring stations (A1 and A2) and thick colored lines are the wave rays shown in Fig. 7. Hatched regions in (a)–(d) indicate where 10–20-day TRWs are not theoretically possible.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
Following the simplified group velocity |Cg| = N|∇h| cos(θ)/|K|, group velocity increases with wavelength but decreases with N and |∇h|. Along Ray 2, the group velocities are smaller than along Ray 1 (Figs. 8a,e), which is due to the smaller value of N in the offshore region (Figs. 8d,h).
c. Propagation of TRWs over the NSCS continental slope
Again, assuming that the topographic beta effect dominates the planetary beta effect, which is a good approximation over the NSCS continental slope, the direction of phase speed and group velocity can be estimated from the simplified dispersion relation ω = N|∇h| sin(θ), using the N and |∇h| over the NSCS (Fig. 6).
Upslope TRW phase propagation dominates over the NSCS continental slope, and there is also a slight westward component to the west of the Dongsha Islands (Fig. 10a). On the east side of the Dongsha Islands, the westward component of the phase speed is more significant due to the meridional trend of the topography. Near the coast of southwest Taiwan (east of 119°E), there is significant eastward propagation of TRW phase, which is still assumed to lie in the range π/2 < θ < π (recall that it is the clockwise angle the wavenumber vector makes with ∇h) (Fig. 10b). If 0 < θ < π/2, the direction of TRW phase propagation should be opposite; this needs to be demonstrated by observation. Between the 500- and 2500-m isobaths, the angle θ is much closer to 180°, which means that the group velocity mainly follows the topography (Fig. 10b). In deeper water, θ decreases, allowing a larger component of downslope energy propagation.
Direction of TRW (a) phase speed and (b) group velocity, inferred from the simplified TRW dispersion relation [i.e., ω = N|∇h| sin(θ)] for period = 14.5 days. Colors in (b) indicate the angle between the wavenumber vector and topographic gradient (i.e., θ). Hatched regions indicate where 10–20-day TRWs are not theoretically possible. The black triangle indicates the Dongsha Islands.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
5. Sources of TRW energy
a. Correlation between upper and bottom flows
EOF analysis has been applied to the observed upper flows at stations A1 and A2. The first three modes contribute more than 90% of the total variance (Figs. 11a–d). These three modes can reveal the general characteristics of the upper flow and can be further utilized to investigate the relationship between the upper and bottom flows.
EOF decomposition of observed flows and regression profile of upper-ocean flow with respect to bottom flow. (a) First three EOFs of upper cross-slope flow at station A1; (b) first three EOFs of upper along-slope flow at station A1; (c),(d) as in (a) and (b), but for station A2. (e) Regression profile of upper-ocean flow with respect to bottom flow at station A1; (f) as in (e), but for station A2. Black lines in (e) and (f) indicate where the regression exceeds the 95% confidence level based on a Student’s t test. STD: standard deviation. Mean: vertical averaged value.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
Power spectra have been computed for each principal component (PC; Fig. 12). At station A1, significant 10–20-day spectral peaks can be found in the first three PCs of the cross-slope flow, especially for the second PC (Figs. 12a–c). However, the 10–20-day spectral power of the along-slope flow is relatively weak (Figs. 12d–f). At station A2, the 10–20-day spectral peaks are much smaller (Figs. 12g–l). We therefore hypothesize that the TRW energy may originate from these upper cross-slope flow fluctuations around station A1.
Power spectra of the (a) first, (b) second, and (c) third principal components (PCs) of the cross-slope flow at station A1; (d)–(f) as in (a)–(c), but for along-slope flow. (g)–(l) As in (a)–(f), but for station A2. The dashed line indicates the 95% confidence level (CL95).
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
To test the time-lag relation between bandpassed bottom flows and upper-flow PCs, we calculate their time-lagged correlations, which are applied after a 10–20-day bandpass filter (Fig. 13). At station A1, the most significant correlation is between the bottom cross-slope flow and the second PC of upper cross-slope flow with almost zero lag (Fig. 13a). At station A2, bottom flows mainly lead the upper flows. That is to say, the bottom 10–20-day fluctuations cannot originate from the upper ocean at station A2.
