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  • View in gallery

    (a) Tasmania, Australia, with our study area (red square), the shelf break (dashed blue line), the ship location (shaded region), and Larapuna Bureau of Meteorology wind station (red plus) indicated. (b) Mooring positions (red crosses) with local bathymetry and the full-depth (black arrow), near-surface (blue arrow), and near-seabed (purple arrow) mean mesoscale current at three mooring sites. At the remaining moorings with working ADCPs, we show the standard deviation of the near-inertial (NI) velocity at the near-surface (blue ellipse) and seabed (purple ellipse). (c) Mean temperature at all shelf moorings.

  • View in gallery

    The (a)–(c) effective Coriolis frequency feff [Eq. (3)] describing the relative vorticity and the (d)–(f) minimum wave frequency ωmin [Eq. (1)] describing the combined influence of relative vorticity and baroclinicity, both scaled by the Coriolis frequency f. We averaged quantities over yearday (a),(d) 38–46, (b),(e) 46–51, and (c),(f) 51–56. We contoured the 40-h low-pass-filtered and averaged (top) alongshore velocity (m s−1) and (bottom) temperature (°C) in black.

  • View in gallery

    The (a) ship-observed wind stress, (b) surface elevation from W21 at tidal frequencies (including 17 constituents), (c) depth-integrated mesoscale currents at W21, and temperature at (d) W21 and (e) M29. We highlight the isotherms corresponding to the SML depth using gray lines, corresponding to the 18.2°C isotherm at W21 and 18.7°C isotherm at M29, although we use the 40-h low-pass-filtered temperature to define the SML thickness. We show NIW events (A–D) in (a) and thermistor locations on M29 by a black marker in (e).

  • View in gallery

    The (left) cross- and (right) alongshore NI velocity observed on yearday 44–50 for moorings M17–M32, from top to bottom, partially including events B and C. We contoured the mesoscale temperature in gray with 1°C separation and the SML thickness in dark blue, which increased from the 18.1°C isotherm at M17 to the 18.7°C isotherm at M29 and M32.

  • View in gallery

    The average (a) feff/f and (b) ωmin/f frequency over day 42–45 (event B), with 36-m depth (dash–dotted) and the mesoscale 16°C contour (solid) indicated in black. The alongshore NI velocity (c) within the SML at 36-m depth, and (d) along the 16°C isotherm for all moorings.

  • View in gallery

    The ship-observed wind stress vs the total velocity at W21 at (a),(c) 85- and (b),(d) 23-m depth via variance preserving cross spectra over anticyclonic (counterclockwise) frequencies in (a) and (b), and signal coherence (left y axis) and phase lags for frequencies with statistically significant coherence (right y axis) in (c) and (d). The total velocity at W21 vs M29 for velocities (e),(g) along the 16°C isotherm and (f),(h) at approximately 21-m depth. Horizontal dashed lines show the 95% significance, vertical dashed lines mark the diurnal (D1) and inertial and semidiurnal (D2) frequencies from left to right, and the gray band indicates the NI range that we bandpass filter. Positive phase indicates the wind leads the velocities in (c) and (d), and W21 leads M29 in (g) and (h).

  • View in gallery

    (top) The ship-observed wind stress, with wind stresses that exceeded 0.1 N m−2 (orange line) and periods when the wind direction varied by more than 45° in a half day (red line) indicated. The remaining paired panels represent individual yeardays, with the median feff (solid) and ωmin (dashed) over the observed SML thickness in the upper panels, and the maximum NI horizontal kinetic energy (HKE; J m−3) within an inertial period centered around midnight on each yearday, and at each depth and mooring, in the lower panels. Note this is the maximum over an inertial period for each depth and mooring and is not a snapshot in time. The low-passed and averaged temperature was contoured in black, with 1°C contours, and the SML thickness is plotted in cyan. The NIW event is noted after the day in the relevant figures.

  • View in gallery

    The (a) depth-averaged ωmin/f and (b) NI energy flux (W m−1) of the total uNI and ρNI. As NI perturbations of the free surface were less than the reported accuracy of our bottom-mounted pressure sensors, ρNI is due to isopycnal perturbations only. We scaled down the fluxes at M29 by 50% and M32 by 75%.

  • View in gallery

    NI alongshore velocity observed on yearday 49–55 (events C and D) at (a) W21, (b) M25, and (c) M29. We contour mesoscale temperature with 1°C separation (gray) and the SML thickness (dark blue). Note we have increased the velocity limits to 0.15 m s−1, where the maximum velocity in Fig. 4 was 0.12 m s−1.

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Generation and Propagation of Near-Inertial Waves in a Baroclinic Current on the Tasmanian Shelf

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  • 1 Oceans Graduate School and the Ocean Institute, University of Western Australia, Crawley, Western Australia, Australia
  • | 2 Institut des Sciences de la Mer, Université du Québec à Rimouski, Rimouski, Quebec, Canada
  • | 3 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
  • | 4 Oceans Graduate School and the Ocean Institute, University of Western Australia, Crawley, Western Australia, Australia
  • | 5 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
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Abstract

Near-inertial waves (NIWs) are often an energetic component of the internal wave field on windy continental shelves. The effect of baroclinic geostrophic currents, which introduce both relative vorticity and baroclinicity, on NIWs is not well understood. Relative vorticity affects the resonant frequency feff, while both relative vorticity and baroclinicity modify the minimum wave frequency of freely propagating waves ωmin. On a windy and narrow shelf, we observed wind-forced oscillations that generated NIWs where feff was less than the Coriolis frequency f. If everywhere feff > f then NIWs were generated where ωmin < f and feff was smallest. The background current not only affected the location of generation, but also the NIWs’ propagation direction. The estimated NIW energy fluxes show that NIWs propagated predominantly toward the equator because ωmin > f on the continental slope for the entire sample period. In addition to being laterally trapped on the shelf, we observed vertically trapped and intensified NIWs that had a frequency ω within the anomalously low-frequency band (i.e., ωmin < ω < feff), which only exists if the baroclinicity is nonzero. We observed two periods when ωmin < f on the shelf, but the relative vorticity was positive (i.e., feff > f) for one of these periods. The process of NIW propagation remained consistent with the local ωmin, and not feff, emphasizing the importance of baroclinicity on the NIW dynamics. We conclude that windy shelves with baroclinic background currents are likely to have energetic NIWs, but the current and seabed will adjust the spatial distribution and energetics of these NIWs.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Tamara Schlosser, tamaralschlosser@gmail.com

