Showing papers on "Internal wave published in 2002"

Ocean waves and oscillating systems : linear interactions including wave-energy extraction

Abstract: 1. Introduction 2. Mathematical description of oscillations 3. Interaction between oscillations and waves 4. Gravity waves on water 5. Wave-body interactions 6. Wave-energy absorption by oscillating bodies 7. Wave interactions with oscillating water columns Bibliography Index.

The Role of Internal Tides in Mixing the Deep Ocean

Abstract: Internal wave theory is used to examine the generation, radiation, and energy dissipation of internal tides in the deep ocean. Estimates of vertical energy flux based on a previously developed model are adjusted to account for the influence of finite depth, varying stratification, and two-dimensional topography. Specific estimates of energy flux are made for midocean ridge topography. Weakly nonlinear theory is applied to the wave generation at idealized topography to examine finite amplitude corrections to the linear theory. Most internal tide energy is generated at low modes associated with spatial scales from roughly 20 to 100 km. The Richardson number of the radiated internal tide typically exceeds unity for these motions, and so direct shear instability of the generated waves is not the dominant energy transfer mechanism. It also seems that wave–wave interactions are ineffective at transferring energy from the large wavelengths that dominate the energy flux. Instead, it appears that most of ...

INTERNAL GRAVITY WAVES: From Instabilities to Turbulence

Abstract: ▪ Abstract We review the mechanisms of steepening and breaking for internal gravity waves in a continuous density stratification. After discussing the instability of a plane wave of arbitrary amplitude in an infinite medium at rest, we consider the steepening effects of wave reflection on a sloping boundary and propagation in a shear flow. The final process of breaking into small-scale turbulence is then presented. The influence of those processes upon the fluid medium by mean flow changes is discussed. The specific properties of wave turbulence, induced by wave-wave interactions and breaking, are illustrated by comparative studies of oceanic and atmospheric observations, as well as laboratory and numerical experiments. We then review the different attempts at a statistical description of internal gravity wave fields, whether weakly or strongly interacting.

Estimating tidally driven mixing in the deep ocean

Abstract: [1] Using a parameterization for internal wave energy flux in a hydrodynamic model for the tides, we estimate the global distribution of tidal energy available for enhanced turbulent mixing. A relation for the diffusivity of vertical mixing is formulated for regions where internal tides dissipate their energy as turbulence. We assume that 30 ± 10% of the internal tide energy flux dissipates as turbulence near the site of generation, consistent with an estimate based on microstructure observations from a mid-ocean ridge site. Enhanced levels of mixing are modeled to decay away from topography, in a manner consistent with these observations. Parameterized diffusivities are shown to resemble observed abyssal mixing rates, with estimated uncertainties comparable to standard errors associated with budget and microstructure methods.

The Shaping of Continental Slopes by Internal Tides

Abstract: The angles of energy propagation of semidiurnal internal tides may determine the average gradient of continental slopes in ocean basins (∼2 to 4 degrees). Intensification of near-bottom water velocities and bottom shear stresses caused by reflection of semi-diurnal internal tides affects sedimentation patterns and bottom gradients, as indicated by recent studies of continental slopes off northern California and New Jersey. Estimates of bottom shear velocities caused by semi-diurnal internal tides are high enough to inhibit deposition of fine-grained sediment onto the slopes.

Numerical Experiments on the Breaking of Solitary Internal Wavesover a Slope–Shelf Topography

Abstract: A theoretical study of the transformation of large amplitude internal solitary waves (ISW) of permanent form over a slope–shelf topography is considered using as basis the Reynolds equations. The vertical fluid stratification, amplitudes of the propagating ISWs, and the bottom parameters were taken close to those observed in the Andaman and Sulu Seas. The problem was solved numerically. It was found that, when an intense ISW of depression propagates from a deep part of a basin onto the shelf with water depth Hs, a breaking event will arise whenever the wave amplitude am is larger than 0.4(Hs − Hm), where Hm is the undisturbed depth of the isopycnal of maximum depression. The cumulative effect of nonlinearity in a propagating ISW leads to a steepening and overturning of a rear wave face over the inclined bottom. Immediately before breaking the horizontal orbital velocity at the site of instability exceeds the phase speed of the ISW. So, the strong breaking is caused by a kinematic instability of t...

