Showing papers on "Internal wave published in 2007"

Internal Tide Generation in the Deep Ocean

Abstract: Internal tides are internal gravity waves generated in stratified waters by the interaction of barotropic tidal currents with variable bottom topography. They play a role in dissipating tidal energy and lead to mixing in the deep ocean. Key dimensionless parameters governing their generation include the tidal excursion compared with the scale of the topography, the bottom slope compared with the angle at which rays of internal waves of tidal frequency propagate, and the height of the topography compared with the depth of the ocean. Recent theoretical developments for parts of this parameter space particularly relevant to the deep ocean show that most of the energy flux is associated with low modes that propagate away from the generation region. For isolated features this energy flux is not strongly dependent on the bottom slope. Intense beams of internal tidal energy are expected near “critical slopes," bottom slopes equal to the ray slope, and lead to local mixing.

Direct numerical simulations of two- and three-dimensional turbulent natural convection flows in a differentially heated cavity of aspect ratio 4

Abstract: A set of complete two- and three-dimensional direct numerical simulations (DNS) in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is presented in this paper. Although the physical phenomenon is three-dimensional, owing to its prohibitive computational costs the majority of the previous DNS of turbulent and transition natural convection flows in enclosed cavities assumed a two-dimensional behaviour. The configurations selected here (Rayleigh number based on the cavity height 6.4 ×10 8 , 2×10 9 and 10 10 , Pr=0.71) are an extension to three dimensions of previous two-dimensional problems. An overview of the numerical algorithm and the methodology used to verify the code and the simulations is presented. The main features of the flow, including the time-averaged flow structure, the power spectra and probability density distributions of a set of selected monitoring points, the turbulent statistics, the global kinetic energy balances and the internal waves motion phenomenon are described and discussed. As expected, significant differences are observed between two- and three-dimensional results. For two-dimensional simulations the oscillations at the downstream part of the vertical boundary layer are clearly stronger, ejecting large eddies to the cavity core. In the three-dimensional simulations these large eddies do not persist and their energy is rapidly passed down to smaller scales of motion. It yields on a reduction of the large-scale mixing effect at the hot upper and cold lower regions and consequently the cavity core still remains almost motionless even for the highest Rayleigh number. The boundary layers remain laminar in their upstream parts up to the point where these eddies are ejected. The point where this phenomenon occurs clearly moves upstream for the three-dimensional simulations. It is also shown that, even for the three-dimensional simulations, these eddies are large enough to permanently excite an internal wave motion in the stratified core region. All these differences become more marked for the highest Rayleigh number.

Energy Transport by Nonlinear Internal Waves

Abstract: Wintertime stratification on Oregon’s continental shelf often produces a near-bottom layer of densefluid that acts as an internal waveguide on which nonlinear internal waves propagate. Shipboard profiling and bottom lander observations capture disturbances that exhibit properties of internal solitary waves, bores and gravity currents. Wave-like pulses are highly turbulent (instantaneous bed stresses are 1 N m 2 ), resuspending bottom sediments into the water column and raising them 30 + m above the seafloor. The waves’ cross-shelf transport of fluid counters the time-averaged Ekman transport in the bottom boundary layer. In the nonlinear internal waves we have observed, the kinetic energy is roughly equal to the available potential energy and is O(0.1) MJ per m of coastline. The energy transported by these waves includes a nonlinear advection term huEi that is negligible in linear internal waves. Unlike linear internal waves, the pressure-velocity energy flux hupi includes important contributions from nonhydrostatic effects and surface displacement. It is found that, statistically, huEi ’ 2hupi. Vertical profiles indicate that up(z) is more important in transporting energy near the seafloor while uE(z) dominates farther from the bottom. With the wave speed, c, estimated from weakly nonlinear wave theory it is verified experimentally that the total energy transported by the waves, hupi + huEi ’ chEi. The high but intermittent energyflux by the waves is, in an averaged sense, O(100) W per m of coastline. This is similar to independent estimates of the shoreward energy flux in the semidiurnal internal tide at the shelfbreak.