Abstract

Near-inertial waves (NIWs) are often an energetic component of the internal wave field on windy continental shelves. The effect of baroclinic geostrophic currents, which introduce both relative vorticity and baroclinicity, on NIWs is not well understood. Relative vorticity affects the resonant frequency feff, while both relative vorticity and baroclinicity modify the minimum wave frequency of freely propagating waves ωmin. On a windy and narrow shelf, we observed wind-forced oscillations that generated NIWs where feff was less than the Coriolis frequency f. If everywhere feff > f then NIWs were generated where ωmin < f and feff was smallest. The background current not only affected the location of generation, but also the NIWs’ propagation direction. The estimated NIW energy fluxes show that NIWs propagated predominantly toward the equator because ωmin > f on the continental slope for the entire sample period. In addition to being laterally trapped on the shelf, we observed vertically trapped and intensified NIWs that had a frequency ω within the anomalously low-frequency band (i.e., ωmin < ω < feff), which only exists if the baroclinicity is nonzero. We observed two periods when ωmin < f on the shelf, but the relative vorticity was positive (i.e., feff > f) for one of these periods. The process of NIW propagation remained consistent with the local ωmin, and not feff, emphasizing the importance of baroclinicity on the NIW dynamics. We conclude that windy shelves with baroclinic background currents are likely to have energetic NIWs, but the current and seabed will adjust the spatial distribution and energetics of these NIWs.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Tamara Schlosser, tamaralschlosser@gmail.com

1. Introduction

Near-inertial waves (NIWs) are a common component of the ocean’s internal wave field and can be the most energetic waves within the internal wave frequency band (e.g., Alford et al. 2016). On windy continental shelves, NIWs can generate large vertical shears in the horizontal velocity that can dissipate energy (MacKinnon and Gregg 2005; van der Lee and Umlauf 2011) and can cause mixing, which may enhance biological production (e.g., Lucas et al. 2014). NIW generation depends on the wind forcing, the relative background vorticity, and the background baroclinicity. As highlighted in the review of Alford et al. (2016), limited studies investigate the influence of relative vorticity on the generation of NIWs (e.g., Whitt and Thomas 2015; Tort and Winters 2018), while the influence of baroclinicity on generating NIWs is poorly understood. The few studies that consider NIW generation on the continental shelf have demonstrated the need to consider vorticity when establishing where NIWs generate and their energetics (e.g., Lerczak et al. 2001; Davies and Xing 2005). The role of vorticity and baroclinicity on NIW propagation has received greater attention (Mooers 1975; Kunze 1985; Whitt and Thomas 2013), but again few studies have investigated these dynamics over the continental shelf where the shallow [O(100) m] seabed influences the waves’ propagation (Federiuk and Allen 1996) and energetics (MacKinnon and Gregg 2005; Rayson et al. 2015).

Here we investigate NIW dynamics on a windy and narrow shelf in the presence of a fast-flowing baroclinic background current. Both the relative vorticity and baroclinicity associated with this current influenced the NIW dynamics, and we assess the importance of each process in modifying the NIW dynamics. We review the processes of NIW generation from wind-forced oscillations (WFOs), and NIW propagation, including the current understanding of the influence of relative vorticity and baroclinicity in section 2. Using moored observations (described in section 3) collected on the Tasmanian Eastern Continental Shelf (TECS), we explore the NIW dynamics in the presence of the East Australian Current Extension (EACE). This current is surface intensified and is sheared in both the horizontal and vertical directions, causing nonzero relative vorticity and baroclinicity, respectively (Oliver et al. 2016). We present observations of near-inertial (NI) motion that we associate with both WFOs and NIWs in section 4. We consider the processes that affect NIW generation (section 4) and propagation (section 5), and find that the local relative vorticity and baroclinicity influence all aspects of the NIW life cycle. We present our conclusions in section 6.

2. Relevant theory

Wind transfers energy to the surface mixed layer (SML) via WFOs, which can generate NIWs. Other mechanisms can also generate NIWs (see Alford et al. 2016), but we consider here only those due to time-varying winds because, as we show below, this process dominates NIW generation on the TECS.

a. Wind-forced oscillations

Wind stresses with frequencies near the Coriolis frequency f can force resonant near-inertial WFOs within the SML (Alford et al. 2016). The introduction of horizontal and/or vertical shear from the background geostrophic flow shifts the minimum wave frequency of freely propagating waves to ωmin,
ωmin=f1+RogRig1,
where we define the Rossby number Rog = ζ/f, the relative vorticity ζ = (∂υg/∂x) + (∂ug/∂y), and the geostrophic velocity in the cross-shore x and alongshore y directions as ug and υg, respectively (Whitt and Thomas 2013). The gradient Richardson number Rig depends on the vertical shear in the background geostrophic current via
Rig=Ng2||ug/z||2,
where Ng is the buoyancy frequency of the geostrophic flow and z is the vertical direction. Whitt and Thomas (2013) define a strongly baroclinic flow as having an Rig of O(1).
In the barotropic limit where ug/z=0 and Rig10, Eq. (1) simplifies to
feff=f1+Rog=f(f+ζ),
where the minimum frequency is the effective local Coriolis frequency feff, which demonstrates the dependence on the relative vorticity (Mooers 1975; Kunze 1985; Whitt and Thomas 2013). Thus, depending on the sign of ζ, the relative vorticity of the mean flow [Eq. (3)] can raise or lower the effective frequency of NI motion. WFOs are then generated over a broad frequency range near feff (Weller 1982). Defining the divergence D = (∂ug/∂x) + (∂υg/∂y), Weller (1982) demonstrated that in divergent (convergent) regions where D < 0 (D > 0), the circular orbits of WFOs will increase (decrease), and so to conserve momentum, WFOs can be amplified (dampened). Oscillations can also exchange energy with a horizontally nondivergent geostrophic background flow, extracting energy when winds have variable directions but equal magnitude in all directions (i.e., isotropic; Whitt and Thomas 2015). A flow with varying relative vorticity, such as eddy currents, will thereby vary the WFO’s frequency and amplitude, with some energy exchanges between the WFOs and the geostophic flow.

