Near-inertial Waves Research Articles

Thin layers of phytoplankton: a model of formation by near-inertial wave shear

Microscale variability of phytoplankton has been detected in vertical profiles in the ocean for decades, yet its mechanism of formation remains unclear. Here a mechanism is presented which can generate thin (10s of centimeters) layers of phytoplankton through the interaction of near-inertial wave shear with horizontal (along-isopycnal) patchiness of phytoplankton. Horizontal biomass patches along isopycnals are advected over each other by the vertical shear of near-inertial waves, generating layers in vertical profiles. The thickness of the phytoplankton layers can be much less than the vertical wavelength of the internal wave, due to tilting and stretching of horizontal patches of phytoplankton. The thickness of the layers is directly related to the vertical shear and the along-isopycnal scale of the phytoplankton patches: shorter horizontal scales generate thinner layers for a given shear. The amplitude of the biomass difference between layers is directly proportional to both the along-isopycnal and vertical biomass gradients. The model predicts the thickness, time of occurrence and duration of layers during the internal wave's cycle. This mechanism is likely a ubiquitous feature of the world's ocean, and would be particularly important in regions of strong horizontal gradients of properties.

Scattering of inertial waves by an ocean front - Comments

Rubenstein and Roberts (1986, hereafter RR86) have studied the scattering of inertial waves by a geostrophic jet. The most remarkable effect of the jet is to concentrate near-inertial energy in the negative vorticity region. This effect is due to the horizontal dispersion of near-inertial waves. It is demonstrated by RR86 Using a stratified linearized model. A similar result has been obtained by Kunze (1985) using a ray-tracing approach and bas been confirmed by observations (Kunze and Stanford 1984). Another result of RR86 concems the mixed layer depth variations. Their Figs. 3 and 8 show a systematic downwelling in the negative vorticity region of the jet and systematic upwelling in the positive vorticity region. Although large upwellings and downwellings occur in the presence of a wind stress perpendicular to the front (Niiler 1969), it is not clear how such systematic effects can result from unforced inertial oscillations. RR86 find this behavior of the mixed layer depth in a shallow-water model where horizontal dispersion is neglected (their Fig. 3 ) and therefore suggest it is due to the nonlinearity of the mass equation. Our failure to reproduce the results of RR86 with a fully nonlinear shallow-water mode1led us to investigate more carefully the role of nonlinear terms, using both direct numerical simulation and asymptotic analysis. In the present note we show that the systematic upweIIings and downwellin~ are spurious effects due to the neglect ofsome (but not all) nonlinear terms in RR86's mixed layer equations.

Flow over a mesoscale ridge: pathways to regime transition

A theoretical and modelling study is undertaken of an airstream of uniform flow (U) and stratification (N) impinging normally upon a two-dimensional bell-shaped ridge of half-width (L) and height (H) that is located on an f-plane. The associated Rossby number (Ro = U/fL) and inverse Froude Number (F = NH/U) are taken to be such that the effects of both the earth’s rotation and non-linear processes can significantly influence the nature of the flow response. It is shown that within this intermediate meso-α/β scale sub-domain of (Ro, F) parameter space there are several distinctive signatures to the flow response, and each signature is associated with the generation of appreciable buoyancy wave energy. As Ro decreases across the sub-domain, the source for this wave energy changes continuously from the conventional direct orographic forcing of vertically propagating waves (for Ro > 1), to that linked with the cusping of a leeward train of low-level near-inertial waves (for Ro~ 1), and thereafter to the forcing induced by the adjustment that accompanies the scale contraction of balanced flow (for Ro < 1). In effect this change highlights the various pathways to regime transition within the intermediate domain.

Dispersion of wind-induced inertial waves by a barotropic jet

This note attempts to reinterpret previous results on the dispersion of wind-induced inertial waves by a geostrophic barotropic jet in the ocean. The approach is to consider the jet vorticity influence on the different baroclinic modes using a vertical normal mode expansion. Numerical and analytical analysis of the linear equations shows that vorticity effects on a single baroclinic mode strongly depend on the ratio of its Rossby radius and the length scale of the geostrophic vorticity: trapping of the near-inertial energy occurs when this ratio is small. When this ratio is of order one, inertial waves are almost unaffected by the geostrophic vorticity because dispersion efficiently overcomes the jet vorticity effects. A 2-D primitive-equation model is used to examine the scattering of wind-induced inertial waves in realistic situations. Results indicate that contribution of the lowest baroclinic modes, unaffected by the jet vorticity, explain some striking features reported in previous studies as the downward phase propagation of near-inertial waves in the positive vorticity region

Decay of a Near-Inertial Wave

Abstract The decay of a downward propagating near-inertial wave was observed over four days. During this short period, the energy of the near-inertial wave decreased by 70%. The shear layers produced by the wave were regions of enhanced turbulent dissipation rates. The authors estimate that 44% of the observed change in the near-inertial energy was lost to turbulence. Estimates of the wave energy lost at the survey site due to the wave propagating out of the region were smaller. Energy lost by horizontal advection of the wave out of the survey region was more difficult to estimate; the horizontal extent of the near-inertial energy was unknown. Advection could account for more than half of the observed energy lost. However, the authors did not detect the near-inertial wave during a 40 km×40 km ADCP survey after completing the six-day station.

