1. Introduction
Near-inertial waves (NIWs) have been observed for over 80 years throughout the world oceans (Gustafson and Otterstedt 1932; Webster 1968; Fu 1981; Alford et al. 2016). They can be generated by numerous mechanisms including, but not limited to, wind forcing from sporadic storm events (Alford et al. 2016), localized wave–wave interaction like the parametric subharmonic instability (MacKinnon and Winters 2005), or the interaction between topography and geostrophic currents (Nikurashin and Ferrari 2010). At station Papa (located in a region of the North Pacific without complicated mean flow or bathymetry), multiyear mooring observations show that NIWs typically present themselves as layers of shear that oscillate near the local inertial frequency. These layers have vertical and lateral length scales of about 100 m and tens of kilometers, respectively. These signals are associated with clear near-inertial (NI) peaks in kinetic energy (KE) frequency spectra (Alford et al. 2016). However, observations of NIWs can be much more complicated in regions where both large-scale background circulation and generation mechanisms undergo significant variability.
In this study, we demonstrate that such variability in the South China Sea can lead to the disappearance of the NIW peak in Eulerian frequency spectra. Here, the presence of strong internal tides (ITs) modulates the NIW field in frequency and vertical wavenumber. In addition to this modulation, the intrinsic frequency of NIWs varies over short periods. The amplitude of these variations is of the same order of magnitude as the relative vorticity variations associated with the Kuroshio and its mesoscale activity. We discuss how these mechanisms can reduce the KE at NI frequencies in a simple Eulerian frame and why a more comprehensive analysis is needed to capture the NIW signal more accurately.
Observations from a mooring array deployed in July and August 2011 in the Luzon Strait (discussed in more detail in section 2a) show no NIW peak in KE frequency spectra in 8 of the 10 moorings (Fig. 1). After comparing the NCEP winds in the Luzon Strait (LS) to the ones at station Papa (section 2c), it is unlikely that weak winds can account for the lack of a NI peak at the LS. Furthermore, Cao et al. (2018) show that even the strong winds induced by the passage of three typhoons in the area did not produce a persistent NI peak, as the intense NIWs initially generated disappeared shortly thereafter. We continue under the premise that NIWs are not absent, but do not manifest themselves as NI peaks in frequency spectra and investigate the numerous mechanisms that could alter the frequency characteristics of NIWs using both our observations and the results from the regional model Luzon Strait Ocean Nowcast/Forecast System model (Ko et al. 2009).
Kinetic energy frequency spectra in the Luzon Strait and at station Papa. The spectra were computed using a multitaper method (Riedel and Sidorenko 1995) for a 30-day period from yearday 170 to yearday 200. The spectra are vertically averaged over the first 1500 m. Velocity and shear are WKB scaled to enable comparison along vertically variable stratification. We normalized the stratification profiles with
Citation: Journal of Physical Oceanography 50, 5; 10.1175/JPO-D-19-0103.1
Pinkel (2008a) describes another mechanism that can spread the NIW signal over a broad frequency range. Some observations of NI shear demonstrate a frequency bandwidth that increases linearly with vertical wavenumber, giving the two-dimensional frequency–wavenumber spectrum an hourglass form. A simple model reproduces this shape by assuming a monochromatic NIW transformed by the effects of lateral advection and random vertical advection (fine-structure contamination). The vertical and lateral displacements due to the internal wave continuum distort the phase of small-scale waves more than large-scale waves. This fine-structure contamination is the signature of Doppler shifting of the observations by time-changing “background” currents, which include internal waves.
Similarly, a narrow-band (sinusoidal) “background” such as the internal tide can vertically displace isopycnal layers and contaminate an Eulerian observation by artificially shifting the NIW peak toward a combination of the NI and tidal frequencies (Alford 2001). In the absence of ITs and internal wave (IW) continuum, NIWs generated at the surface produce bands of shear (often ~100 m thick in the vertical) with upward propagating phase and downward propagating energy. In the presence of strong ITs, these NI shear layers are distorted by the vertical motion of the isopycnal layers forced by the tide (Sherman and Pinkel 1991) and the tidal heaving of the NI motions is identifiable in an Eulerian frequency spectrum as “contamination” peaks at f ± D1 or f ± D2 (Alford 2001) (where D1 and D2 are the diurnal and semidiurnal tidal frequencies). This contamination by the vertical heaving can be corrected by projecting the Eulerian velocities on to a semi-Lagrangian (i.e., isopycnal-following) coordinate system (Pinkel et al. 1991; Anderson 1993; Alford 2001; Pinkel 2008a).