In the general case, when both barotropic and baroclinic effects are important (i.e., Rog > 0 and Rig1>0), Eq. (1) cannot be simplified to Eq. (3) (Mooers 1975; Kunze 1985; Whitt and Thomas 2013). Although baroclinicity influences the minimum wave frequency, the effect of rotation has much larger length scales than the stratification, and hence the resonant frequency is feff for typical oceanic conditions (Whitt and Thomas 2015). The relative influence of stratification and rotation is determined by the Burger number, Bu = NgzSML/fLWFO, where zSML is the SML thickness at O(10) m, LWFO is the length scale of the WFO with a typical value of O(105) m, and hence Bu ≪ 1. For such small Bu, the effect of rotation dominates over stratification, and so WFOs are generated with a frequency near feff, independent of ωmin.

b. Near-inertial wave generation

If WFOs are generated by steady winds, WFOs apply a consistent lateral pressure gradient to the base of the SML, and energy slowly leaves the SML (Pollard 1970). However, a moving storm or a time-varying wind causes the forced oscillations to apply an unsteady pressure gradient at the base of the SML, which can then generate baroclinic NIWs. These NIWs then rapidly propagate downward, leading to the transfer of energy from the SML to the rest of the water column (Pollard 1970). At the coastline, the cross-shore flow induced by WFOs is brought to rest, resulting in a pressure gradient and the generation of both barotropic and baroclinic NIWs (Pettigrew 1981; Shearman 2005). This is one of the few mechanisms that generate barotropic NIWs.

In a barotropic background current where Rig10, NIWs are generated at a modified frequency near feff for large regions of relative vorticity (Tort and Winters 2018). However, when the region of relative vorticity is small compared to the spatial scale of the wind field, the NIW frequency will shift to some value between the local and ambient feff, with a frequency closer to the ambient feff when the length scale associated with the vorticity field is exceeded by the length scale associated with wind field (Tort and Winters 2018). It is likely that the WFO frequency equally depends on the relative spatial scales of feff and the wind field, although this was not considered by Tort and Winters (2018).

On the continental shelf with a barotropic background current, numerous studies have shown NIWs are preferentially generated at regions of nonzero relative vorticity, rather than at the coastline where a lateral pressure gradient always exists (e.g., Lerczak et al. 2001; Chant 2001). Generation is enhanced in regions of negative vorticity where feff < f (Lerczak et al. 2001).

To our knowledge, no studies have explored NIW generation in the baroclinic limit of Eq. (1), where Rig10. We expect NIWs to be generated at a frequency near feff, but the relative magnitude of the spatial scales of forcing and ambient flow fields will likely influence the generated wave frequency ω.

c. Near-inertial wave propagation

Once NIWs have been generated, they will propagate in regions where their frequency ω remains either super (ω > ωmin) or near-inertial (ωωmin). With no horizontally or vertically sheared background flow (Rog = 0 and Rig10), ωmin = f and as f increases toward the poles, NIWs preferentially propagate equatorward (Alford 2003). In the barotropic limit, when ωmin = feff, NIWs can be laterally trapped in regions of local negative vorticity where feff < f (Kunze 1985). This can create the “chimney effect”, where NIWs rapidly propagate downward within a trapped region as they continuously reflect between locations where ω = feff until they dissipate (Lee and Niiler 1998).

In the baroclinic limit, NIWs can also be vertically trapped because ωmin can vary with depth via Rig(z, t) [Eq. (2)]. In regions where ωωmin, either 1) the NIW will be reflected, or 2) the group velocity of the NIW will reduce to zero causing the NIW to be trapped along the isopycnal where ω = ωmin (Whitt and Thomas 2013). Due to the influence of baroclinicity, NIWs may have a frequency within the anomalously low frequency band where ωmin < ω < feff (Mooers 1975). In this region, NIWs are amplified, and their propagation behavior is highly modified by baroclinicity (Whitt and Thomas 2013).

On the continental shelf, the seabed friction will further modify the propagation and dissipation of NIWs (Federiuk and Allen 1996; MacKinnon and Gregg 2005; Rayson et al. 2015). Compared with the open ocean, friction can rapidly dissipate NIWs on the shelf (Rayson et al. 2015), and may also energize certain wave modes (MacKinnon and Gregg 2005). The evolution of internal waves in shallow water depends on the ratio of the bottom slope β to the characteristic slope α=(ω2f2)/(N2ω2) of the wave (Baines 1982). However, nonnegligible relative vorticity and baroclinicity will modify the angle of reflection and wave intensification at near-critical topography (Federiuk and Allen 1996; Whitt and Thomas 2013).

3. Methodology

a. Study site and experiment

In February 2015, we collected moored and ship-based observations along a cross-shelf transect on the continental shelf. The TECS at the study site is 28 km wide (Fig. 1). In austral summer months, the EACE transports warm and salty water southward beyond the site down to a latitude of approximately 42°S (Ridgway 2007). From 2010 to 2015, a nearby wind station (Fig. 1a, red cross) measured velocities oriented predominantly in the alongshore direction. The estimated wind stress (speed) in summer months were of 50th and 95th percentile magnitudes of 0.052 N m−2 (5.5 m s−1) and 0.23 N m−2 (11.6 m s−1), respectively.

Fig. 1.
Fig. 1.

(a) Tasmania, Australia, with our study area (red square), the shelf break (dashed blue line), the ship location (shaded region), and Larapuna Bureau of Meteorology wind station (red plus) indicated. (b) Mooring positions (red crosses) with local bathymetry and the full-depth (black arrow), near-surface (blue arrow), and near-seabed (purple arrow) mean mesoscale current at three mooring sites. At the remaining moorings with working ADCPs, we show the standard deviation of the near-inertial (NI) velocity at the near-surface (blue ellipse) and seabed (purple ellipse). (c) Mean temperature at all shelf moorings.

Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0208.1

We deployed five moorings on the TECS from 5 to 24 February 2015, while a sixth mooring, deployed for a longer period, provided concurrent observations on the continental slope (Table 1). Of these six moorings, four consisted of traditional moorings and two were autonomous profilers (Wirewalkers; Pinkel et al. 2011) with bottom-mounted acoustic Doppler current profilers (ADCPs; Teledyne RDInstruments) deployed within ~300 m of the profilers. Our naming convention includes a letter to designate the type of mooring (M for traditional mooring or W for profiler) and a number to designate its distance from the shoreline in kilometers. The continental slope mooring T4, denoted herein as M32, was deployed at 478-m depth as part of the Tasman Tidal Dissipation Experiment (T-TIDE; Pinkel et al. 2015). In summary, we present high-resolution velocity and temperature measurements from four distinct moorings across the shelf and a fifth mooring on the continental slope; due to the ADCP failing at W10, only temperature measurements are presented from this shelf profiler.

Table 1.

The mooring specifications for the five moorings deployed along a cross-shelf transect on the TECS. Our naming convention includes a letter to indicate the type of mooring (M for traditional, W for profile), and a number indicating the distance from shore in kilometers. One mooring deployed on the slope was provided through collaboration with T-TIDE, but for consistency we renamed it M32 (Pinkel et al. 2015). All ADCPs were upward-looking unless otherwise indicated. Thermistor letters: a = Seabird 39, b = Seabird 56, c = Seabird 37, d = Seabird 39 with pressure sensor, e = RBR Concerto, f = RBR Solo; ASB = above sea bed.

Table 1.

Further information on the site, including the velocity at diurnal and semidiurnal frequencies, can be found in Schlosser et al. (2019). Here we focus on the energetic NI band, where Schlosser et al. (2019) focused on the diurnal coastal-trapped waves that were subinertial (i.e., ω < ωmin) over the entire field campaign.

b. Data analysis

1) Horizontal and vertical shear

To estimate the minimum wave frequency ωmin [Eq. (1)], we estimated the geostrophic currents and density by first isolating the mesoscale variations with a PL66 filter (40-h cutoff; Alessi et al. 1985), which we denote with the subscript “meso.” We then applied a 3-day moving average in time, and a 4-m moving average over depth to compute the geostrophic quantities, denoted with a subscript g. We considered the vector quantity ug, with velocity components directed in the cross-shore ug, alongshore υg, and vertical wg directions, with corresponding cross-shelf x, along-shelf y, and vertical z directions. The modeling of Oliver et al. (2016) demonstrated that the alongshore gradients in ug are typically small. We thus assumed ∂ug/∂y ≈ 0.

2) NIW variability

The NIW frequency depends on the local latitude and the resonant frequency feff. NIWs hence typically have frequencies within ±20% of f, although in some regions they can exist over an even larger frequency range. To describe NI variations, we bandpass filtered our signals with a fourth-order Butterworth filter with cutoffs at 14.1 and 22.1 h (i.e., within ±22% of f) since the inertial period is 18.1 h. The frequencies in this bandwidth are denoted with a subscript “NI.” We quantified the variation in cross-shelf NI energy by estimating the horizontal kinetic energy (J m−3) as HKE(z,t)=1/2[ρmeso(z,t)||uNI(z,t)||2], where uNI is the horizontal NI velocity and indicates the magnitude of the vector. We then estimated the NI energy flux via
EF(t)=H0uNI(z,t)pNI(z,t)dz,
where we related the NI density perturbation ρNI(z, t) to the pressure perturbation via pNI(z,t)=gz0ρNI(z,t)dz for z ≥ − H, where g is gravity, and we integrated from each depth z between the total water depth H and the surface, to the surface. Here the vertical axis is zero at the sea surface with negative values below it. The observed NI perturbations of the free surface ηNI were less than the reported accuracy of our pressure sensors so we assumed ηNI = 0. Our estimated NI energy flux hence includes uNI and ρNI from isopycnal displacements from the barotropic NIW, baroclinic NIWs, and WFOs.

To determine the NIW properties, we performed modal decomposition with the dynamic vertical modes (Gill 1982). We compared the observed wave properties, such as the vertical phase difference, to the theoretical dynamic modes expected with ∂υg/∂z = 0. We did not decompose the barotropic and baroclinic uNI and ρNI dynamic modes because they are not orthogonal in the presence of geostrophic vertical shear (Mooers 1975). Instead, we present the total NI perturbations including both the barotropic and baroclinic components.

3) Surface mixed layer thickness

We assessed a number of methods to define the SML thickness, including using the maximum temperature difference between the shallowest and deepest observed temperature (e.g., MacKinnon and Gregg 2005), finding the depth where the vertical shear in the surface-intensified NI motion exceeded a certain threshold, and following an individual isotherm. We visually compared the resulting predicted SML thickness to the vertical range where NI motion was surface intensified and found we best estimated the depth region where WFOs existed when the base of the SML was defined using an individual isotherm depth. Surface temperatures increased away from the coast, so we used slightly different isotherms to define the SML base across the shelf (Fig. 1c). At M17, we used the depth of the 18.1°C isotherm to define the base of the SML, while at M29 we used a warmer isotherm of 18.7°C. At M32, the temperature was not measured shallower than 52 m, but in the upper 100 m the temperatures at M32 and M29 were comparable. We thus assigned the same SML thickness for these two moorings (Fig. 1c).