Observations of Flow and Turbulence in the Nocturnal Boundary Layer over a Slope

Abstract: Measurements were conducted on an eastern slope of the Salt Lake Basin (SLB) as a part of the Vertical Transport and Mixing Experiment (VTMX) conducted in October 2000. Of interest was the nocturnal boundary layer on a slope (in particular, katabatic flows) in the absence of significant synoptic influence. Extensive measurements of mean flow, turbulence, temperature, and solar radiation were made, from which circulation patterns on the slope and the nature of stratified turbulence in katabatic winds were inferred. The results show that near the surface (,25‐50 m) the nocturnal flow is highly stratified and directed downslope, but at higher levels winds strongly vary in magnitude and direction with height and time, implying the domination of upper levels by air intrusions. These intrusions may peel off from different slopes surrounding the SLB, have different densities, and flow at their equilibrium density levels. The turbulence was generally weak and continuous, but sudden increases of turbulence levels were detected as the mean gradient Richardson number ( ) dropped to Rig about unity. With a short timescale fluctuated on the order of a few tens of seconds while modulating with Rig a longer (along-slope internal waves sloshing) timescale of about half an hour. The mixing efficiency (or the flux Richardson number) of the flow was found to be a strong function of , similar to that found in laboratory Rig experiments with inhomogeneous stratified shear flows. The eddy diffusivities of momentum and heat were evaluated, and they showed a systematic variation with when scaled with the shear length scale and the rms Rig vertical velocity of turbulence.

An investigation of stably stratified turbulent channel flow using large-eddy simulation

Abstract: Boundary-forced stratified turbulence is studied in the prototypical case of turbulent channel flow subject to stable stratification. The large-eddy simulation approach is used with a mixed subgrid model that involves a dynamic eddy viscosity component and a scale-similarity component. After an initial transient, the flow reaches a new balanced state corresponding to active wall-bounded turbulence with reduced vertical transport which, for the cases in our study with moderate-to-large levels of stratification, coexists with internal wave activity in the core of the channel. A systematic reduction of turbulence levels, density fluctuations and associated vertical transport with increasing stratification is observed. Countergradient buoyancy flux is observed in the outer region for sufficiently high stratification. Mixing of the density field in stratified channel flow results from turbulent events generated near the boundaries that couple with the outer, more stable flow. The vertical density structure is thus of interest for analogous boundary-forced mixing situations in geophysical flows. It is found that, with increasing stratification, the mean density profile becomes sharper in the central region between the two turbulent layers at the upper and lower walls, similar to observations in field measurements as well as laboratory experiments with analogous density-mixing situations. Channel flow is strongly inhomogeneous with alternative choices for the Richardson number. In spite of these complications, the gradient Richardson number, Ri g , appears to be the important local determinant of buoyancy effects. All simulated cases show that correlation coefficients associated with vertical transport collapse from their nominal unstratified values over a narrow range, 0.15 Ri g < 0.25. The vertical turbulent Froude number, Fr w , has an O (1) value across most of the channel. It is remarkable that stratified channel flow, with such a large variation of overall density difference (factor of 26) between cases, shows a relatively universal behaviour of correlation coefficients and vertical Froude number when plotted as a function of Ri g . The visualizations show wavy motion in the core region where the gradient Richardson number, Ri g , is large and low-speed streaks in the near-wall region, typical of unstratified channel flow, where Ri g is small. It appears from the visualizations that, with increasing stratification, the region with wavy motion progressively encroaches into the zone with active turbulence; the location of Ri g ≃ 0.2 roughly corresponds to the boundary between the two zones.

Spatial-temporal variability in surface layer deepening and lateral advection in an embayment of Lake Victoria, East Africa