In the South China Sea, particularly in the LS, the ocean circulation is characterized by intense subinertial motions, strong internal tides, and a very energetic IW continuum, three processes able to impact the NIW field through the mechanisms described above. Extracting the NIW signal from records influenced by these processes requires methods beyond simple frequency spectra of Eulerian records. In the present study, we track NIWs from the one dimensional results provided by classic Eulerian KE frequency spectra to a two dimensional description of the semi-Lagrangian shear distribution as function of time. We demonstrate a strong interaction between NIWs and ITs and suggest a relationship between the NIW intrinsic frequency variability and changes in relative vorticity due to mesoscale variability in the Kuroshio. More generally, our results highlight how internal waves and the subinertial motions can obscure the near-inertial signal derived from simple analysis techniques and the importance of employing a more comprehensive methodology.
2. Data and oceanographic background
a. Moorings
Current measurements were made during the Internal Waves in Straits Experiment (IWISE), a research initiative to study the generation, propagation, and dissipation of internal tides in the LS (Alford et al. 2015). A pilot experiment was conducted during summer 2010, consisting of two short-term moorings and 19 shipboard stations using lowered acoustic Doppler current profiler (LADCP) alongside conductivity, temperature, and depth (CTD) measurements (Alford et al. 2011). The 19 shipboard stations were located along a northern and a southern line, chosen to characterize IT generation and circulation over the meridional ridges of the LS. From July to August 2011, an eight-element moored array (black stars on Fig. 2) was deployed along the same northern and southern lines as the 19 shipboard stations from the 2010 pilot experiment. The goal of the array was to occupy the same locations studied during the pilot experiment for a longer period to measure the time variability of ITs over several spring–neap cycles. Most moorings were populated with an upward-looking, 75-kHz ADCP that measured velocity in the upper water column (<500 m) with 8-m vertical resolution and 5-min temporal resolution. Below the ADCP, depending on the depth, one or two stacked McLane moored profilers (MPs) measured horizontal velocity, temperature, and salinity over the entire column (~1000 m per MP). The MPs profile at a nominal speed of 0.25 m s−1, resulting in a complete profile approximately every hour. As a result of the challenging environment, not all moorings returned full-depth data. The mooring array is organized in two zonal lines, allowing us to estimate the local relative vorticity ξ using ξ ~ (1/2)(∂V/∂x). For these moorings and the following ones in the South China Sea, NI velocities are naively estimated using an order 3 Butterworth bandpass filter with cutoff frequencies defined by f ± 0.05 cpd (signals with periods between ~32 and 37 h).
Time-averaged velocity across the Luzon Strait during the experiment. Colored vectors show 5-day averaged velocities at 150 m from the mooring array. Gray vectors are time-mean velocity vectors at the surface during the experiment from the operational Mercator global ocean analysis and forecast system with a 1/12° resolution. The background colors show bathymetry from ETOPO1 (Amante and Eakins 2009).
Citation: Journal of Physical Oceanography 50, 5; 10.1175/JPO-D-19-0103.1
The A1 mooring (Fig. 2), located at the eastern edge of the northern line, was instrumented with a “Stablemoor” subsurface float at a depth of 705 m that housed upward- and downward-looking 75-kHz RDI Long Ranger ADCPs. These ADCPs measured velocity over depth ranges from 120 to 650 m and from 725 to 1200 m with 5-min temporal resolution. An upward-looking 300-kHz ADCP at 80 m measured near-surface velocity. From 80- to 1409-m depth, Seabird (SBE)-37 MicroCATs (temperature, salinity, and pressure) were deployed above the Stablemoor platform every 40 m with 2-min sampling rate. Pressure records from the SBE-37 MicroCATs are used to correct for mooring knockdown (Pickering et al. 2015). Besides mooring S7, all the moorings recorded more than 40 days (spanning from yearday 161 to yearday 216) of useful data over the upper 500 m. At greater depth, only A1, S9, N1, and N2 are used for analysis.