Statistical and dynamical analyses of generation mechanisms of solitary internal waves in the northern South China Sea

Abstract: [1] This study analyzes the effects of thermocline shoaling on the ocean internal wave (IW) generation in the north South China Sea (NSCS). Seven years of satellite synthetic aperture radar (SAR) images from 1995 to 2001 are used for the statistical analysis of IW occurrence, and field measurements of sea surface wind, sea state, and vertical temperature profiles are used for analyzing IW generation and SAR imaging conditions. Latitudinal distribution of IW packets shows that 22% of IW packets distributed in the east of 118E obviously originate from the Luzon Strait, and 78% of IW packets west of 118E may propagate from the east or evolve into the solitons originating from the east boundary owing to the fission effect of shoaling thermocline. The yearly distribution of IW occurrence frequencies reveals an interannual variability, implying that there are long-term and large-scale processes modifying the SAR-observed IW occurrence. The monthly SAR-observed IWoccurrence frequencies show that the high frequencies are distributed from April to July and reach a peak in June with a maximum frequency of 20%. The low occurrence frequencies are distributed in winter from December to February of next year with a minimum frequency of 1.5% in February. This study proposes that the IW generation needs the necessary and sufficient conditions: initial disturbance formation and wave amplitude growth. Owing to the dissipation effect on the initial disturbance, only fully grown waves have a chance to radiate out of the source region. A physical model and PKdVequation are adopted for analyzing the sufficient conditions for solitary IW amplitude growth. The results indicate that the thermocline shoaling provides the forcing to soliton amplitude growth, so that the soliton amplitude growth ratio (SAGR) serves as a decisive factor for the IW occurrence frequency. Theoretical analysis predicts a linear relation between the two. Application of theoretical models to field measurements in the Luzon Strait gives a correlation coefficient as high as 0.845 with a confidence level of 99% for months from March to November. The linear regression gives a correlation coefficient (R 2 ) of 0.6519 and a SAGR threshold (minimum) value of

Physical and ecological processes of internal waves on an isolated reef ecosystem in the South China Sea

Abstract: [1] Field measurements at Dongsha Atoll in the northern South China Sea showed frequent drops in daily water temperature up to 8°C during intrusions of large nonlinear internal waves. The internal waves had a period of about 4 hours and velocity amplitude of 0.3 m s−1. Large variations of dissolved oxygen were observed a week after cold-water intrusion, which was followed in another 2 days by a significant increase of chlorophyll content. The 7–8-day delay suggests that phytoplankton blooms occurred after the nutrients were released through microbial decomposition of organics brought up by the internal waves. This study highlights the effects of internal waves and the possible role of the microbial food web on nutrient regeneration in a tropical reef ecosystem.

Internal waves across the Pacific

Abstract: [1] The long-range propagation of the semidiurnal internal tide northward from the Hawaiian ridge and its susceptibility to parametric subharmonic instability (PSI) at the “critical latitude,” λc = 28.8°N, were examined in spring 2006 with intensive shipboard and moored observations spanning 25–37°N along a tidal beam. Velocity and shear at λc were dominated by intense vertically-standing, inertially-rotating bands of several hundred meters vertical wavelength. These occurred in bursts following spring tide, contrasting sharply with the downward-propagating, wind-generated features seen at other latitudes. These marginally-stable layers (which have inverse 16-meter Richardson number Ri16−1 = 0.7) are interpreted as the inertial waves resulting from PSI of the internal tide. Elevated near-inertial energy and parameterized diapycnal diffusivity, and reduced asymmetry in upgoing/downgoing energy, were also observed at and equatorward of λc. Yet, simultaneous moored measurements of semidiurnal energy flux and 1-km-deep velocity sections measured from the ship indicate that the internal tide propagates at least to 37°N, with no detectable energy loss or phase discontinuity at λc. Our observations indicate that PSI occurs in the ocean with sufficient intensity to substantially alter the inertial shear field at and equatorward of λc, but that it does not appreciably disrupt the propagation of the tide at our location.

Highly resolved self-excited density waves in a complex plasma.