Lag correlations. (a) Maximum lag correlation between bottom flow and principal components (PCs) of upper flow. (b) Bottom along-slope flow lags bottom cross-slope flow at station A1 (red lines indicate the correlations exceed 95% confidence level based on a Student’s t test); (c) as in (b), but for station A2.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
We regressed the upper-ocean flows onto the bottom flows (Figs. 11e,f). The regression profile of the upper cross-slope flow involves a negligible vertical averaged component (0.002) relative to its standard deviation (0.017), and presents the character of first baroclinic mode (Fig. 11e). It is similar to the second EOF at station A1 (Fig. 11a). This is consistent with the results of the correlation analysis above, that the TRWs at station A1 are mainly associated with the upper cross-slope flow through the first baroclinic mode (i.e., the second EOF). However, the regression profile of the upper flow is not significant at station A2, and it is a mix of the first and second EOFs (Fig. 11f).
A wavelet power spectrum analysis (Grinsted et al. 2004) has been applied to the bottom cross-slope flow at station A1 to identify the burst period of TRWs (Fig. 14a). Large-amplitude bottom cross-slope flow is consistent with the occurrence of strong 10–20-day period energy (Figs. 14a,b). Using the first three EOFs, we reconstructed the upper cross-slope flow, and then identified the depth where the flow reversed (Fig. 14c). The flow reversal depth represented the boundary of the upper and lower layers of the ocean with different motion characteristics, and indicated the first baroclinic mode. When there was a burst of TRWs, the flow reversal depth deepened, which implied the upper-ocean layer stretched, and the lower layer shrank. Potential vorticity conservation implies that downslope movement or the development of anticyclonic circulation will occur. Such fluctuation will tend to be trapped by the topography, by conservation of potential vorticity. The lag between along-slope flow and cross-slope flow at station A1 (i.e., ~97 h; Fig. 13b) confirmed this TRW excitation process. The cross-slope movement was first excited by the first baroclinic fluctuation, and then the along-slope movement was induced under the potential vorticity constraint. Thus, a lag between cross-slope flow and along-slope flow occurs.
(a) Wavelet power spectrum of bottom cross-slope flow at station A1; values that pass a 95% significance level test against red noise are shown. (b) Time series of cross-slope speed at station A1; only values larger than half the standard deviation (STD) (~0.24 cm s−1) are shown. (c) The flow reversal depth of reconstructed cross-slope flow using the first three EOFs; the red dashed line indicates the mean reversal depth and depth larger than mean reversal depth are painted cyan. (d) Surface relative vorticity normalized by local planetary vorticity f at station A1; violet dots indicate the period when the cross-slope speed at station A1 is larger than half its STD as in (b). The relative vorticity in (d) is calculated from satellite altimeter data. The mesoscale eddy period is identified when the local relative vorticity is larger than half its STD; red (blue) lines in (d) denote a warm (cold) mesoscale eddy period. In (a), the time series of cross-slope flow has been normalized by its STD and the thick black lines indicate where edge effects might distort the picture.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
However, the along-slope flow is synchronized with cross-slope flow at station A2 (Fig. 13c). This implies that these 10–20-day movements are not forced TRWs but are TRWs originating from the east as suggested by the results of the ray-tracing model (Fig. 7). When the TRWs arrive at station A2, a bottom flow anomaly along the principal axis (Fig. 4) is induced, involving both the along-slope and cross-slope components.
b. Mesoscale eddy and bottom fluctuations
The time series of relative vorticity in Fig. 14d indicates the mesoscale eddy period. Basically, the TRW period is associated with a surface mesoscale eddy or the transition period of surface warm and cold mesoscale eddies (or cold transition to warm mesoscale eddies). We identified the burst of TRWs based on the bottom cross-slope flow speed (Fig. 14b,d), and eight bursts of TRWs were identified. The second of these was selected as a case study to illustrate the relationship between the TRWs and mesoscale eddies, as it includes both warm and cold mesoscale eddies.
c. Case study
The excitation mechanism suggested above appears to involve mesoscale eddies, as described in Pickart (1995) and Oey and Lee (2002). A specific mesoscale eddy period has been selected to confirm the relationship between the burst of TRWs and the upper layer eddy (marked in Fig. 14c).