Abstract: Vertical and horizontal exchanges in Pilkington Bay, a shallow (9 m) embayment of Lake Victoria, were determined from a surface energy budget, time series measurements of temperature, and quasi synoptic transects of conductivity, temperature, and depth conducted over a 2-d period. The surface energy budget is the first from a tropical lake over a diurnal timescale. Strong stratification developed during morning and early afternoon (.40 cycles h 21 ) but was eroded beginning in the afternoon by the combination of wind and heat loss. Surface heat losses contributed .70% of the energy for surface layer deepening 82% of the time from midafternoon until midmorning. Circulation times of the surface layer were ,2 min as it deepened to 1.5 m in the afternoon and were ,12 min at night even when mixing extended to the lake bottom. Spatial differences in the rates of heating and cooling and in the depth of wind mixing caused fronts to develop on spatial scales of kilometers within the bay. Convergence of these fronts led to downwelling of surface waters and upwelling of deep waters during the stratified period. Horizontal pressure gradients due to differential heating contributed to thermocline downwelling, lateral movement of deep, anoxic waters, and generation of high-frequency internal waves, all of which contribute to vertical and horizontal transports. Although wind and heat loss at one location generally determine the depth of the surface layer and thermocline, the depths of these key features may be strongly influenced by rates of heating and cooling elsewhere in a basin. The temporal and spatial scales of advection and vertical mixing determine the flux paths of particles and solutes in aquatic ecosystems and, ultimately, lacustrine productivity. Time series measurements of surface meteorology, from which surface energy budgets can be calculated, and water column temperatures can be used as an indirect approach to determine these pathways. The data also can be used to determine internal wave dynamics, the energetics of mixing, and the role of intrusions and density driven flows in advection. With this information, the rates of circulation within the upper mixed layer and vertical and horizontal transports can be assessed. The diurnal cycle of stratification and mixing is deter

Model estimates of M2 internal tide energetics at the Hawaiian Ridge

Abstract: [1] A primitive equation model is used to examine the structure and energetics of M 2 internal tides generated at the Hawaiian Ridge Recent estimates based on altimeter data suggest that 20 GW of barotropic tidal dissipation occurs at the ridge, with conversion to internal tides believed to be the dominant dissipation mechanism The model simulates an internal tide that accounts for 97 GW of radiated energy away from the ridge in the northeast and southwest directions The strongest generation occurs at three sites where enhanced barotropic currents flow across elongated topographic features The depth-integrated baroclinic energy flux and energy densities at these sites are on the order of 10 4 W m -1 and 10 4 J m -2 , respectively A modal decomposition indicates that 62% of the outgoing energy flux is accounted for by the first internal mode, 15% is accounted for by the second mode, and less than 5% is accounted for by each subsequent higher mode The tidal dissipation due to bottom friction along the ridge is estimated to be 01 GW The level of turbulent dissipation near the ridge owing to tidal energy conversion remains to be determined to assess fully the barotropic-baroclinic energy budget

A numerical investigation of solitary internal waves with trapped cores formed via shoaling

Abstract: The formation of solitary internal waves with trapped cores via shoaling is investigated numerically. For density fields for which the buoyancy frequency increases monotonically towards the surface, sufficiently large solitary waves break as they shoal and form solitary-like waves with trapped fluid cores. Properties of large-amplitude waves are shown to be sensitive to the near-surface stratification. For the monotonic stratifications considered, waves with open streamlines are limited in amplitude by the breaking limit (maximum horizontal velocity equals wave propagation speed). When an exponential density stratification is modified to include a thin surface mixed layer, wave amplitudes are limited by the conjugate flow limit, in which case waves become long and horizontally uniform in the centre. The maximum horizontal velocity in the limiting wave is much less than the wave's propagation speed and as a consequence, waves with trapped cores are not formed in the presence of the surface mixed layer.

Tidal Conversion by Supercritical Topography

Abstract: Calculations are presented of the rate of energy conversion of the barotropic tide into internal gravity waves above topography on the ocean floor. The ocean is treated as infinitely deep, and the topography consists of periodic obstructions; a Green function method is used to construct the scattered wavefield. The calculations extend the previous results of Balmforth et al. for subcritical topography (wherein waves propagate along rays whose slopes exceed that of the topography everywhere), by allowing the obstacles to be arbitrarily steep or supercritical (so waves propagate at shallower angles than the topographic slopes and are scattered both up and down). A complicated pattern is found for the dependence of energy conversion on e, the ratio of maximum topographic slope to wave slope, and the ratio of obstacle amplitude and separation. This results from a sequence of constructive and destructive interferences between scattered waves that has implications for computing tidal conversion rates for the global ocean.