Abstract: Experimental results on self-excited density waves in a complex plasma are presented. An argon plasma is produced in a capacitively coupled rf discharge at a low power and gas pressure. A cloud of microparticles is subjected to effective gravity in the range of 1-4 g by thermophoresis. The cloud is stretched horizontally (width/height approximately 45 mm/8 mm). The critical pressure for the onset of the waves increases with the temperature gradient. The waves are propagating in the direction of the ion drift. The wave frequency, phase velocity, and wavelength are measured, and particle migrations affected by the waves are analyzed at a time scale of 1 ms/frame and a subpixel space resolution.

Hotspots of deep ocean mixing on the Oregon continental slope

Abstract: [1] Two deep ocean hotspots of turbulent mixing were found over the Oregon continental slope. Thorpe-scale analyses indicate time-averaged turbulent energy dissipation rates of e > 10−7 W/kg and eddy diffusivities of Kρ ∼ 10−2 m2/s at both hotspots. However, the structure of turbulence and its generation mechanism at each site appear to be different. At the 2200-m isobath, sustained >100-m high turbulent overturns occur in stratified fluid several hundred meters above the bottom. Turbulence shows a clear 12.4-h periodicity proposed to be driven by flow over a nearby 100-m tall ridge. At the 1300-m isobath, tidally-modulated turbulence of similar intensity is confined within a stratified bottom boundary layer. Along-slope topographic roughness at scales not resolved in global bathymetric data sets appears to be responsible for the bulk of the turbulence observed. Such topography is common to most continental slopes, providing a mechanism for turbulence generation in regions where barotropic tidal currents are nominally along-isobath.

Modelling Internal Solitary Waves in the Coastal Ocean

Abstract: In the coastal oceans, the interaction of currents (such as the barotropic tide) with topography can generate large-amplitude, horizontally propagating internal solitary waves. These waves often occur in regions where the waveguide properties vary in the direction of propagation. We consider the modelling of these waves by nonlinear evolution equations of the Korteweg–de Vries type with variable coefficients, and we describe how these models are used to describe the shoaling of internal solitary waves over the continental shelf and slope. The theories are compared with various numerical simulations.

Convection waves: Observations of gravity wave systems over convectively active boundary layers

Abstract: Widespread gravity wave systems have been found to exist over convectively active boundary layers (CBLs) in the presence of vertical wind shear. In contrast to mountain waves, these ‘convection waves’ occur over flat terrain and are ubiquitous over fields of shallow fair weather cumuli or clear air thermals. They extend vertically to at least 9km a.m.s.l., probably to the tropopause. First discovered by glider pilots as ‘thermal waves’, they have now been systematically investigated by research aircraft during the NCAR Convection Wave Project, which also incorporates an effort in numerical simulation. the flight results are reported in this paper, while the numerical simulations are described in a companion paper. Typical wavelengths of convection waves were found to range from 5 to 15 km, (average 9 km) and typical vertical motion amplitudes from ± 1 to ± 3 m s−1. In all cases vertical wind shear exceeded 3×10−3s−1. Under these conditions cloud tops were measured to move with relative velocities of 8 to 10 m s−1 against their environment, hence they present an obstacle to the surrounding airflow. the analogy to mountainous obstacles launching gravity waves into the atmosphere is suggestive and borne out by the aforementioned numerical simulations, which describe this process step by step. The interaction between the CBL and the overlying stable layers is studied by spectral and cross-spectral analysis of aircraft data including coherence and phase relations between wave motions and cloud population underneath. Consideration is given to other potential sources of the observed gravity waves. At this stage the conclusions of our pilot study may be considered tentative. Some implications for further research are also discussed.

Global Patterns of Low-Mode Internal-Wave Propagation. Part I: Energy and Energy Flux

Abstract: Extending an earlier attempt to understand long-range propagation of the global internal-wave field, the energy E and horizontal energy flux F are computed for the two gravest baroclinic modes at 80 historical moorings around the globe With bandpass filtering, the calculation is performed for the semidiurnal band (emphasizing M2 internal tides, generated by flow over sloping topography) and for the near-inertial band (emphasizing wind-generated waves near the Coriolis frequency) The time dependence of semidiurnal E and F is first examined at six locations north of the Hawaiian Ridge; E and F typically rise and fall together and can vary by over an order of magnitude at each site This variability typically has a strong spring–neap component, in addition to longer time scales The observed spring tides at sites northwest of the Hawaiian Ridge are coherent with barotropic forcing at the ridge, but lagged by times consistent with travel at the theoretical mode-1 group speed from the ridge Phase c