Two additional moorings (Fig. 2) were deployed on the 1584- and 2584-m isobaths of the South China Sea continental slope during the same period as the IWISE moorings. These moorings were equipped with SBE-39s and SBE-56s over the whole water column. Above 515 m, these instruments were spaced by 60 m and spaced by 500 m below. At 515 m, the moorings had an upward-looking 75-kHz ADCP.
To contrast the behavior of NIWs within a circulation driven by strong ITs and an intense mesoscale field induced by the Kuroshio, we also examine measurements from a mooring deployed at station Papa, located in a relatively quiescent region of the North Pacific. Maintained by the National Oceanic and Atmospheric Administration/Pacific Marine Environmental Laboratory (NOAA/PMEL), the subsurface mooring was deployed on 13 June 2008. It operated continuously until 14 June 2010, except for a 2-day gap in June 2009 during its turnaround. The mooring was equipped with an upward-looking ADCP at 800-m depth with 16-m vertical resolution and a shallower upward-looking ADCP at 154-m depth with 4-m resolution. The temporal resolution for both ADCPs was 30 min. For our comparison, we use data from station Papa from yearday 165 to yearday 216 in 2008.
b. Models
To investigate the influence of the relative vorticity on the NIW behavior, we used the output from the Luzon Strait Ocean Nowcast/Forecast System (LZSNFS) model (Ko et al. 2009). The system is an integration of a dynamical ocean model and a statistical data analysis model. It uses ocean bottom topography from the Digital Bathymetry Database with 2-min resolution and open boundary conditions derived from a larger-scale model for the entirety of the East Asian seas. The barotropic tidal currents of eight tidal constituents (K1, O1, P1, Q1, K2, M2, N2, and S2) are obtained from TPXO7.2 (Egbert and Erofeeva 2002). The LZSNFS model includes the reflection of the internal tide from the continental shelf to the west but does not contain remote internal tides from outside the domain, including the Mariana Arc (Chen et al. 2013; Ma et al. 2013; Pickering et al. 2015). We used the LZSNFS model to compute relative vorticity ξ at the mooring locations.
The two moorings located on the South China Sea continental slope are outside the domain of the LZSNFS. To document the large scale circulation there, we used the surface velocities from the Operational Mercator global ocean analysis and forecast system (http://marine.copernicus.eu). This 1/12° model does not include tides but provides daily and monthly mean data of temperature, salinity, currents, sea level, mixed layer depth, and ice parameters over the full water column of the global ocean.
c. Winds
To understand the near-inertial response of the ocean to the wind in the LS, we used gridded NCEP–NCAR surface winds (https://rda.ucar.edu). Despite a relatively coarse resolution (6 h and 0.5° for the temporal and spatial resolution), these winds accurately reproduce the winds observed at a meteorological station located south of Taiwan (not shown) and provide a proxy to estimate the wind work on the surface of the ocean. We compute the energy flux from the wind to inertial motions via a mixed layer (ML) inertial current slab model (Pollard and Millard 1970), assuming a fixed 50-m mixed layer depth (MLD).
d. Oceanographic background
1) Circulation in the South China Sea
The subinertial variability in LS is forced by one of the branches of the Kuroshio, which enters the South China Sea through the LS. North of the LS, the Kuroshio veers back eastward to reenter in the Pacific Ocean. The Kuroshio branch trajectory can vary about 30° in a few days but is generally northward (Fig. 2). South of the LS, in the wake of the Philippine islands (Wang et al. 2003; Xiu et al. 2010; Chen et al. 2011), this branch continuously generates westward propagating eddies. One of these eddies grew and moved to the South China Sea continental slope during the period of observation, and two moorings (RN, RS) recorded velocities with opposite directions.
In the LS, the distribution of KE in the frequency domain shows strong tidal peaks (about 100 times above the background spectrum). The ITs are strong not only because of strong barotropic forcing but also because they are generated on two meridional ridges, separated from each other by a semidiurnal tidal wavelength (~100 km). This unique geometry causes the resonance of the semidiurnal IT, with significant baroclinic energy amplification (Tang and Peacock 2009; Echeverri and Peacock 2010; Alford et al. 2011; Buijsman et al. 2014; Alford et al. 2015). The presence of the Kuroshio and its associated mesoscale variability raise the level of subinertial KE in the LS an order of magnitude above what is observed at station Papa (Fig. 1). Around f, we only observe NI peaks at moorings N1 and MPS (Fig. 1). Besides these two moorings, the lack of prominent NI peaks in the LS contrasts greatly with a more typical environment (station Papa) where the NI peak is a dominant feature of the KE frequency spectrum.