Gravity Waves from Fronts: Parameterization and Middle Atmosphere Response in a General Circulation Model

Abstract: Current parameterizations of the gravity wave processes that are relevant to middle atmosphere general circulation modeling need to have specified somewhere in the lower atmosphere a number of characteristics of the gravity wave spectrum that arise from different possible gravity wave sources (i.e., the so-called gravity wave source spectrum). The aim of this study is to take into account in the specification of the gravity wave source spectrum a space and time modulation of the gravity wave wind variance and propagation direction associated with the occurrence of frontal systems. Given that fronts are poorly resolved at the truncations commonly used in middle atmosphere models (typically T21‐T42), first a method is devised to diagnose conditions that are considered to be the precursor of frontogenesis in a space and time-dependent low-resolution flow. This is achieved by evaluating horizontal isotherm compression due to flow deformation and convergence. Second, when particular conditions are satisfied, the precursor to frontogenesis is used as an indicator of subgridscale gravity wave emission in the model. Third, the wind variance and the propagation direction of the gravity waves at the source level are specified according to empirical evidences of frontal generation of gravity waves. The MAECHAM4 middle atmosphere response to this gravity wave forcing is presented. The study is restricted to fronts since they are thought to be one of the major nonstationary gravity wave sources in the extratropics, other gravity wave source mechanisms being left for later examination.

Nonlinear energy transfer within the oceanic internal wave spectrum at mid and high latitudes

Abstract: [1] In order to examine how the energy supplied by M2 internal tides cascades through the local internal wave spectrum down to dissipation scales, two sets of numerical experiments are carried out where the Garrett-Munk-like quasi-stationary internal wave spectra at 49°N (experiment I) and 28°N (experiment II), respectively, are first reproduced and then perturbed instantaneously in the form of an energy spike at the lowest vertical wave number and M2 tidal frequency. These experiments attempt to simulate the nonlinear energy transfer within the quasi-stationary internal wave fields near the Aleutian Ridge and the Hawaiian Ridge, respectively, both of which are generation regions of large-amplitude M2 internal tides. In experiment I, the energy spike stays at the lowest wave number, where it is embedded and the spectrum remains quasi-stationary after the energy spike is injected. In experiment II, in contrast, the energy level at high horizontal and vertical wave numbers rapidly increases after the injection of the energy spike, exhibiting strong correlation with the enhancement of high vertical wave number, near-inertial current shear. This implies that as the high vertical wave number, near-inertial current shear is intensified, high horizontal wave number internal waves are efficiently Doppler shifted so that the vertical wave number rapidly increases and enhanced turbulent dissipation takes place. The elevated spectral density in the high vertical wave number, near-inertial frequency band, which plays the key role in cascading energy to dissipation scales, is thought to be caused by parametric subharmonic instability. In experiment I, in contrast, the M2 tidal frequency is 1.2 times the inertial frequency at 49°N so that M2 internal tide is free from parametric subharmonic instability. Accordingly, even though significant M2 internal tidal energy may be generated, it is not available to support local deep water mixing.

Boundary layer intrusions from a sloping bottom: A mechanism for generating intermediate nepheloid layers

Abstract: [1] Laboratory experiments were used to investigate the growth of intrusions due to internal-wave reflection from a sloping boundary. When normalized by the incident energy density flux, the average intrusion spreading velocity was found to be a linear function of the frequency ratio ω/ωc, where ω is the frequency of the incident wave and ωc is the critical frequency, at which the wave characteristic has the same angle as the bottom slope. Evenly spaced layers, indicating thin perturbations in the background density gradient, developed within the mixing region and spread into the tank interior. The vertical spacing of these layers also bore a linear relationship to ω/ωc. A linear model of internal-wave reflection suggests that these layers may be related to an isopycnal displacement, or overturn, scale. Intrusion growth occurred at a range around the critical frequency and was strongest at slightly supercritical conditions. A balance relating the spreading rate of intrusions to the divergence of energy density flux across the boundary layer is derived. Fitting the laboratory results to this theoretical prediction suggested a weak net buoyancy flux. This balance might be of use in predicting spreading rates of intermediate nepheloid layers generated by internal-wave mixing at oceanic margins.