During this period, station A1 was influenced successively by a cold and a warm eddy (Fig. 15). Both eddies formed to the west of the Luzon Strait, propagated northwestward and dissipated at the continental shelf (Fig. 15). When the cold eddy propagated onto the continental slope, its western outer edge touched station A1 and induced large cross-slope flow (Figs. 15a–c). Large 10–20-day bandpassed kinetic energy surrounding the cold eddy influenced station A1, but exerted no influence on station A2. A warm eddy propagated along almost the same path behind the cold eddy, carrying large 10–20-day bandpassed kinetic energy within its main body, which influenced station A1 directly (Figs. 15d–f). Throughout, the main bodies of both the cold and warm eddies did not reach station A2 (Figs. 15e,f). In the upper ocean, there was significant cross-slope movement within the 10–20-day band at station A1. The direction of cross-slope flow reversed around 400–500 m during mid-November and early December, showing the characteristics of first baroclinic mode flow, accompanied by a large amplitude bottom cross-slope flow (Figs. 16a–c). The flow reversed depth is similar to the results of Fig. 14c at this period, but deeper than the regression pattern (Fig. 11e), due to the variance of flow reversed depth (Fig. 14c). TRWs occurred in response to the strong upper-ocean oscillation (Fig. 16c). However, there was no significant relationship between the upper ocean and bottom oscillations at station A2, which indicated that the TRWs were not generated locally (Figs. 16d–f). The burst of TRWs at station A2 lagged that at station A1 by about 11 days (Figs. 16c,f), which confirms that the TRWs at station A2 propagated from around station A1.
Distribution of 10–20-day bandpassed sea surface kinetic energy (blue shading) and geostrophic flow (the blue/red curved arrows). Yellow (black) dots are cold (warm) mesoscale eddy centers. Results at (a) 6 Nov 2014, (b) 14 Nov 2014, (c) 22 Nov 2014, (d) 28 Nov 2014, (e) 8 Dec 2014, and (f) 16 Dec 2014. All the data are derived from the AVISO satellite altimeter product. The mesoscale eddy centers are based on daily AVISO data and plotted every 2 days. Black lines indicate the 200- and 2000-m isobaths.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
Profiles of observed cross-slope velocity. (top),(middle) Upper-layer ocean flow and (bottom) the bottom flow. (a)–(c) Station A1 and (d)–(f) station A2. A 10–20-day bandpass filter has been applied to all data. In (c) and (f) velocities with amplitude larger than half their standard deviation are blackened.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
Why is there no local generation of TRWs at station A2? To understand this, we calculate the ratio of the 10–20-day bandpassed kinetic energy to the total surface kinetic energy using the satellite geostrophic velocity (Fig. 17). The ratio is large between the Dongsha Islands and the Luzon Strait. However, it decreases drastically west of station A1, which is consistent with the power spectral analysis of bottom flow (Fig. 12). That is to say, the 10–20-day energy is too weak to effectively generate TRWs locally at station A2.
Distribution of the ratio of 10–20-day bandpassed surface kinetic energy to full spectrum kinetic energy [i.e., ratio = (standard deviation of 10–20-day bandpassed)/(standard deviation of full spectrum)]. The flow data are from the AVISO satellite altimeter product. Black lines indicate the 500-, 1500-, and 2500-m isobaths.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
Based on the AVISO SSHA from 1 January 1993 to 31 December 2017, the paths of mesoscale eddies that crossed the slope and penetrated into the continental slope are shown in Fig. 18. We selected a section of the 2500-m isobath between 116° and 119°E and divided it into three equal lengths (i.e., s1, s2, and s3). Most eddies arrived at the continental slope area through s1 from the west of the Luzon Strait (Figs. 18a,d). The number of eddies that crossed s2 is only about half the number that crossed s1 (Figs. 18b,e), while only a few eddies went through s3 (Figs. 18c,f). Mesoscale eddies mainly went through s1 and then influenced the continental slope area, which may also explain why TRWs were mainly excited around station A1.