Equatorial Ocean Response to Rapidly Translating Wind Bursts

The response of the ocean at low latitude to idealized westerly wind bursts can be described as a wave wake composed of equatorial gravity and Rossby-gravity modes. The excited waves are those with phase speeds that match the zonal translation speed of a wind burst, typically 10 m s−1. These modes sum to produce oscillations near the local inertial frequency at each latitude, analogous to near-inertial internal gravity waves generated by moving storms at midlatitude. Linear theory predicts that typical wind burst amplitudes (stresses of 0.1 Pa) will generate substantial current oscillations [O (1 m s−1)] in the upper ocean. Response is initially confined to the region directly beneath a wind burst, after which the wake descends and refracts equatorward as a propagating beam. Waves are of sufficient amplitude to dominate shear and vertical strain in the upper ocean. Phase differences between oscillations at neighboring latitudes induce motion in the meridional-vertical plane at ever-decreasing meridional scales. Mixing associated with predicted low Richardson numbers is expected to check development of nonlinearity from vertical and meridional advection by the waves.

An investigation of the properties of low-frequency internal waves in the northeastern China Seas

A simple and practical method for separating low-frequency internal waves from low-frequency barotropic waves was employed to analyze the observation data. Analysis of some data gathered in the northestern China Seas revealed strong semidiurnal internal tides and near-inertial internal waves at the stations in the East China Sea and near-inertial waves but no semidiurnal internal tides at the station in the centre of the Yellow Sea. The geographic properties of low-frequency internal waves in the region are discussed primarily on the basis of the mechanism of internal tide generation on the continental shelfbreak, and the mechanisms of local generation and global generation.

Instability of a Mixed Layer Model and the Generation of Near-Inertial Motion. Part II: Mixed Layer Deepening

In Part I we examined the stability of a model of the mixed layer, neglecting the deepening rate. Here we examine the effects of the deepening but neglect the oscillations in the steady state. We find that the two types of instability found previously are modified. The long wavelength [O(10) km] instability becomes more stable while the converse is true for the short wavelength [O(1) km] instability with the purely kinematic effect of the slowly deepening mixed layer on the equally slow vertically propagating near-inertial waves being of most importance. The short wavelength instability might be expected to be observed if the lateral friction is sufficiently large. There is also a different short wavelength instability which is basically independent of the ocean interior which might be expected to appear if friction is sufficiently small.

A Study of Geostrophy in Tropical Pacific Ocean Currents during the NORPAX Tahiti Shuttle using a Shipboard Doppler Acoustic Current Profiler

Continuous velocity measurements from a shipboard Doppler acoustic long on the NORPAX shuttle experiment in the central equatorial Pacific are presented. The time mean of these velocities shows the classical zonal equatorial currents as well as their meridional circulation. The velocities are used with concurrent CTD data to examine the geostrophic balance of zonal currents in the upper 117 m. Estimates of the errors of the acoustic data are produced from a comparison between that data and concurrent profiling current-meter data, and are used to establish the reliability of the balances observed. Both the time mean and the time varying balances are investigated, as well as the departures from geostrophic balance. The mean zonal velocities between 4°S and 10°N are found to be in approximate geostrophic balance. Departures from geostrophy in the mean are observed near the surface at the equator. The meridional advection of meridional momentum appears to be only partly responsible for this departure. The time varying flow was partly geostrophic poleward of 1°, but not so equatorward. A large excess of geostrophic velocity variance (relative to observed velocity variance) exists near the equator, probably due to high frequency internal wave signals in the density data. North of 4°N an excess of observed velocity variance was found, due probably to near-internal waves. In both latitude bands the fluctuating departures from geostrophy are probably to near-inertial waves. In both latitude bands the fluctuating departures from geostrophy are probably balanced by meridional acceleration. More than sufficient acceleration exists near the equator to account for the observed imbalance, while in the North Equatorial Countercurrent the acceleration is barely sufficient, implying a close balance between acceleration and nongeostrophic pressure gradients.