Anelastic and Compressible Simulations of Stellar Oxygen Burning

Abstract: In this paper we compare fully compressible (Meakin & Arnett 2006, 2007 ) and anelastic (Kuhlen et al. 2003) simulations of stellar oxygen shell burning. It is found that the two models are in agreement in terms of the velocity scale (vc ~ 107 cm s-1) and thermodynamic fluctuation amplitudes (e.g., ρ'/ρ ~ 2 × 10-3) in the convective flow. Large fluctuations (~11%) arise in the compressible model, localized to the convective boundaries, and are due to internal waves excited in stable layers. Fluctuations on the several percent level are also present in the compressible model due to composition inhomogeneities from ongoing entrainment events at the convective boundaries. Comparable fluctuations (with amplitudes greater than ~1%) are absent in the anelastic simulation, because they are due to physics not included in that model. We derive an analytic estimate for the expected density fluctuation amplitudes at convective boundaries by assuming that the pressure fluctuations due to internal waves at the boundary, p, balance the ram pressure of the convective motions, ρv. The predicted amplitudes agree well with the simulation data. The good agreement between the anelastic and the compressible solution within the convection zone and the agreement between the stable layer dynamics and analytic solutions to the nonradial wave equation indicate that the compressible hydrodynamic techniques used are robust for the simulated stellar convection model, even at the low Mach numbers found, M ~ 0.01.

Observed Oceanic Response over the Upper Continental Slope and Outer Shelf during Hurricane Ivan

Abstract: Hurricane Ivan passed directly over an array of 14 acoustic Doppler current profilers deployed along the outer continental shelf and upper slope in the northeastern Gulf of Mexico. Currents in excess of 200 cm s−1 were generated during this hurricane. Shelf currents followed Ekman dynamics with overlapping surface and bottom layers during Ivan’s approach and transitioned to a dominant surface boundary layer as the wind stress peaked. Slope currents at the onset of Ivan were wind driven near the surface, but deeper in the water column they were dominated during and after the passage of Ivan by subinertial waves with a period of 2–5 days that had several characteristics of topographic Rossby waves. Currents on the slope at 50 m and greater depths commonly exceeded 50 cm s−1. Surprisingly, the strongest currents were present to the left of the storm track on the shelf while more energetic currents were to the right of the hurricane path on the slope during the forced stage. Near-inertial motion last...

On the extreme statistics of long‐crested deep water waves: Theory and experiments

Abstract: [1] Quasi-resonant four-wave interactions may influence the statistical properties of deep water long-crested surface gravity waves. As a consequence, the wave height exceedance probability can substantially deviate from the expected distribution obtained by assuming that waves are linear. Here the occurrence probability of extreme events recently derived by N. Mori and P. Janssen (2006) is compared with wave tank data, where strong departures from Gaussian behavior are observed. Experimental wave height, maximum wave height distribution, and probability of occurrence of freak waves are compared with theoretical expectations. The theory well predicts extreme waves in nonlinear wavefields.

Assessing the West Ridge of Luzon Strait as an Internal Wave Mediator

Abstract: The Luzon Strait is blocked by two meridional ridges at depths, with the east ridge somewhat higher than the west ridge in the middle reaches of the Strait. Previous numerical models identified the Luzon Strait as the primary generation site of internal M2 tides entering the northern South China Sea (Niwa and Hibiya, 2004), but the role of the west-versus-east ridge was uncertain. We used a hydrostatic model for the northern South China Sea and a nonhydrostatic, process-oriented model to evaluate how the west ridge of Luzon Strait modifies westward propagation of internal tides, internal bores and internal solitary waves. The dynamic role of the west ridge depends strongly on the characteristics of internal waves and is spatially inhomogeneous. For M2 tides, both models identify the west ridge in the middle reaches of Luzon Strait as a dampener of incoming internal waves from the east ridge. In the northern Luzon Strait, the west ridge is quite imposing in height and becomes a secondary generation site for M2 internal tides. If the incoming wave is an internal tide, previous models suggested that wave attenuation depends crucially on how supercritical the west ridge slope is. If the incoming wave is an internal bore or internal solitary wave, our investigation suggests a loss of sensitivity to the supercritical slope for internal tides, leaving ridge height as the dominant factor regulating the wave attenuation. Mechanisms responsible for the ridge-induced attenuation are discussed.