The Kuroshio and its eddies also have a strong signature in the depth structure of velocity (Fig. 3, left panels). North of the LS, the currents are northward over the first 500 m with large tidal oscillations over the whole water column (mooring N1, MPN). Northeast of the LS (mooring A1), the currents show a spring–neap tidal cycle enhanced above 700 m. The presence of eddies next to Taiwan can be seen in the vertical structure of velocity. The velocity data south of the LS also show eddies passing by S9, S6, MPS with surface intensified currents. On the South China Sea continental slope, the eddy present for the entire period of the experiment drives most of the variability observed at moorings RN and RS. Mooring RN (RS) experiences eastward (westward) currents over the first 500 m.
(left) Raw and (right) near-inertial meridional velocities υ from the South China Sea moorings.
Citation: Journal of Physical Oceanography 50, 5; 10.1175/JPO-D-19-0103.1
The naively estimated NI oscillations (Fig. 3, right panels) usually exceed 5 cm s−1, except at moorings S9, MPN, and N2 where these oscillations are weaker. These oscillations are variable in depth and time and do not show a clear upward propagating phase, which is expected for wind-generated NIWs. Since the scope of the mooring array is small compared to the size of the coherent structures of wind, we assume the moorings experienced similar wind events. Consequently, the observed differences in the NIW field between each locations are most likely due to other mechanisms than a lack of wind.
2) Strong winds in the Luzon Strait and lack of near-inertial peaks
The lack of prominent NI peaks in the LS suggests processes that weaken or mask NIWs in the region. Weak wind forcing would be a natural explanation for lack of NIWs in the LS. We compare the LS winds to those at station Papa between yearday 170 and 215 (Fig. 4). The time-averaged wind work at station Papa is about 0.344 mW m−2 and is associated with a prominent NI peak in the averaged KE spectrum. For comparison, the winds in the LS for the same period were stronger with a time-averaged wind work 20 times higher (locally >6.6 mW m−2), especially in the eastern domain of the LS. With such a substantial energy input from the wind, one would expect to observe a strong NIW signal in the velocity or the shear. We find some evidence of such activity in the NI velocities (Fig. 3). However, the signal is too variable in depth and time to be accurately represented in a simple depth-averaged Eulerian frequency spectrum. Hereafter we use more sophisticated techniques to examine the spreading of the NI peak.
(top) Estimation of the wind work for a 50-m-thick mixed layer at the MPS location and station Papa. (bottom) Maps of the time average of wind velocities (arrows) and work (contour) in the Luzon Strait. The mean wind work in the LS is 6.6 × 10−3 W m−2. The mean wind work at station Papa is 2.2 × 10−4 W m−2.
Citation: Journal of Physical Oceanography 50, 5; 10.1175/JPO-D-19-0103.1
3. Methods
a. Semi-Lagrangian frame
b. Kinetic energy and shear spectra
Hereafter, we refer to the diurnal (1 cpd) and semidiurnal (2 cpd) frequencies as D1 and D2. The other frequencies from 3 to 6 cpd are denoted as D3–D6.
4. Results
a. Isopycnal frequency content
Vertical heaving by strong tides in the LS can distort an Eulerian observation of a NIW and alter the frequency distribution of NIWs signal in frequency spectra (Anderson 1993; Alford 2001). At S9, which has depth–time series of density, we computed the vertical displacements of the isopycnals and projected the velocities onto these layers to observe the currents in a sL frame (Fig. 5). The sL frame tends to organize the shear field into coherent layers at lower frequencies. For example, between yearday 190 and 195, the tide causes vertical oscillations of the isopycnal layers greater than 100 m. After projection, the sL shear shows organized layers with upward and downward propagating phase coherent over a period longer than one day.
(top) Vertical shear from zonal velocities at S9 between 650- and 1100-m depth. The black lines represent the positions of isopycnal layers with an average spacing of 200 m. The black dashed lines show the McLane profiles. The shear and isopycnal layer present 100-m vertical diurnal variations. (bottom) Shear projected on the isopycnal layers. The vertical axis represents the time averaged positions of the isopycnal layers.