Scattering of Inertial Waves by Rough Bathymetry

Abstract Interactions between near-inertial waves and rough bathymetry are studied theoretically and numerically. Rough bathymetric features cause scattering, even when their length scales are much smaller than the wavelengths of the incident waves. The scattering efficiency depends on the relative slopes of the incident wave propagation and bottom features. Scattered wavelength are comparable to wavelengths of the bathymetry. In a steady-state situation over an isolated bump, most of the kinetic energy is associated with upward propagating waves, in agreement with observations. A spectral model shows that first-mode incident waves with wavelengths >150 km, and second-mode waves with wavelengths >50 km are completely scattered into smaller wavelengths, primarily into wavelengths smaller than the bathymetry spectrum roll-off, 40 km. This model is applied to a spectrum of incident internal waves. The principal interactions involve the scattering of low-frequency, low-wavenumber incident waves into higher wa...

Near-Inertial Ocean Current Response to Hurricane Frederic

Abstract Hurricane Frederic passed with 80 to 130 km of the U.S. Naval Oceanographic Office current meter arrays in water depths ranging from 100 to 470 m near the DeSoto Canyon region, and within 150 km of an Ocean Thermal Energy Conversion (OTEC) mooring in 1050 m of water. Excitation of near-inertial waves by the moving hurricane was observed throughout the water column along the canyon walls and at the OTEC site. The frequencies of the waves were blue-shifted between 1% to 6% above the local inertial frequency. The horizontal wavelength of 250 km is consistent with an energetic first baroclinic-mode response, but is considerably below the linear theory prediction of 550 km. The inferred vertical wavelengths of the immediate response exceeded 1000 m along the northern and eastern sides of the canyon since the currents throughout the water column increased within hours of the hurricane passage. Later, the vertical wavelengths were about equal to the water depth. The vertical group velocities associated ...

Transport of mud on continental shelves: Evidence from the Texas Shelf

Transmissivity and suspended-sediment data from three cruises on the East Texas continental shelf confirm that a bottom nepheloid layer (BNL) exists across the shelf; this layer is most turbid in the nearshore and outer shelf regions. In addition, surface nepheloid layers exist close to shore due to river and bay outflows, and on the outer shelf intermediate nepheloid layers are present as a result of quasi-horizontal advection from the BNL. The character of the BNL is not directly linked to local hydrography or substrate, being instead a function of the shelf dynamics. In the nearshore regime high-energy coastal processes and high sediment input from bays and rivers maintain the BNL. At the shelf edge, the BNL is formed by near-inertial internal waves and shelf waves which resuspend and transport fine sediment. Present-day sediment deposition on the East Texas Shelf can be directly related to the above processes. Mud is accumulating in the nearshore environment, due to river input, and on the inner and midshelf regions as a result of deposition from BNLs and SNLs. On the outer shelf, BNLs and INLs transport fine sediment further offshore, so that in effect suspended sediment bypasses the outer shelf.

The Mean and Near-Inertial Velocity Fields in a Warm-Core Ring

Abstract Velocity and temperature profiles collected in warm-core ring 82-I in January 1983 are used to describe the mean and fluctuating fields of the ring. The ring was relatively small, containing no Sargasso See water. Its signature vanished below 600 m and its velocity maximum was 50 cm s−1 at 35 km radius. The mean flow was in cyclogeostrophic balance and much of the core in solid body rotation with vorticity −0.5f. Potential vorticity was uniform along isopycnals below the depth of atmospheric influence. Horizontal Reynolds-stress forces did not contribute significantly to the mean momentum balance. Downward-propagating near-inertial waves account for the most energetic of the fluctuating velocities. Energy levels four times greater than typically observed were found inside the ring, consistent with the expectation of trapping and critical-layer amplification of near-inertial waves in regions of negative vorticity as a consequence of a depressed lower bound of the internal waveband, feff = f + ζ/2....

Vertical Reynolds Stress Divergence in the Upper Ocean Associated with Linear Wind-Driven, Near-Inertial Waves of Finite Wavelength

Abstract Study of a schematic linear, wind-driven, inertio–gravity wave model in the upper ocean finds resonant, near-inertial waves of finite horizontal wavelength to have both horizontal and vertical motions. The mean product of these horizontal motions with the vertical motion yields an internal vertical Reynolds stress that is zero at the sea surface and nonzero at the base of the mixed layer and in the main pycnocline below. Assuming near-inertial waves of finite wavelength to be generated by finite wavelength disturbances in the atmosphere, advected by the mean wind, the internal vertical Reynolds stress at the base of the mixed layer is directed 45° to the right of the mean wind direction. Below the mixed layer, near-inertial waves in the mixed layer. This generation mechanism produces an internal vertical stress throughout the main pycnocline, directed initially 45° to the right of the mean wind direction, but rotating into it with increasing depth. The divergence of this internal vertical Reynold...