Evolution of a shoaling internal solitary wavetrain

Abstract: [1] Field observations of an internal solitary wavetrain impacting a shoaling bottom are presented. Measurements of the spatio-temporal characteristics of the shoaling waves are given, as well as estimations of the mixing they may have caused upon impact. The observations are discussed in the context of numerical simulations, laboratory experiments, and hypotheses recently raised on the origin and evolution of internal solitary waves in coastal environments.

Decay and return of internal solitary waves with rotation

Abstract: The effect of rotation on the propagation of internal solitary waves is examined. Wave evolution is followed using a new rotating extension of a fully nonlinear, weakly nonhydrostatic theory for waves in a two-layer system. When a solitary wave solution of the nonrotating equations is used as the initial condition, the wave initially decays by radiation of longer inertia-gravity waves. The radiated inertia-gravity wave always steepens, leading to the formation a secondary solitary-like wave. This decay and reemergence process then repeats. Eventually, a nearly localized wave packet emerges. It consists of a long-wave envelope and shorter, faster solitary-like waves that propagate through the envelope. The radiation from this mature state is very weak, leading to a robust, long-lived structure that may contain as much as 50% of the energy in the initial solitary wave. Interacting packets may either pass through one another, or merge to form a longer packet. The packets appear to be modulated, fully nonline...

Boundary mixing in the thermocline of a large lake

Abstract: [1] High-resolution measurements of near-bottom temperature stratification and current velocity were performed on the sloping boundary of a large lake at the depth of the seasonal thermocline. The measurements cover nearly the entire stratified period and reveal the periodic occurrence of strong temperature and current velocity fluctuations, which can be attributed to shoaling high-frequency internal waves with periods between 5 and 20 min. Two different techniques are applied to obtain a long-term record of dissipation rates of turbulent kinetic energy from the current velocity measurements. Shoaling of high-frequency internal waves is associated with a strong and rapid increase of turbulent dissipation rates of up to four orders of magnitude. Since the occurrence of high-frequency internal waves on the slope is correlated with the passage of the dominant basin-scale internal Kelvin wave with a period of four days, energy dissipation rates on the slope vary with the same period. Diapycnal diffusivities, estimated by combining the dissipation estimates with simultaneously measured density stratification, follow a similar dynamics and a comparison with a basin-scale diffusivity estimate based on tracer measurements reveal the importance of boundary mixing, which, at this particular site, is mainly driven by the interaction of high-frequency internal waves with the sloping boundary.

Simultaneous synthetic schlieren and PIV measurements for internal solitary waves

Abstract: Large-amplitude internal solitary waves in a stratification comprising a thick, lower, homogeneous layer separated from a thin, upper, homogeneous layer by a broad gradient region are studied using simultaneous measurements of the density and velocity fields. Density field measurements are achieved through synthetic schlieren, operating in an absolute mode to allow efficient and accurate measurements of density in systems with strong curvatures and large perturbations to the density field. The images used for these density measurements are interleaved with images used for particle image velocimetry by phase locking two video cameras (one configured for the density measurements and the other for the velocity measurements) with a computer-driven LCD monitor, allowing the background texture required for synthetic schlieren to be turned off for the particle image velocimetry measurements on the mid-plane of the experimental tank. The simultaneous measurements of both density and velocity fields not only allow greater insight into the internal wave dynamics, but also allow the velocity measurements to be corrected for the normal errors associated with the refractive index variations. As an illustration of the power of this technique, we determine for the first time in an internal solitary wave the spatial structure of the local gradient Richardson number, finding regions where this falls below the limit for linear stability.