Remote-sensing evidence for the local generation of internal soliton packets in the central Bay of Biscay

Abstract: Large-amplitude internal solitary waves (or “solitons”) occurring in packets near the shelf break in the Bay of Biscay are well-documented and understood. The presence of similar features has now also been reported in the central Bay, ≈150 km from the nearest shelf break topography. The present paper analyses available remote-sensing synthetic aperture radar (SAR) data from the ERS satellites in this region. By doing so, we are able to provide convincing support for the hypothesis that these waves, instead of having travelled along the thermocline from the shelf break, are instead generated locally in the central Bay by the surfacing of a beam of internal tidal energy originating from the shelf break. This reinforces the results of a previous independent study, while at the same time providing a much more extensive investigation than was then possible. We have also exploited the large swath width (100 km) and high spatial resolution (100 m×100 m) of the SAR to examine for the first time the full surface structure of the internal waves in the central Bay, which are found to have a mean wavelength of 1.35 km, and a mean along-crest “coherence” length of 21.55 km.

Wind‐driven internal waves and Langmuir circulations in a numerical ocean model of the southern Baltic Sea

Abstract: [1] A one-dimensional numerical ocean model of the southern Baltic Sea is used to investigate suitable parameterizations of unresolved turbulence and compare with available observations. The turbulence model is a k-e model that includes extra source terms PIW and PLC of turbulent kinetic energy (TKE) due to unresolved, breaking internal waves and Langmuir circulations, respectively. As tides are negligible in the Baltic Sea, topographic generation of internal wave energy (IWE) is neglected. Instead, the energy for deepwater mixing in the Baltic Sea is provided by the wind. At each level the source term PIW is assumed to be related to a vertically integrated pool of IWE, E0, and the buoyancy frequency N at the same level, according to PIW(z) ∝ E0Nδ(z). This results in vertical profiles of e (the dissipation rate of TKE) and Kh (the eddy diffusivity) according to e ∝ Nδ and Kh ∝ Nδ−2 below the main pycnocline. Earlier observations are inconclusive as to the proper value of δ, and here a range of values of δ is tested in hundreds of 10-year simulations of the southern Baltic Sea. It is concluded that δ = 1.0 ± 0.3 and that a mean energy flux density to the internal wave field of about (0.9 ± 0.3) × 10−3 W m−2 is needed to explain the observed salinity field. In addition, a simple wind-dependent formulation of the energy flux to the internal wave field is tested, which has some success in describing the short- and long-term variability of the deepwater turbulence. The model suggests that ∼16% of the energy supplied to the surface layer by the wind is used for deepwater mixing. Finally, it is also shown that Langmuir circulations are important to include when modeling the oceanic boundary layer. A simple parameterization of Langmuir circulations is tuned against large-eddy simulation data and verified for the Baltic Sea.

Observation of depression solitary surface waves on a thin fluid layer.

Abstract: We report the observation of depression solitary surface waves on a layer of mercury when its depth is thin enough compared to the capillary length. These waves, as well as the well known elevation solitary waves, are studied with a new measurement technique using inductive sensors. The shape of the solitary waves, their amplitude-dependent velocity, and their damping rates by viscosity are found in good agreement with theoretical predictions.

Third‐order transport due to internal waves and non‐local turbulence in the stably stratified surface layer

Abstract: Until recently the concern of the traditional theory of the atmospheric stable boundary layer (SBL) was, almost without exception, the nocturnal SBL developing after sunset on the background of a neutral or slightly stable residual layer In the nocturnal SBLs the nature of turbulence is basically local Its lower portion is well described by the classical Monin–Obukhov surface-layer similarity theory Things are different in long-lived SBLs situated immediately below the stably stratified free flow Here, the surface-layer turbulence is affected by the free-flow Brunt–Vaisala frequency, N The surface layer represents approximately one-tenth of the SBL, so that it is separated from the free atmosphere by the upper nine-tenths of the SBL comprising hundreds of metres Traditional concepts fail to explain such distant links Zilitinkevich and Calanca extended the traditional Monin–Obukhov similarity theory by including N in the surface-layer scaling, and provided experimental evidence in support of this extension In the present paper, physical mechanisms responsible for non-local features of the long-lived SBL turbulence are identified as: radiation of internal waves from the SBL upper boundary to the free atmosphere, and the internal-wave transport of the squared fluctuations of velocity and potential temperature The third-order wave-induced fluxes are included in an advanced turbulence-closure model to correct the wind and temperature profiles in the surface layer The model explains why developed turbulence in the surface layer can exist at much larger Richardson numbers than the classical theory predicts Results from the new model are in good agreement with the extended similarity theory and experimental data Copyright © 2002 Royal Meteorological Society