4) Cross spectra of wind stress and velocity

In the Southern Hemisphere, pure-inertial waves rotate counterclockwise or anticyclonically, and are preferentially generated by anticyclonic winds (Pollard 1970). We isolated the anticyclonic NI energy via rotary cross spectra at frequencies ω > 0. To determine the generation location and characteristics of the observed NI velocity, we used cross spectra between the ship-observed wind stress and the observed velocity at one mooring, as well as between the velocity observed at two different moorings. We computed the wind stress (N m−2) as τw=CDρAV(t)||V(t)||, where V(t) is the ship-measured wind velocity, CD is the drag coefficient, estimated as 1.4 × 10−3 (Smith 1988), and ρA is the air density estimated as 1.2 kg m−3. To improve the frequency resolution around f, we applied a sine-multitaper window in the time domain with seven Slepian tapers (Alford and Whitmont 2007). To compute cross spectra we used the jLab software package (Lilly 2017).

4. Wave properties

a. Background conditions

Over our 18-day sample period, a strong background current flowed south on the TECS, while the thermocline shallowed toward the coast (Fig. 1). The southward, alongshore current was always strongest near the surface. During the first 13 days (before yearday 51), the surface current increased in magnitude with distance offshore between M17 and M29, generally resulting in feff > f on the outer shelf (from M17 to M25, Figs. 2a,b). During the remaining 5 days, the surface current was the strongest onshore, resulting in feff < f on the outer shelf (Fig. 2c). Across the shelf, the isotherms deepened with increasing distance offshore (Figs. 2d–f, black contour), corresponding to a southward flowing current in geostrophic balance. The 40-h low-pass-filtered (i.e., mesoscale) temperature varied in time, leading to changes in the strength and depth of the thermocline, and the thickness of the SML (Figs. 2d–f). The thermocline coincided approximately with the 16°C isotherm and was separated from the SML by an intermediate layer of stratification. As ug/z>0, ωmin < feff [Eqs. (1) and (3)] for the entire sample period and at all depths (Fig. 2). In particular, before day 51 we observed regions where ωmin < f < feff, while afterward, feff and ωmin were both less than f and of similar magnitude on the shelf.

Fig. 2.
Fig. 2.

The (a)–(c) effective Coriolis frequency feff [Eq. (3)] describing the relative vorticity and the (d)–(f) minimum wave frequency ωmin [Eq. (1)] describing the combined influence of relative vorticity and baroclinicity, both scaled by the Coriolis frequency f. We averaged quantities over yearday (a),(d) 38–46, (b),(e) 46–51, and (c),(f) 51–56. We contoured the 40-h low-pass-filtered and averaged (top) alongshore velocity (m s−1) and (bottom) temperature (°C) in black.

Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0208.1

Winds were generally sporadic, lasting <1 day in the same direction, which is ideal for generating NI motions (Fig. 3a). On day 42.7 a strong wind stress (speed) of 0.34 N m−2 (14.3 m s−1) deepened the 18°C isotherm by 66 m at M29 (Figs. 3a,e). After this deepening, winds weakened in magnitude and persisted to the west till day 46, resulting in a shallowing of the SML.

Fig. 3.
Fig. 3.

The (a) ship-observed wind stress, (b) surface elevation from W21 at tidal frequencies (including 17 constituents), (c) depth-integrated mesoscale currents at W21, and temperature at (d) W21 and (e) M29. We highlight the isotherms corresponding to the SML depth using gray lines, corresponding to the 18.2°C isotherm at W21 and 18.7°C isotherm at M29, although we use the 40-h low-pass-filtered temperature to define the SML thickness. We show NIW events (A–D) in (a) and thermistor locations on M29 by a black marker in (e).

Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0208.1

b. Wind-forced oscillations

The NI velocity and horizontal kinetic energy (HKE) were often intensified within the SML and near the thermocline at one or more moorings (Fig. 4). After the strong winds on day 42, the near-surface velocity increased at all moorings, but strengthened more significantly at M25, before the near-surface velocity weakened across the shelf on day 44 (Figs. 4 and 5c). At moorings M17 to M29, the near-surface velocity remained small, and did not exceed 0.1 m s−1 until day 48 (Fig. 4), following the anticyclonic wind on day 47. Near-surface NI velocities decreased and the SML thickness increased with distance offshore (Fig. 4).

Fig. 4.
Fig. 4.

The (left) cross- and (right) alongshore NI velocity observed on yearday 44–50 for moorings M17–M32, from top to bottom, partially including events B and C. We contoured the mesoscale temperature in gray with 1°C separation and the SML thickness in dark blue, which increased from the 18.1°C isotherm at M17 to the 18.7°C isotherm at M29 and M32.

Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0208.1

Fig. 5.
Fig. 5.

The average (a) feff/f and (b) ωmin/f frequency over day 42–45 (event B), with 36-m depth (dash–dotted) and the mesoscale 16°C contour (solid) indicated in black. The alongshore NI velocity (c) within the SML at 36-m depth, and (d) along the 16°C isotherm for all moorings.

Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0208.1

According to a rotary cross-spectral analysis, the wind stress was coherent with the near-surface velocity at W21 over the NI frequency band in the anticyclonic direction (Figs. 6a,b, shaded region). The near-surface velocity lagged winds by an average of 33.5° or 1.7 h. The time tL for the wind stress to diffuse throughout the SML depends on the velocity shear stress u*, and the SML thickness h, via tL~O(h/u*) (e.g., Spigel and Imberger 1980). For typical u* of O(10−2) m s−1 (Spigel and Imberger 1980), and observed h of O(10–100) m, we expect tL of O(10–60) min. The observed phase lag of 1.7 h was therefore consistent with the time taken for the wind to energize the entire SML.

Fig. 6.
Fig. 6.

The ship-observed wind stress vs the total velocity at W21 at (a),(c) 85- and (b),(d) 23-m depth via variance preserving cross spectra over anticyclonic (counterclockwise) frequencies in (a) and (b), and signal coherence (left y axis) and phase lags for frequencies with statistically significant coherence (right y axis) in (c) and (d). The total velocity at W21 vs M29 for velocities (e),(g) along the 16°C isotherm and (f),(h) at approximately 21-m depth. Horizontal dashed lines show the 95% significance, vertical dashed lines mark the diurnal (D1) and inertial and semidiurnal (D2) frequencies from left to right, and the gray band indicates the NI range that we bandpass filter. Positive phase indicates the wind leads the velocities in (c) and (d), and W21 leads M29 in (g) and (h).

Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0208.1

The rotary cross spectra between the near-surface velocity at W21 and M29 also shows that these velocities were coherent in the anticyclonic direction over the NI frequency band (Figs. 6c,d, shaded region). On average, W21 lagged M29 by 7.2 min (2.4°). The wind response was thereby coherent over a horizontal scale of at least 10 km, consistent with the presence of a WFO (D’Asaro 1985). Our cross-spectra analysis shows that our time-averaged surface NI velocity had the characteristics of pure-inertial WFOs.

Except during days 43–46, the wind stress was highly variable in time (Fig. 3a) and hence applied a time-varying force to the water surface. WFOs, in turn, transfer this unsteady wind forcing to the base of the SML, which can locally generate NIWs (Pollard 1970). WFOs can also vary in their amplitude across the shelf if the geostrophic current converges and/or diverges (i.e., D ≠ 0) (Weller 1982), and their frequency will be near the local or ambient resonant frequency feff (Tort and Winters 2018). On average we observed spatially coherent WFOs with a 2.4° phase lag between nearby moorings, but the instantaneous frequency, phase, and amplitude of WFOs varied across the shelf when feff also varied (Fig. 5c).

c. Near-inertial waves

Subsurface velocities over the NI frequency band were large and often exceeded the near-surface NI velocities (Fig. 4). Before day 50, when the shelf had feff > f, the subsurface NI velocity on the shelf were typically largest around the thermocline, coinciding approximately with the 16°C isotherm (Fig. 4). The vertical location of the NI velocity maxima followed the downward tilt of the isotherms with distance offshore before day 51, while after this day the velocity maxima remained at approximately the same depth (Fig. 7). The largest HKE on the shelf consistently occurred at M25. The NI velocity varied more below the SML for the deeper M29 and M32 moorings than the shallower ones onshore (Fig. 4). The NI velocity ellipse was circular on the shelf but was increasingly elliptical at the steep shelf break and continental slope, with the alongshore NI velocity (Fig. 4, right) on average 18% larger than the cross-shore velocity at M29 and M32 at the same depth and time (Fig. 4, left).

Fig. 7.
Fig. 7.

(top) The ship-observed wind stress, with wind stresses that exceeded 0.1 N m−2 (orange line) and periods when the wind direction varied by more than 45° in a half day (red line) indicated. The remaining paired panels represent individual yeardays, with the median feff (solid) and ωmin (dashed) over the observed SML thickness in the upper panels, and the maximum NI horizontal kinetic energy (HKE; J m−3) within an inertial period centered around midnight on each yearday, and at each depth and mooring, in the lower panels. Note this is the maximum over an inertial period for each depth and mooring and is not a snapshot in time. The low-passed and averaged temperature was contoured in black, with 1°C contours, and the SML thickness is plotted in cyan. The NIW event is noted after the day in the relevant figures.

Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0208.1

The NI HKE near the thermocline first increased and then decreased during four different events, denoted A–D in chronological order (Fig. 7). During events A, B, and D, changes in NI HKE were centered on the shelf, while event C was centered on the continental slope (i.e., M29 and M32). Each event started with large wind stresses, followed by an increase in the NI velocity throughout the SML and then further down in the water column over <1 day. Within around 2 days, the surface velocities then decreased. For event B, for example, the HKE near the thermocline increased from 8 to 42 J m−3 from day 42 to 43 at M25 (Fig. 7). Over this time, the near-surface velocity also increased, but subsequently rapidly decreased from day 44 onward (Figs. 7 and 5a). By comparison, WFOs in the open ocean typically decay over time scales of 1–2 weeks (D’Asaro 1989). On the continental shelf, the NI velocity can decay over short time scales due to seabed friction (Rayson et al. 2015), unless strong stratification isolates the surface water from the bottom boundary (Chant 2001). At W21, the stratification N exceeded 0.01 rad s−1 at the thermocline for the entire sample period and the SML thickness was always <43% of the total water depth. Hence, the observed rapid reduction in the near-surface NI velocity was more likely due to a transfer of energy to NIWs rather than direct bottom friction dissipation.

To examine whether the observed subsurface velocity was due to local NIW generation below the SML, we calculated the anticyclonic rotary cross spectra between the wind stress and the velocities measured at 85-m depth at W21. If NIWs were locally generated, first the effects of surface winds would be felt throughout the SML within O(10–60) min, and subsequently a wave would propagate downward from the base of the SML to the observed depth of 85 m. From dynamic modes, a mode-one wave would have a vertical group speed of about 10−3 m s−1 (Gill 1982). So in 8 h, a mode-one wave at W21 could travel from the median SML depth of 30 m vertically downward to an approximate depth of 60 m. The observed wind was significantly coherent with the subsurface velocity over the NI frequency band, with the water lagging the wind by 184° or 9.3 h (Figs. 6a,b, shaded region). We estimate a mode-one wave could be generated by an impulse of wind and then propagate to 60-m depth in approximately 9 h, while we observed NIWs taking 9.3 h to propagate to 85-m depth. These two estimates are in good agreement, given we assumed ∂υg/∂z = 0 for this approximation of mode-one vertical group speed. The coherency between local winds and the velocity at NI frequencies, and the associated phase lag, therefore suggests energy was locally transferred from winds to WFOs, and in turn from WFOs to NIWs with a total lag time of O(9) h.