Citation: Journal of Physical Oceanography 50, 5; 10.1175/JPO-D-19-0103.1
The frequency distribution of the sL shear at S9 demonstrates the reduction of the frequency spreading due to this kinematic effect (Fig. 6). A broad peak near f (0.2–1 cpd), absent in the Eulerian frame, is now visible in the sL spectrum. Though our observations are not sufficient to conclusively show it, we argue in the discussion (section 5) that the width of the peak is due to Doppler shifting by the Kuroshio.
Clockwise frequency Eulerian (blue line) and semi-Lagrangian (red line) shear spectra between 700- and 1000-m depth at S9. The colored dashed lines represent the counterclockwise component. The black dashed line represents GM76.
Citation: Journal of Physical Oceanography 50, 5; 10.1175/JPO-D-19-0103.1
b. Distribution of Eulerian kinetic energy and shear
1) Frequency spectra
Returning to Eulerian spectra, can a NIW signal at only one depth be masked in a depth-averaged spectrum? The KE and shear depth–frequency distribution (Figs. 7 and 8) do not show peaks at f in the upper part (<500 m) of the water column. However, at moorings MPS, N1, N2, and S9, the depth–frequency spectra show a peak in KE at f below 500 m for MPS and N1 and below 1000 m for S9 and N2 (Fig. 7). Likely associated with propagation along sloping beams, these peaks are too small to contribute as significant signatures in the vertically averaged quantity presented previously (Fig. 1). This is particularly true at S9, where the NIW activity seems relatively weak. There, we observe a NI peak below 1200 m. At these locations and above these depths, the spectra do not show any significant NI kinetic energy, such that depth-averaged quantities show absent or only weak NI peaks.
Kinetic energy rotary spectra over the first 1500 m for the (left) southern and China continental slope moorings and (right) northern moorings. These data are compared with station Papa (bottom-right panel). The blue dashed lines highlight the f − D1, f − D2, f + D1, and f + D2 frequencies. The solid blue line represent the local near inertial frequency. Velocities are WKB scaled to enable comparison along vertically variable stratification.
Citation: Journal of Physical Oceanography 50, 5; 10.1175/JPO-D-19-0103.1
As in Fig. 7, but for shear.
Citation: Journal of Physical Oceanography 50, 5; 10.1175/JPO-D-19-0103.1
Simple frequency spectra are the average over all wavenumbers. Can motions at wavelengths other than those of the NIW can mask them? Velocity spectra are dominated by low tidal modes, which have large vertical scales in this region. To better emphasize NI motions whose vertical wavenumber spectra are often bluer than those of ITs (Alford 2010; Alford et al. 2016), we examine the shear spectra (Fig. 8). The shear signal demonstrates the presence of NI oscillations at depth > 500 m at almost all locations except MPS, where NI oscillations are present above 500 m. It also confirms their absence near the surface at all other locations.
2) Vertical wavenumber–frequency spectra
A more sophisticated way of proceeding is vertical wavenumber–frequency spectra. These spectra in an Eulerian frame highlight the contrast with station Papa where the shear signal is almost exclusively contained in the NI and tidal frequency bands. There, NIWs are Doppler shifted by lateral motions of the tides or the internal wave continuum shaping the distribution of shear as an hourglass in the kz–σ space. In the LS, this diagnostic shows a high shear level at all frequencies and wavenumber compared to station Papa. The tidal (diurnal and semidiurnal) signal is confined at low wavenumbers at all locations (Fig. 9) and sparse NI peaks at MPS, N1, RN, and RS. At MPS and N1, the NI shear signal is propagating downward and is confined around −4 × 10−3 cpm (~250 m). The moorings on the south China continental slope (RN, RS) show NIWs propagating both upward and downward, but their energy is shifted to higher frequencies. Some locations (S6, S9, N2) show slightly increased shear signal at f ± D1 or f ± D2. These small peaks are the signature of the isopycnal heaving by the internal tides, as described above. We cannot project the N2 and S6 velocities onto a sL frame, but the presence of these peaks suggests that a frequency shift similar to the one observed at S9 (Fig. 6) occurs at these locations.
Vertical wavenumber–frequency rotary spectrum of the shear at each locations and station Papa. The solid magenta lines show the inertial frequency. The dot–dashed magenta lines show f ± D1 and f ± D2. The dashed black lines represent the tidal frequencies D1 and D2. The near-inertial energy propagating downward corresponds to the negative wavenumbers and negative frequencies.