Paths of mesoscale eddies from AVISO data, together with numbers of eddies crossing a section along the 2500-m isobath between 116° and 119°E, which was divided into three equal lengths (i.e., s1, s2, and s3). (a) Paths of cold eddies that propagated from the deep basin to continental slope area through s1. (b),(c) As in (a), but for s2 and s3; (d)–(f) as in (a)–(c), but for warm eddies. The bars in the top-left corner are the numbers of eddies for the corresponding sections.
Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0247.1
6. Conclusions
Analysis of a 1-yr velocity record indicates that there is significant propagation of ~14.5-day TRWs along the NSCS continental slope. These ~14.5-day TRWs account for more than 40% of total bottom velocity variability at stations A1 and A2. The estimated wavelength is about 13 km, and the group velocity is O(10) cm s−1 with a downslope component.
A ray-tracing model shows that the energy of the TRWs mainly propagates westward along the NSCS continental slope with a small downslope component. The wavelength increases over the offshore continental slope and decreases over the onshore continental slope, generally separated by the 1500-m isobath. The TRW dispersion relation suggests that upslope TRW phase propagation dominates over the NSCS continental slope. There is also a slight westward component between the Dongsha and Xisha Islands and an eastward component near the coast of southwest Taiwan.
The possible energy source of the TRWs is around the east side of the Dongsha Islands, that is, east of station A1. There is a significant 10–20-day oscillation in the upper-ocean cross-slope flow, which is associated with mesoscale eddies. This oscillation is transferred to the bottom cross-slope flow through the first baroclinic mode (the second EOF). Under the constraint that potential vorticity must be conserved, cyclonic (anticyclonic) movement is induced, which forms a periodic oscillation that is trapped by the topography, that is, TRWs. However, to the west of the Dongsha Islands, the 10–20-day oscillation in the upper ocean is too weak to effectively generate TRWs locally.
Some issues still remain. The reason for the distribution of upper-ocean 10–20-day fluctuations is unknown. Further investigation is required to determine whether it is associated with the Kuroshio intrusion or the topography of the Dongsha Islands.
Acknowledgments
The bathymetry and WOA01 data for this paper are available at http://apdrc.soest.hawaii.edu/data/data.php. The processed mooring data used to construct figures in this work are also available, and these data can be obtained from the corresponding author, Dongxiao Wang (email: dxwang@scsio.ac.cn). This work is supported by National Natural Science Foundation of China (41776026, 41776036), National key research and development program (2017YFA0603201), and National Natural Science Foundation of China (41676012, 41606030, 41776025, and 41521005). Qiang Wang is also sponsored by the Pearl River S&T Nova Program of Guangzhou (201906010051). The ADCPs velocity profile and RCM velocities are supplied by the Xisha Deep Sea Observatory, a member of the Network of Field Observation and Research Stations of the Chinese Academy of Sciences.
REFERENCES
Boyer, T., S. Levitus, H. Garcia, R. Locarnini, C. Stephens, and J. Antonov, 2005: Objective analyses of annual, seasonal, and monthly temperature and salinity for the world ocean on a 0.25° grid. J. Climate, 25, 931–945, https://doi.org/10.1002/joc.1173.
Ducet, N., P. Y. Le Traon, and G. Reverdin, 2000: Global high-resolution mapping of ocean circulation from TOPEX/Poseidon and ERS-1 and -2. J. Geophys. Res., 105, 19 477–19 498, https://doi.org/10.1029/2000JC900063.
Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.
Grinsted, A., J. C. Moore, and S. Jevrejeva, 2004: Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes Geophys., 11, 561–566, https://doi.org/10.5194/npg-11-561-2004.