We examined the energy flux estimates to determine the generation sites for the NIWs. We considered the local feff, as previous studies have shown NIWs are preferentially generated at regions where feff < f (e.g., Lerczak et al. 2001). At all moorings, NIWs propagated predominantly northward/equatorward (Fig. 8, arrow direction). During event B, energy fluxes at M17–M29 were directed toward the northeast when their magnitude sharply increased on day 42, reaching a maximum energy flux for this event on day 44 at all moorings. This spatial pattern and the lack of a monotonically increasing velocity phase across the shelf (Fig. 5d) indicate an NIW was generated at the same time on the shelf. This NIW was generated where the SML had fefff and ωminf (Fig. 7), where at all moorings fefff. Prior to event C, we observed small westward/onshore fluxes at M32 on day 47, followed by northward fluxes estimated at all moorings from day 48 (Fig. 8). On day 47, in the SML feff < f and ωmin < f at M32, while feff > f and ωmin < f further inshore on the shelf (Fig. 7). Hence on day 47, a NIW was generated where feff < f. During the next event, D, energy fluxes were directed eastward/offshore at M25 and M29, but northward/equatorward elsewhere (Fig. 8). The energy fluxes and NI velocities did not increase at M32 following the offshore flux at M29 (Figs. 7 and 8), suggesting the NIW did not propagate from the shelf to M32. Synchronous NIW generation across the shelf best explains the observed fluxes, where this NIW was generated where ωminfeff < f. In summary, across the events, NIWs were generated at any locations on the shelf or slope where feff < f, but if feff > f, then NIWs were generated at locations where feff was smallest and ωminf.

Fig. 8.
Fig. 8.

The (a) depth-averaged ωmin/f and (b) NI energy flux (W m−1) of the total uNI and ρNI. As NI perturbations of the free surface were less than the reported accuracy of our bottom-mounted pressure sensors, ρNI is due to isopycnal perturbations only. We scaled down the fluxes at M29 by 50% and M32 by 75%.

Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0208.1

From our observations, NIWs could be generated preferentially in regions where ωminf, which does not agree with the scaling arguments presented by Whitt and Thomas (2015). Their scaling arguments showed that if Bu ≪ 1, which is the case in the SML, the effect of rotation dwarfs stratification, and hence the resonant frequency is feff and not ωmin. We did, however, observe NIWs generated where both feff was smallest and ωminf, so any dependence on ωmin should be further considered. The process of NIW generation in the presence of strong baroclinicity requires further research via targeted numerical modeling simulations with constant feff but changing ωmin, which is beyond the scope of this study.

5. Wave propagation and trapping

The geostrophic current modulated the generation of NIWs by modifying the cross-shelf value of feff. NIWs were generated anywhere on the shelf or slope where feff < f, and when feff > f over the shelf and slope, then NIWs were generated where feff was smallest and ωminf. Regions of ωmin < f were thereby potentially having some influence in controlling where NIWs were generated, but this requires further research. The propagation of NIWs has received greater attention than NIW generation in literature (e.g., Mooers 1975; Kunze 1985; Whitt and Thomas 2013). Freely propagating waves are trapped in regions where ωωmin, that is, they can freely propagate within regions where they remain near- or superinertial, but cannot propagate into a region where they are subinertial. At regions where ω = ωmin, NIWs will either reflect to remain within a region where ω > ωmin, or they will travel along isopycnals where ω = ωmin (Whitt and Thomas 2013). Since we assumed ∂ug/∂y = 0, NIWs can always propagate equatorward. Whether or not NIWs can propagate in the cross-shore and vertical directions will, however, depend on ωmin, which varied both with depth and across the shelf (Figs. 2d–f). In regions where ωmin < ω < feff, NIWs are within the anomalously low-frequency band that exists due to baroclinicity, and waves with a frequency within this band are likely amplified and vertically trapped (Mooers 1975).

a. Lateral trapping

The NIW energy fluxes indicated that the waves propagated predominantly northward/equatorward at all moorings (Fig. 8). As explored above, these fluxes were typically directed northward with small flux magnitudes in the cross-shore direction. A net offshore flux was only found at the moorings M25 and M29 for <2 days. We did not find offshore fluxes at the nearby W21 and M32 moorings, indicating offshore propagation did not occur across the entire shelf and slope. At M29 and M32, ωmin > f beneath 80 m during the entire sample period (Figs. 2d–f). Further inshore, at M17–M25, ωmin > f from day 46–51, while before day 46 and after day 51 ωminf on the shelf (M17–M25) and above 80-m depth on the slope (M29 and M32) (Figs. 2d–f). The persistence of ωmin > f on the continental slope explains the observed lack of cross-shelf propagation: when ωmin > f at M29 or M32, NIWs could not propagate offshore and remain near- or superinertial, and so were laterally trapped on the shelf and limited to propagating equatorward. During periods when ωmin decreased toward shore, onshore propagating NIWs were likely not observed over the midshelf (i.e., between M17 and W21) since these waves would have been refracted alongshore as the seabed shallows (Wunsch 1969). Our observations thereby highlight that when ωmin > f for extended periods of time on the continental slope, NIWs cannot propagate offshore, thus allowing only equatorward propagation along the TECS.

Previous studies on NIWs propagation have focused primarily on their cross-shore propagation rather than their alongshore propagation (e.g., Shearman 2005; Lerczak et al. 2001; Davies and Xing 2005). These studies’ analyses describe NIW propagation in regions of ωmin < f that are unbounded in the offshore direction, but our observations indicate that alongshore NIW propagation was prevalent in boundary currents with regions of both ωmin < f and ωmin > f on the continental shelf and slope. Furthermore, the continental shelf and slope can weakly trap NIWs, so that NIWs behave like alongshore propagating coastal-trapped waves on the shelf and freely propagating NIWs on the continental slope (Chapman 1982; Dale et al. 2001; Lerczak et al. 2003), where coastal-trapped waves propagate toward the equator on the TECS (Schlosser et al. 2019). We thereby suggest that future studies in the coastal ocean should consider whether NIWs propagate in the alongshore direction, particularly in regions where boundary currents laterally trap NIWs so that they cannot leave the shelf.