Citation: Journal of Physical Oceanography 50, 5; 10.1175/JPO-D-19-0103.1
In the following section, we show that results obtained from the same diagnostics but within different vertical coordinate systems can significantly differ. Contrary to the Eulerian ones, vertical wavenumber–frequency spectra of shear computed in a sL frame exhibit a clear NI peak, allowing us to investigate the temporal variability of the NIW frequency shift.
c. Time dependency of the NIW frequency shift
The time series of shear computed from the sL velocities at S9 (Fig. 10) is broken into three segments (A, B, C) to describe how the presence of mesoscale structure can impact the NIW field. Segments A and C bracket a subsurface eddy inducing southward flow from (approximately) 500–900 m (segment B), in an otherwise mostly northward-flowing environment.
(top) Meridional velocities and (middle) shear at S9 over the whole water column. (bottom) Low-pass-filtered (2 days) meridional velocities. The record is divided into three segments A, B, and C described in section 4c.
Citation: Journal of Physical Oceanography 50, 5; 10.1175/JPO-D-19-0103.1
The vertical wavenumber–frequency distribution of the shear during segment A shows a strong anticlockwise rotation signal centered around f when the energy is propagating upward with positive wavenumbers (Fig. 11). The fraction of the signal propagating downward (negative wavenumbers) is slightly shifted at lower frequencies and is spread around f. The bulk of the shear is located in the semidiurnal and diurnal tidal bands at low wavenumbers (|kz| < 0.005 cpm) while most of the signal around f is localized at smaller scales. Segment B presents a different shear distribution, as the diurnal and semidiurnal tides are weak compared to the subinertial signal (Fig. 11). This strong low frequency signal is associated with the presence of a mesoscale eddy. A clear signal around f and kz ± 0.015 cpm is shifted at lower frequencies with higher |kz|. During segment C, the upward and downward propagating signal near f occurs at higher wavenumber than the tidal signal and slightly higher frequencies than f.
Vertical wavenumber–frequency rotary spectra of the semi-Lagrangian shear for segments A, B, and C (see Fig. 10) of mooring S9. Spectra are calculated using data between 700 and 1000 m. The solid (dashed) black line shows the inertial (diurnal) frequency.
Citation: Journal of Physical Oceanography 50, 5; 10.1175/JPO-D-19-0103.1
The three periods presented in Fig. 11 show different behavior. The signal propagating upward in segments A and C is stronger than the one propagating downward. We can see an illustration of this strong upward propagating signal on Fig. 10 around yearday 210 in the middle of the water column where shear layers with downward propagating phase are moving toward the surface. Depending on the vertical direction of the propagating shear signal and the background environment (strong tide or presence of mesoscale), the shear signal is centered around f or exhibits a blue or red frequency shift. Furthermore, the frequency shift of the downward and upward propagating shear signal can be different during the same period. This suggests that the dynamics in the upper part (above 700 m) of the water column (Kuroshio and eddies) impact the waves generated at the surface differently than the ones propagating upward.
5. Discussion
a. Variation of the relative vorticity forced by the Kuroshio
As shown, the strong variability of the Kuroshio can impact the results of time-averaged diagnostics (e.g., KE or shear spectra over the full record). Indeed, changes in the intensity or path of the Kuroshio, or its associated eddies, can shift and spread the NIWs intrinsic frequency (Kunze 1985). As previously described, the southern line of moorings is located south of the Kuroshio in an area where eddies are generated west of the Philippines archipelago. The northern line of moorings is situated on the path of the Kuroshio branch, which oscillates with time. Both lines experience strong variations in current and vorticity intensity. Using both model and observations, estimates of relative vorticity variability (Fig. 12) show that the effective inertial frequency can vary ~0.2 cpd or more over a few days. This is about the same order of magnitude as the frequency shift observed at S9 between segments B and C. We do not expect correlation since we are comparing our observations to the relative vorticity computed from a model or the relative vorticity estimated with only the spatial variations of the meridional velocities.
Time evolution of feff using ξ = (1/2)(∂V/∂x) estimated from S9 at 150-m depth. The maximum feff variations reach about −0.2 cpd in the few days. The solid black line at 0.66 cpd is the inertial frequency.