Hamilton, P., 1990: Deep currents in the Gulf of Mexico. J. Phys. Oceanogr., 20, 1087–1104, https://doi.org/10.1175/1520-0485(1990)020<1087:DCITGO>2.0.CO;2.
Hamilton, P., 2007: Deep-current variability near the Sigsbee Escarpment in the Gulf of Mexico. J. Phys. Oceanogr., 37, 708–726, https://doi.org/10.1175/JPO2998.1.
Hogg, N. G., 1981: Topographic waves along 70°W on the continental rise. J. Mar. Res., 39, 627–649.
Hogg, N. G., 1988: Stochastic waves radiation by the Gulf Stream. J. Phys. Oceanogr., 18, 1687–1701, https://doi.org/10.1175/1520-0485(1988)018<1687:SWRBTG>2.0.CO;2.
Johns, W. E., and D. R. Watts, 1986: Time scales and structure of topographic Rossby waves and meanders in the deep Gulf Stream. J. Mar. Res., 44, 267–290, https://doi.org/10.1357/002224086788405356.
LeBlond, P. H., and L. A. Mysak, 1978: Waves in the Ocean. Elsevier, 602 pp.
Lighthill, M. J., 1978: Waves in Fluids. Cambridge University Press, 520 pp.
Louis, J. P., B. D. Petrie, and P. C. Smith, 1982: Observations of topographic Rossby waves on the continental margin off Nova Scotia. J. Phys. Oceanogr., 12, 47–55, https://doi.org/10.1175/1520-0485(1982)012<0047:OOTRWO>2.0.CO;2.
Marks, K. M., and W. H. F. Smith, 2006: An evaluation of publicity available global bathymetry grids. Mar. Geophys. Res., 27, 19–34, https://doi.org/10.1007/s11001-005-2095-4.
Nan, F., H. Xue, X. Xiu, F. Chai, M. Shi, and P. Guo, 2011: Oceanic eddy formation and propagation southwest of Taiwan. J. Geophys. Res., 116, C12045, https://doi.org/10.1029/2011JC007386.
Nan, F., H. Xue, F. Chai, D. X. Wang, F. Yu, M. C. Shi, P. F. Guo, and P. Xiu, 2013: Weakening of the Kuroshio intrusion into the South China Sea over the past two decades. J. Climate, 26, 8097–8110, https://doi.org/10.1175/JCLI-D-12-00315.1.
Nan, F., H. Xue, and F. Yu, 2015: Kuroshio intrusion into the South China Sea: A review. Prog. Oceanogr., 137, 314–333, https://doi.org/10.1016/j.pocean.2014.05.012.
Nencioli, F., C. M. Dong, T. Dickey, L. Washburn, and J. C. McWilliams, 2010: A vector geometry–based eddy detection algorithm and its application to a high-resolution numerical model product and high-frequency radar surface velocities in the Southern California Bight. J. Atmos. Oceanic Technol., 27, 564–579, https://doi.org/10.1175/2009JTECHO725.1.
Oey, L. Y., 1996: Simulation of mesoscale variability in the Gulf of Mexico. J. Phys. Oceanogr., 26, 145–175, https://doi.org/10.1175/1520-0485(1996)026<0145:SOMVIT>2.0.CO;2.
Oey, L. Y., and H. C. Lee, 2002: Deep eddy energy and topographic Rossby waves in the Gulf of Mexico. J. Phys. Oceanogr., 32, 3499–3527, https://doi.org/10.1175/1520-0485(2002)032<3499:DEEATR>2.0.CO;2.
Pickart, R. S., 1995: Gulf Stream–generated topographic Rossby waves. J. Phys. Oceanogr., 25, 574–584, https://doi.org/10.1175/1520-0485(1995)025<0574:GSTRW>2.0.CO;2.
Pickart, R. S., and D. R. Watts, 1990: Deep western boundary current variability at Cape Hatteras. J. Mar. Res., 48, 765–791, https://doi.org/10.1357/002224090784988674.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992: Numerical Recipes. 2nd ed. Cambridge University Press, 963 pp.