On the interaction of small-scale oceanic internal waves with near-inertial waves

Ray theory is used to investigate the interaction of a short high-frequency progressive internal wave of infinitesimal amplitude with a long progressive near-inertial wave of arbitrary amplitude. Weak-interaction theory would, if applicable, predict that the largest changes in short-wave properties occur when the resonance condition c = cg is satisfied, where c is the phase velocity of the long wave and cg is the group velocity of the short wave. The present calculation confirms this prediction only when the long wave has exceedingly small amplitude (peak velocities of order 0.1 cm/s).However, when the background velocity has a realistic amplitude (e.g. oceanic values are of order 20 cm/s) the resonance condition fails to be relevant. For example, waves which initially have c = cg become trapped in low-shear regions and consequently experience very small changes in wavenumber. Other short waves, which initially have cg [Lt ] c and hence violate the resonance condition, exhibit large and permanent changes in vertical wavenumber.Remarkably, it is found that these permanent changes are much more likely to be decreases, rather than increases, in wavenumber. This can be explained as follows. Short waves which enter an inertial-wave packet experience both increases and decreases in wavenumber. However, at times when the wavenumber is relatively large, the group velocity is relatively small and the short wave is unlikely to escape from the inertial packet, whereas small wavenumber and large group velocity assist the escape of the short-wave group. Consequently the short waves that leave the inertial packet tend to have a smaller average wavenumber than those that enter. Thus the net effect of a near-inertial packet on a collection of short waves appears to be an increase in vertical wavelength and frequency.

Observations of Persistent Mixing and Near-Inertial Internal Waves

Abstract Repeated profiles of microstructure and shear alongside a drogued buoy show a 10 m thick mixing zone at the same depth as a near-inertial feature. Because the profile was diffusively stable and free of thermohaline intrusions, internal wave breakdown is the only mechanism capable of producing mixing. Both the near-inertial feature and the mixing patch were observed for over three days and then faded out. It is not possible to determine whether they disappeared because the near-inertial feature was dissipated by the mixing or because the drogue drifted away; both are plausible. Kinematical models of mixing use a standard internal wave spectrum to predict the frequency of occurrence and persistence of shear instabilities. Observed distributions of ϵ and χ patches thinner than 2 m are similar to the model predictions, although the dissipation rates are low. Most are just at or below the transition dissipation rate ϵtr. Laboratory experiments have established that if ϵ<ϵtr the turbulence is too weak ...

Velocity Profiles in a Warm-Core Ring

A transect of velocity profiles across Gulf Stream warm-core ring 82-B shows that the thermostad contained virtually no vertical shear. Enhanced downward-propagating near-inertial wave shear was present at the base of the core, consistent with these waves encountering critical layers as they try to leave the region of negative vorticity. Wave amplification and a shrinking vertical wavelength at the critical layer should lead to instability and shear production of turbulence. High dissipation rates have been observed at the base of ring 81-D's core.

Observations of Hurricane-Generated, Near-Inertial Slope Modes

Velocity Profiles and current meter measurements taken near Site D(39°10′N, 70°00′W) on the continental rise south of New England are used to study the variability of the near-inertial wave field along a sloping bottom. While the typical vertical scales of the waves are on the order of 100 m, some energetic downward propagating near-inertial features are observed with unusually large vertical scales, on the order of the ocean depth. Comparison with an internal wave model on a linear bottom slope shows that these energetic waves are dominated by the lowest three downward and seaward printing dynamical “slope” modes. The lowest mode arrives first at Site D from the north, the higher modes follow several days later. The observed scales and propagation directions suggest that the energetic near-inertial waves were generated by a hurricane and then reflected at the steep continental slope to the north of Site D. The low-order, flat-bottom modes that usually dominate the far-field response of a hurricane are changed by the sloping bottom into “slope” modes, which then propagate toward deeper water. Energy intensification of these modes towards the bottom suggests that sloping bottoms may play a significant role in the near-inertial wave field below the main thermocline.

Near-Inertial Wave Interactions with Mean Flow and Bottom Topography near Caryn Seamount

Abstract Velocity measurements near Caryn Seamount in the Sargasso Sea reveal intensified mean and near-inertial motions in the upper ocean. Embedded in a regional eastward flow is an anticyclonic eddy that appears to be tied to the topography. An energetic downward-propagating near-inertial wave packet is found at the eddy's base. This wave appears to be trapped in the eddy, undergoing critical-layer amplification as it tries to leave. Near the bottom, enhanced upgoing near-inertial wave energy is found within 1000 m of the top of the seamount.

On the interaction of small-scale oceanic internal waves with near-inertial waves: Broutman, D. and W.R. Young, 1986. J. Fluid Mech., 166: 341–358

On the interaction of small-scale oceanic internal waves with near-inertial waves: Broutman, D. and W.R. Young, 1986. J. Fluid Mech., 166: 341–358