The boiling-water phenomena at Camarinal Sill, the strait of Gibraltar

Abstract: A detailed description of high-amplitude steady topographic internal waves recorded at Camarinal Sill during a survey on the R.V. “Investigador” is presented. These internal waves are generated during the maximum outflow (westward) stage of the tidal current and remain over the sill for more than 4 h until the outflow slackens, then being released towards the Mediterranean. Their amplitudes are comparable to the well-known internal bore of Camarinal Sill, occurring during maximum outflow during spring tides. However, they respond to a different physical origin and their spatial features are also quite different. In fact, the favourable hydraulic conditions for the generation of steady waves over the sill inhibit the internal bore generation, and vice versa. Analysis of the observations suggests that steady internal waves are the result of a resonant response of the stratified fluid over the sill to the forcing of the flow on the across-sill topography. An important consequence of the steady internal waves with clear biological implications is the significant mixing phenomena that are induced. Mixing is enabled by an enhancement of the shear at the trough together with a significant induced vertical advection.

Observations of Enhanced Diapycnal Mixing near the Hawaiian Ridge

Abstract: Profiles of potential density obtained from CTD casts at two stations at different distances from the Hawaiian ridge are examined for evidence of diapycnal turbulent mixing as indicated by density inversions and internalwave vertical strain. Results from independent casts are used to produce ensemble-averaged vertical distributions for the number of inversions and the Thorpe scale. Both parameters were found to be higher over the slope of the topography at 2500-m depth than in the deep ocean, 110 km to the north. Thorpe scale‐based estimates of the rate of dissipation of turbulent kinetic energy and turbulent vertical diffusivity are elevated by an order of magnitude over the slope relative to deep ocean background levels. The vertical distributions of these mixing parameters are nonuniform and exhibit signs of locally enhanced dissipation, possibly due to internal tides generated at the ridge. At the deep station, turbulence is at background levels from the surface down to 2000 m. Below this, a localized zone of enhanced mixing is observed, within which the dissipation rate is O(1029 W kg21) and turbulent diffusivity is greater than O(1024 m2 s 21), perhaps due to an internal tide ray originating at the ridge. The full-depth topographical enhancement of mixing near the ridge also appears in the vertical strain field. Estimates of dissipation rate and turbulent diffusivity, based on an internal wave‐wave interaction model, give results similar to direct Thorpe scale methods, except in weakly stratified environments where both methods are subject to uncertainty. Near the topography, the variation in mixing intensity observed between casts is sensitive to sporadic large mixing events, which are triggered by internal waves associated with the spring tide. The upper portion of the water column (stronger stratification) is more responsive to the tide than the deep regions.

On the breaking of internal solitary waves at a ridge

Abstract: An experimental laboratory study has been carried out to investigate the propagation of an internal solitary wave of depression and its distortion by a bottom ridge in a two-layer stratified fluid system. Wave profiles, density fields and velocity fields have been measured at three reference locations, namely upstream, downstream and over the ridge. Experiments have been performed with wave amplitudes in the range 0.2– 1.9 times the depth of the upper layer, and a ratio between the lower and the upper layer in the range 3.0–8.5. The ridge slope was varied from 0.1 to 0.33 and the maximum ridge height was two-thirds of the thicker fluid layer. Over the ridge, the flow has been classified into: (i) cases when the bottom ridge has little influence on the propagation and spatial structure of the internal solitary wave, (ii) cases where the internal solitary wave is significantly distorted by the blocking effect of the ridge (though no wave breaking occurs), and (iii) cases for which the internal solitary wave is broken as it encounters and passes over the bottom ridge. A detailed description of the processes leading to wave breaking is given. Breaking has been found to take place when the fluid velocity in the lower layer exceeds 0.7 of a local nonlinear wave speed, defined at the top of the ridge. The breaking condition is also expressed in terms of the amplitude of the incident wave, the layer thickness ratio and the relative height of the ridge. The wave breaking can be determined from the input parameters of the experiment. The transmitted waves have been found to always consist of a leading pulse (solitary wave) followed by a dispersive wavetrain. The (solitary) wave amplitude is significantly reduced only when breaking takes place at the ridge. Internal waves of mode two are generated in cases with strong breaking.