Rhines, P. B., 1970: Edge-, bottom-, and Rossby waves in a rotating stratified fluid. Geophys. Fluid Dyn., 1, 273–302, https://doi.org/10.1080/03091927009365776.
Shu, Y., and Coauthors, 2016: Persistent and energetic bottom-trapped topographic Rossby waves observed in the southern South China Sea. Sci. Rep., 6, 24338, https://doi.org/10.1038/srep24338.
Smith, P. C., and B. D. Petrie, 1982: Low-frequency circulation at the edge of the Scotian Shelf. J. Phys. Oceanogr., 12, 28–46, https://doi.org/10.1175/1520-0485(1982)012<0028:LFCATE>2.0.CO;2.
Thompson, R. O. R. Y., 1977: Observation of Rossby waves near site D. Prog. Oceanogr., 7, 135–162, https://doi.org/10.1016/0079-6611(77)90003-9.
Thompson, R. O. R. Y., and J. R. Luyten, 1976: Evidence for bottom trapped topographic Rossby waves from single moorings. Deep-Sea Res., 23, 629–635, https://doi.org/10.1016/0011-7471(76)90005-X.
Vukovich, F. M., B. W. Crissman, M. Bushnell, and W. J. King, 1979: Some aspects of the oceanography of the Gulf of Mexico using satellite and in-situ data. J. Geophys. Res., 84, 7749–7768, https://doi.org/10.1029/JC084iC12p07749.
Wang, D. X., B. Hong, J. P. Gan, and H. Z. Xu, 2010: Numerical investigation on propulsion of the counter-wind current in the northern South China Sea in winter. Deep-Sea Res., 57, 1206–1221, https://doi.org/10.1016/j.dsr.2010.06.007.
Wang, D. X., and Coauthors, 2013a: Progress of regional oceanography study associated with western boundary current in the South China Sea. Chin. Sci. Bull., 58, 1205–1215, https://doi.org/10.1007/s11434-012-5663-4.
Wang, D. X., Q. Wang, W. Zhou, S. Cai, L. Li, and B. Hong, 2013b: An analysis of the current deflection around Dongsha Islands in the northern South China Sea. J. Geophys. Res. Oceans, 118, 490–501, https://doi.org/10.1029/2012JC008429.
Wang, G. H., S. P. Xie, T. D. Xie, and R. X. Huang, 2011: Deep South China Sea circulation. Geophys. Res. Lett., 38, L05601, https://doi.org/10.1029/2010GL046626.
Wang, Q., Y. X. Wang, W. D. Zhou, D. X. Wang, D. D. Sui, and J. Chen, 2015: Dynamic of the upper cross isobaths flow on the North South China Sea in summer. Aquat. Ecosyst. Health, 18, 357–366, https://doi.org/10.1080/14634988.2015.1112124.
Wang, Q., L. Zeng, J. Li, J. Chen, Y. K. He, J. L. Yao, D. X. Wang, and W. D. Zhou, 2018: Observed cross-shelf flow induced by mesoscale eddies in the northern South China Sea. J. Phys. Oceanogr., 48, 1609–1628, https://doi.org/10.1175/JPO-D-17-0180.1.
Yang, Y., and Coauthors, 2016: The topography effect on the sudden deceleration of the mesoscale eddy propagation speed around the Dongsha Islands in northern South China Sea. Aquat. Ecosyst. Health, 19, 242–249, https://doi.org/10.1080/14634988.2016.1215747.
Yuan, D., W. Han, and D. Hu, 2007: Anti-cyclonic eddies northwest of Luzon in summer-fall observed by satellite altimeters. Geophys. Res. Lett., 34, L13610, https://doi.org/10.1029/2007GL029401.
Zu, T. T., D. X. Wang, C. X. Yan, I. Belkin, W. Zhuang, and J. Chen, 2013: Evolution of an anticyclonic eddy southwest of Taiwan. Ocean Dyn., 63, 519–531, https://doi.org/10.1007/s10236-013-0612-6.