Intense mixing of lower thermocline water on the crest of the Mid-Atlantic Ridge.

Abstract: Buoyancy exchange between the deep and the upper ocean, which is essential for maintaining global ocean circulation, mainly occurs through turbulent mixing This mixing is thought to result primarily from instability of the oceanic internal wave field, but internal waves tend to radiate energy away from the regions in which they are generated rather than dissipate it locally as turbulence and the resulting distribution of turbulent mixing remains unknown Another, more direct, mixing mechanism involves the generation of turbulence as strong flows pass through narrow passages in topography, but the amount of turbulence generated at such locations remains poorly quantified owing to a lack of direct measurements Here we present observations from the crest of the Mid-Atlantic Ridge in the subtropical North Atlantic Ocean that suggest that passages in rift valleys and ridge-flank canyons provide the most energetic sites for oceanic turbulence Our measurements show that diffusivities as large as 003 m2 s(-1) characterize the mixing downstream of a sill in a well-stratified boundary layer, with mixing levels remaining of the order of 10(-4) m2 s(-1) at the base of the main thermocline These mixing rates are significantly higher than the diffusivities of the order of 10(-5) m2 s(-1) that characterize much of the global thermocline and the abyssal ocean Our estimates suggest that overflows associated with narrow passages on the Mid-Atlantic Ridge in the North Atlantic Ocean produce as much buoyancy flux as has previously been estimated for the entire Romanche fracture zone, a large strait in the Mid-Atlantic Ridge that connects the North and South Atlantic basins This flux is equivalent to the interior mixing that occurs in the entire North Atlantic basin at the depth of the passages, suggesting that turbulence generated in narrow passages on mid-ocean ridges may be important for buoyancy flux at the global scale

The role of surface vertical mixing in phytoplankton distribution in a stratified reservoir

Abstract: We investigated convection caused by surface cooling and mixing attributable to wind shear stress and their roles as agents for the transport of phytoplankton cells in the water column by carrying out two daily surveys during the stratified period of the Sau reservoir. Green algae, diatoms, and cryptophyceae were the dominant phytoplankton communities during the surveys carried out in the middle (July) and end (September) of the stratified period. We show that a system with a linear stratification and that is subject to weak surface forcing, with weak winds , 4ms 21 and low energy dissipation rate values of the order of 10 28 m 2 s 23 or lower, enables the formation of thin phytoplankton layers. These layers quickly disappear when water parcels mix because there is a medium external forcing (convection) induced by the night surface cooling, which is characterized by energy dissipation rates on the order of ,5 3 1028 m2 s23. During both surveys the wind generated internal waves during the entire diurnal cycle. During the day, and because of the weak winds, phytoplankton layers rise in the water column up to a depth determined by both solar heating and internal waves. In contrast, during the night phytoplankton mixes down to a depth determined by both convection and internal waves. These internal waves, together with the wind-driven current generated at the surface, seem to be the agents responsible for the horizontal transport of phytoplankton across the reservoir.

Three‐dimensional shoaling of large‐amplitude internal waves

Abstract: [1] The three-dimensional (3-D) shoaling of large-amplitude internal waves (LAIW) is studied in the framework of a fully nonlinear nonhydrostatic numerical model. The vertical fluid stratification, parameters of the propagating waves and bottom topography were taken close to those observed in the northern part of the Andaman Sea. It was found that three-dimensional evolution of LAIWs propagating from the deep part of a basin onto the shelf differs from two-dimensional shoaling in many ways largely because of the process of wave refraction developing in the areas of local bottom elevations or depressions. In the 3-D case the wave refraction produces concave and convex fragments of the wave fronts which may lead to the transverse redistribution of energy along the wave. Results demonstrate that concave wave fragments work as optical lenses focusing the wave energy to the centers of curvature. This process is especially important for LAIWs in shallow water zones where wave amplitudes are close to the saturation level. In general, the wave refraction leads to more fast wave breaking than that in the 2-D case. As a results, it should be expected to find localized regions of higher levels of water mixing and turbulence in the vicinity of local banks and headlands where LAIWs produce concave patterns. The areas of local bottom depressions, on the contrary, should be considered as potential places with lower level of background mixing.