Citation: Journal of Physical Oceanography 50, 5; 10.1175/JPO-D-19-0103.1
b. Frequency shift due to horizontal subinertial motion
Our study presents the frequency transfer of the NIWs signal at higher frequency induced by the vertical heaving of isopycnal layers in the South China Sea. The spectral level of shear at high frequencies (>f) decreases by an order of magnitude when using sL velocities instead of Eulerian velocities (Fig. 6). This projection corrects for Doppler shifts only associated with vertical velocities. The impact of horizontal velocities on the frequency distribution of shear or KE remains an open question, but, if present, it should also spread the signal in frequency (Pinkel 2008a) at high wavenumbers. We cannot investigate this issue more thoroughly as the vertical resolution of S9 is too coarse. However, we can estimate the Doppler frequency shifts due to horizontal motions using the subinertial current at S9 (Fig. 10). The change in frequency associated with the Doppler effect is Δf = kVsub where Vsub is the subinertial current, and k is the NIW wavenumber. Assuming a 100-km horizontal wavelength and horizontal subinertial currents Vsub = 0.2 m s−1, the frequency changes associated with the Doppler effect are Δf = 0.17 cpd. This Doppler shift is similar to the Δf ~ 0.2 cpd observed at S9.
c. Near-inertial wave direction propagation
At S9, the downward energy flux of NIW in a sL frame is comparable to the near-inertial energy input by winds observed for the period but we also show periods with strong upward shear and, depending on the direction propagation, a shear signal centered around different frequencies, participating in the frequency spread of the NI peak (Fig. 11). The upward propagating signal is stronger than the downward one suggesting that NIWs propagating upward are not the reflection at the bottom of NIWs generated at the surface.
The increase of shear activity near the bottom (Fig. 10) suggests intense internal wave activity arising from the interaction between topography and the local currents (subinertial and tidal). Geostrophic flows impinging on topography are known to generate waves (Nikurashin and Ferrari 2010; St. Laurent et al. 2011; Naveira Garabato et al. 2013; Cusack et al. 2017). These waves can radiate upward and contribute to the high level of the upward propagating signal observed at shallower depths. Also, strong tidal flows over supercritical topography can induce wave breaking, thus generating NIWs (Chen et al. 2019). In the South China Sea, NI energy contributed by tidal forcing can be of comparable magnitude as that contributed by the summer wind, providing a possible explanation for the presence of these upward propagating signals.
6. Summary
In this paper, we use moored observations collected in the Luzon Strait during the IWISE experiment in summer 2011 to help account for the apparent absence of a prominent inertial peak in frequency spectra. The Luzon Strait is a pathway of one of the Kuroshio branches, and two meridional ridges generate powerful resonant internal tides (Echeverri and Peacock 2010; Alford et al. 2011). Velocity observations show strong tidal signals and continuum KE levels ~15 times greater than the canonical GM76 level (Pickering et al. 2015). Yet, there is no significant near-inertial peak for 8 of the 10 moorings used in this study, despite sufficient wind stress (Fig. 4), prompting questions on what mechanisms might account for its absence. Our results show that vertical heaving by the strong internal tides in the Luzon Strait can Doppler shift NIW to frequencies higher than f in Eulerian spectra, as in Alford (2001). This effect is partly corrected by using a semi-Lagrangian or isopycnal-following frame. Spectra of these sL velocities show restored kinetic energy centered around f. However, since most variability is located at low vertical wavenumbers, the presence of a near-inertial peak only emerges after computing vertical wavenumber–frequency distribution of shear. Using these diagnostics, we show the frequency shifts of NIWs over periods of only a few days. These rapid and frequent shifts in frequency, which we hypothesize as due to Kuroshio-induced mesoscale variability, smooth the NI peak in frequency spectra computed over a long period (~30 days). Consequently, an environment with strong tide and mesoscale energy fundamentally alters the appearance of NIWs in Eulerian spectra by dynamics of NIWs by disturbing the expected structure of the superposed shear layers. In these conditions, these waves lose their coherence, making these ubiquitous oscillations harder to track and study.
Acknowledgments
This work was supported by ONR Grant N00014-09-1-0219. We thank the Captain and crew of the RVs Revelle and ORI, and the U.S. and Taiwanese mooring technicians for their hard work and skill in preparing, deploying, and recovering the moorings. We thank Dr. Steven Ramp for providing the data of the RN and RS moorings, and Anna Savage and John Mickett for the fruitful discussions.
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