Observations of the internal tide and associated mixing across the Malin Shelf

Abstract: [1] An energetic internal tide was observed at two contrasting shelf continental sites to the west of Scotland. The first site was 5 km shoreward of the continental shelf break, and the second was 45 km directly to the east of the first site. Each site was instrumented with a seabed mounted acoustic Doppler current profiler and thermistor chain for a 2 week period in July 1996, when thermal stratification was well developed. In addition to the measurements of the evolution of the water column structure and flow field, two series of measurements of the rate of dissipation of turbulent kinetic energy were made at each of the sites. The barotropic tide was found to contain an unusually strong diurnal component, thought to be due to a coastally trapped wave; as a result, there is a significant diurnal component to the baroclinic energy spectra. Significant peaks are also present in the baroclinic energy spectra at interaction frequencies between the main semidiurnal (M2) and diurnal (K1) tidal constituents at both sites. Observations of profiles of the rate of dissipation of turbulent kinetic energy show a significant proportion of the measured rate of dissipation took place within the thermocline. Close to the shelf edge, detailed observations of a hydraulic jump and nonlinear internal waves are analyzed to show significantly stronger mixing at this site (characterized by diffusion coefficients of 1.6 and 6.1 × 10−4 m2 s−1) than at the site farther onshore (where the diffusion coefficient is estimated to be 0.7 × 10−4 m2 s−1).

On the nature of internal wave spectra near a continental slope

Abstract: [1] Amongst the most energetic motions in the deep ocean are internal waves supported by stable vertical stratification in density. Previously, these waves were considered freely propagating as described by a smooth continuum internal wave band (IWB) frequency spectrum. We studied details of the IWB using yearlong current observations from the Bay of Biscay. Instead of observing continuum IWB spectra near a continental slope, we show that (at least) the first half-decade of the IWB is dominated by motions at localized frequencies determined by strong non-linear interactions between waves at the fundamental semidiurnal tidal and atmospherically induced inertial frequencies.

Aspects of Deep Ocean Mixing

Abstract: The turbulent motions responsible for ocean mixing occur on scales much smaller than those resolved in numerical simulations of oceanic flows. Great progress has been made in understanding the sources of energy for mixing, the mechanisms, and the rates. On the other hand, we still do not have adequate answers to first order questions such as the extent to which the thermohaline circulation of the ocean, and hence the earth's climate, is sensitive to the present mixing rates in the ocean interior. Internal waves, generated by either wind or flow over topography, appear to be the principle cause of mixing. Mean and eddy flows over topography generate internal lee waves, while tidal flows over topography generate internal tides. The relative importance of these different internal wave sources is unknown. There are also great uncertainties about the spatial and temporal variation of mixing. Calculations of internal tide generation are becoming increasingly robust, but we do not know enough about the subsequent behavior of internal tides and their eventual breakdown into turbulence. It does seem, however, that most internal tide energy flux is radiated away from generation sites as low modes that propagate over basin scales. The mechanisms of wave-wave interaction and topographic scattering both act to transfer wave energy from low modes to smaller dissipative scales.

Internal gravity wave emission from a pancake vortex: An example of wave–vortex interaction in strongly stratified flows

Abstract: At small Froude numbers the motion of a stably stratified fluid consists of a quasisteady vortical component and a propagating wave component. The vortical component is organized into layers of horizontal motions with well-pronounced vertical vorticity and often takes the form of so-called “pancake” vortices. An analytical model of such a vortex that is a solution of the Euler–Boussinesq equations at a vanishing Froude number is constructed as a superposition of horizontal two-dimensional Kirchhoff elliptic vortices. This vortex is nonstationary and internal gravity waves are, therefore, excited by its motion. The radiation properties are studied by matching the vortex field with the far internal gravity wave field according to the procedure applied in acoustics to determine vortex sound. The structure of the gravity wave field is completely quantified. By calculating energy and angular momentum fluxes carried by outgoing waves and attributing them to the adiabatic change of the vortex parameters, we calculate the backreaction of the internal gravity waves radiation and show that, as in the case of acoustic radiation by the Kirchhoff vortex, this adiabatic evolution leads to an elongation of the vortex, and its eventual destabilization.