Internal gravity waves generated by a turbulent bottom Ekman layer

Abstract: Internal gravity waves excited by the turbulent motions in a bottom Ekman layer are examined using large-eddy simulation. The outer flow is steady and uniformly stratified while the density gradient is set to zero at the flat lower wall. After initializing with a linear density profile, a mixed layer forms near the wall separated from the ambient stratification by a pycnocline. Two types of internal wave are observed. Waves with frequencies larger than the free-stream buoyancy frequency are seen in the pycnocline, and vertically propagating internal waves are observed in the outer layer with characteristic frequency and wavenumber spectra. Since a signature of the pycnocline waves is observed in the frequency spectrum of the mixed layer, these waves may affect the boundary-layer turbulence. The dominant outer-layer waves have a group velocity directed 35-60° from the vertical axis, which is consistent with previous laboratory studies. The energy flux associated with the radiated waves is small compared to the integrated dissipation in the boundary layer, but is of the same order as the integrated buoyancy flux. A linear model is proposed to estimate the decay in wave amplitude owing to viscous effects. Starting from the observed wave amplitudes at the bottom of the pycnocline, the model prediction for the spectral distribution of the outer layer wave amplitude compares favourably with the simulation results.

Laboratory experiments on the generation of internal tidal beams over steep slopes

Abstract: We designed a simple laboratory experiment to study internal tides generation. We consider a steep continental shelf, for which the internal tide is shown to be emitted from the critical point, which is clearly amphidromic. We also discuss the dependence of the width of the emitted beam on the local curvature of topography and on viscosity. Finally, we derive the form of the resulting internal tidal beam by drawing an analogy with an oscillating cylinder in a static fluid.

Stratified turbulence forced in rotational and divergent modes

Abstract: We perform numerical box simulations of strongly stratified turbulence. The equations solved are the Boussinesq equations with constant Brunt-Vaisala frequency and forcing either in rotational or divergent modes, or, with another terminology, in vortical or wave modes. In both cases, we observe a forward energy cascade and inertial-range scaling of the horizontal kinetic and potential energy spectra. With forcing in rotational modes, there is approximate equipartition of kinetic energy between rotational and divergent modes in the inertial range. With forcing in divergent modes the results are sensitive to the vertical forcing wavenumber K-v(f) If k(v)(f) is sufficiently large the dynamics is very similar to the dynamics of the V V simulations which are forced in rotational modes, with approximate equipartition of kinetic energy in rotational and divergent modes in the inertial range. Frequency spectra of rotational, divergent and potential energy are calculated for individual Fourier modes. Waves are present at low horizontal wavenumbers corresponding to the largest scales in the boxes. In the inertial range, the frequency spectra exhibit no distinctive peaks in the internal wave frequency. In modes for which the vertical wavenumber is considerably larger than the horizontal wavenumber, the frequency spectra of rotational and divergent modes fall on top of each other. The simulation results indicate that the dynamics of rotational and divergent modes develop on the same time scale in stratified turbulence. We discuss the relevance of our results to atmospheric and oceanic dynamics. In particular, we review a number of observational reports indicating that stratified turbulence may be a prevalent dynamic process in the ocean at horizontal scales of the order of 10 or 100m up to several kilometres.

Experimental study of internal gravity waves generated by supercritical topography

Abstract: Oscillatory tides flowing over rough topography on the ocean floor generate internal gravity waves, which are a major source of ocean mixing. Linear inviscid theory can describe waves generated by gentle topography with slopes that are less steep than the propagation angle of the internal waves; such topography is termed subcritical. However, a clear physical picture of internal waves generated by topography with slopes steeper than the angle of internal waves (supercritical topography) is lacking. In this paper we present an experimental study at Reynolds number ∼O(100) of internal gravity waves generated by a circular cylinder that oscillates horizontally (at a frequency Ω), thus mimicking barotropic tidal flow over bottom topography. Fundamental waves of frequency Ω emanate from locations on the cylinder where the topographic slope equals the slope of internal waves. For small oscillating amplitude A (weak forcing), our experimental results compare well with predictions of the viscous linear theory of ...