During the entire sample period, ωmin > f below 80-m depth on the continental slope (Figs. 2d–f), due to the background alongshore flow weakening from M29 to M32, and occasionally changing from southward to northward flow at depths > 80 m. This region of ωmin > f likely affected the NIWs by inhibiting them from propagating offshore unless their frequency ω was at least 20% larger than f (i.e., ω > 1.2f) from day 38 to 51, or ω > 1.1f after day 51. Given feff < 1.15f between M17 and M29 over the entire field campaign, with feff < 1.0f after day 51, it is unlikely NIWs would be generated on the shelf with sufficiently large frequencies to be able to propagate offshore. In addition, offshore-generated NIWs would only have been able to propagate onto the shelf if ω > 1.1f, or these waves would be reflected back offshore at locations on the slope where ω = ωmin. The EACE thus obstructed the NIWs generated offshore of M32 from propagating onto the TECS. NIWs were also likely to reflect along the steep and supercritical (α/β ≫ 1) slope of the shelf break and continental slope near M29 and M32, with baroclinicity affecting this process (Federiuk and Allen 1996; Whitt and Thomas 2013). Reflection by ωmin and the supercritical slope could create the “chimney effect,” whereby NIWs reflect back and forth and rapidly deepen (Lee and Niiler 1998). This may explain why we observed more depth-variable velocities at the deeper M29 and M32 moorings (Fig. 4).

b. Vertical trapping

During some events, the vertical gradients of the NIW’s velocity phases were distinctively different across the shelf. For event B, which occurred from day 42 to 44, HKE was large along the isotherms across the shelf (Fig. 7), and the vertical gradient in the NI velocity phase ϕ (ϕ/z) was near zero. Whitt and Thomas (2013) showed that NIWs propagate at an angle to the isotherms when ω > ωmin, but may travel along isotherms and be intensified if ω = ωmin and ω < feff. On average, over day 42–45 and along the 16°C isotherm (Fig. 5d), the NI velocity had ω ≤ 1.0f at M17–M32. At this time, ωmin < f < feff at most depths and moorings (Figs. 5a,b). Hence during this event, NIWs were vertically trapped and likely intensified because ω ≤ 1.0f and ωωmin, where this only occurred due to the baroclinicity associated with the background current.

For event D, which occurred after day 51, the NI velocities were large at approximately 90 m beneath the surface at W21–M29, while the closest isotherm to this depth (15°C) deepened from 83 m at W21 to 87 m at M25 (Fig. 9). The ϕ/z was larger at W21 than M29, while ωmin increased from W21 to M29. At this 90-m depth, the NIW frequency was on average 0.98f from day 51 to 55 at the W21 and M25 moorings, while ωmin increased from 0.9f to 1.0f between the moorings W21 and M29 (Fig. 2f). The observed NIWs, therefore, had ω > ωmin and propagated downward at W21, but since ωmin was larger offshore at M29, the NIWs became increasingly near-inertial (i.e., ωωmin) and traveled downward with a reduced velocity—akin to the observations during event B. In summary, during events B and at some moorings during event D, the NIWs were vertically trapped along isotherms and could not vertically propagate because ω = ωmin. Vertical trapping occurred at isolated regions on the shelf when ωmin increased with distance across the shelf (Figs. 2f and 9).

Fig. 9.
Fig. 9.

NI alongshore velocity observed on yearday 49–55 (events C and D) at (a) W21, (b) M25, and (c) M29. We contour mesoscale temperature with 1°C separation (gray) and the SML thickness (dark blue). Note we have increased the velocity limits to 0.15 m s−1, where the maximum velocity in Fig. 4 was 0.12 m s−1.

Citation: Journal of Physical Oceanography 49, 10; 10.1175/JPO-D-18-0208.1

6. Summary and conclusions

We observed near-inertial waves (NIWs) on a continental shelf in the presence of a baroclinic geostrophic current. The baroclinic East Australian Current Extension was sheared in the cross-shelf and vertical directions, resulting in relative vorticity and baroclinicity, respectively. The relative vorticity modified the resonant frequency feff, while both relative vorticity and baroclinicity modified the minimum frequency of freely propagating waves ωmin. Wind-forced oscillations (WFOs) and NIWs were locally generated in regions where feff < f, provided the wind stress was both larger than 0.1 N m−2 and was not sustained in one direction for longer than 1 day. If feff > f across the entire shelf and on the slope, NIWs were generated where feff was smallest and ωminf. Otherwise, NIWs were generated where feff < f, as found by other studies (e.g., Lerczak et al. 2001). The applied wind forcing generated the WFOs, but the baroclinic current determined the NIW generation site, and hence the energy transferred from the surface mixed layer down into the water column.

By modifying ωmin, the shear from the baroclinic current also controlled the direction of propagation of NIWs. We estimated near-inertial energy fluxes to determine the direction of NIW propagation. The NIWs propagated predominantly equatorward because ωmin > f on the continental slope for the entire field campaign—obstructing shelf-generated waves from propagating to the open ocean. Past studies of NIWs on continental shelves have focused on cross-shelf propagation, but our observations emphasize that the alongshore propagating component of the waves must also be considered. Alongshore propagation is particularly important when, due to the presence of a background current, the continental shelf and slope has limited regions with ωmin < f.

The observed NIWs were also trapped in the vertical because of the baroclinicity associated with the background current, resulting in an anomalously low-frequency band between ωmin and feff. Waves with a frequency within this band were likely intensified and vertically trapped, although vertical trapping did not always occur across the entire shelf when ωmin varied across the shelf. Our results reinforce the importance of considering the effects of baroclinicity and relative vorticity on NIW dynamics, as both processes influenced wave propagation, and potentially wave generation. We conclude that windy continental shelves with strong background currents are likely to have energetic NIW fields, but a background baroclinic current will adjust the behavior, energetics, and spatial distribution of these NIWs.

Acknowledgments

An Australian Research Council Discovery Project (DP 140101322), and a UWA Research Collaboration Award funded this work. T. L. Schlosser acknowledges the support of an Australian Government Research Training Program (RTP) Scholarship. We thank the crew, volunteers and scientists who aided in the field data collection aboard the R/V Revelle, which was funded by the National Science Foundation (OCE-1129763). The continental slope mooring (T4/M32) was also funded by the National Science Foundation (OCE-1129763), and was conceived, planned and executed by Matthew Alford, Jennifer MacKinnon, Jonathan Nash, Harper Simmons and Gunnar Voet. We thank Harper Simmons for the combined R/V Revelle multibeam and Geoscience Australia bathymetry used in this study. We thank the anonymous reviewers whose feedback improved this work.

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