Showing papers on "Internal wave published in 2008"

Oceanic Rogue Waves

Abstract: Oceanic rogue waves are surface gravity waves whose wave heights are much larger than expected for the sea state. The common operational definition requires them to be at least twice as large as the significant wave height. In most circumstances, the properties of rogue waves and their probability of occurrence appear to be consistent with second-order random-wave theory. There are exceptions, although it is unclear whether these represent measurement errors or statistical flukes, or are caused by physical mechanisms not covered by the model. A clear deviation from second-order theory occurs in numerical simulations and wave-tank experiments, in which a higher frequency of occurrence of rogue waves is found in long-crested waves owing to a nonlinear instability.

Geophysical and astrophysical fluid dynamics beyond the traditional approximation

Abstract: [1] In studies on geophysical fluid dynamics, it is common practice to take the Coriolis force only partially into account by neglecting the components proportional to the cosine of latitude, the so-called traditional approximation (TA). This review deals with the consequences of abandoning the TA, based on evidence from numerical and theoretical studies and laboratory and field experiments. The phenomena most affected by the TA include mesoscale flows (Ekman spirals, deep convection, and equatorial jets) and internal waves. Abandoning the TA produces a tilt in convective plumes, produces a dependence on wind direction in Ekman spirals, and gives rise to a plethora of changes in internal wave behavior in weakly stratified layers, such as the existence of trapped short low-frequency waves, and a poleward extension of their habitat. In the astrophysical context of stars and gas giant planets, the TA affects the rate of tidal dissipation and also the patterns of thermal convection.

Direct Breaking of the Internal Tide near Topography: Kaena Ridge, Hawaii

Abstract: Barotropic to baroclinic conversion and attendant phenomena were recently examined at the Kaena Ridge as an aspect of the Hawaii Ocean Mixing Experiment. Two distinct mixing processes appear to be at work in the waters above the 1100-m-deep ridge crest. At middepths, above 400 m, mixing events resemble their open-ocean counterparts. There is no apparent modulation of mixing rates with the fortnightly cycle, and they are well modeled by standard open-ocean parameterizations. Nearer to the topography, there is quasi-deterministic breaking associated with each baroclinic crest passage. Large-amplitude, small-scale internal waves are triggered by tidal forcing, consistent with lee-wave formation at the ridge break. These waves have vertical wavelengths on the order of 400 m. During spring tides, the waves are nonlinear and exhibit convective instabilities on their leading edge. Dissipation rates exceed those predicted by the open-ocean parameterizations by up to a factor of 100, with the disparity in...

Internal Hydraulic Jumps and Overturning Generated by Tidal Flow over a Tall Steep Ridge

Abstract: Recent observations from the Hawaiian Ridge indicate episodes of overturning and strong dissipation coupled with the tidal cycle near the top of the ridge. Simulations with realistic topography and stratification suggest that this overturning has its origins in transient internal hydraulic jumps that occur below the shelf break at maximum ebb tide, and then propagate up the slope as internal bores when the flow reverses. A series of numerical simulations explores the parameter space of topographic slope, barotropic velocity, stratification, and forcing frequency to identify the parameter regime in which these internal jumps are possible. Theoretical analysis predicts that the tidally driven jumps may occur when the vertical tidal excursion is large, which is shown to imply steep topographic slopes, such that dh/dxN/ω > 1. The vertical length scale of the jumps is predicted to depend on the flow speed such that the jump Froude number is of order unity. The numerical results agree with the theoreti...

Reflexion and Diffraction of Internal Waves analyzed with the Hilbert Transform

Abstract: We apply the Hilbert transform to the physics of internal waves in two-dimensional fluids. Using this demodulation technique, we can discriminate internal waves propagating in different directions: this is very helpful in answering several fundamental questions in the context of internal waves. We focus more precisely in this paper on phenomena associated with dissipation, diffraction and reflection of internal waves.

Reflection and diffraction of internal waves analyzed with the Hilbert transform

Abstract: We apply the Hilbert transform to the physics of internal waves in two-dimensional fluids. Using this demodulation technique, we can discriminate internal waves propagating in different directions: This is very helpful in answering several fundamental questions in the context of internal waves. We focus more precisely in this paper on phenomena associated with dissipation, diffraction, and reflection of internal waves.

Global distribution of atmospheric waves in the equatorial upper troposphere and lower stratosphere: COSMIC observations of wave mean flow interactions

Abstract: [1] Temperature profiles derived from Constellation Observing System for Meteorology, Ionosphere and Climate Global Positioning System Radio Occultation satellite constellation data are used to study equatorial gravity wave potential energy associated with waves having vertical wavelengths of less than 7 km and their interaction with the background quasi-biennial oscillation (QBO) wind. The data are binned into grids of size 20° in longitude and 5° in latitude. Results show evidence of vertically propagating convectively generated gravity waves interacting with the background mean flow. Enhancements in potential energy around the descending 0 m s−1 QBO eastward shear phase line are observed. Equatorially trapped Kelvin waves and Mixed Rossby Gravity Waves with zonal wave numbers s ≤ 9 are obtained by bandpass filtering wave number-frequency temperature spectra. Their temporal, spatial and vertical structures, propagation and wave-mean flow interactions are examined with respect to the background mean flow. Equatorial waves observed by COSMIC are compared with those seen in OLR data, with differences discussed.

Internal tides and vertical mixing over the Kerguelen Plateau

Abstract: Within the context of the natural iron-fertilization study KEOPS, time series measurements of CTD and LADCP profiles at a site (50.6°S, 72°E; 528 m) coinciding with an annual phytoplankton bloom over the Kerguelen Plateau were made during the January–February 2005 KEOPS cruise. An important activity of highly nonlinear semidiurnal internal tides having peak-to-peak isopycnal displacements of up to 80 m is identified. These internal tides appear to be a principal agent for promoting elevated vertical mixing indispensable for upward transfer of iron within the seasonal thermocline. We estimate local vertical eddy diffusivities of the order of 4×10?4 m2 s?1 using a Thorpe scale analysis. Although this estimate is higher by an order of magnitude than the canonical value O (0.1×10?4 m2 s?1) in the open ocean away from boundaries, it is consistent with nonlinear internal wave/wave interaction theories, as verified by independent diffusivity estimates using the vertical wavenumber spectral methods for shear and strain. It is also suggested that the general ocean circulation may play an important role in preconditioning the bloom in that the relatively sluggish circulation over the shallow plateau (compared to the much more dynamic neighbouring deep ocean) may foster the bloom's observed annual recurrence over the plateau.

Nonlinear Disintegration of the Internal Tide

Abstract: The disintegration of a first-mode internal tide into shorter solitary-like waves is considered. Since observations frequently show both tides and waves with amplitudes beyond the restrictions of weakly nonlinear theory, the evolution is studied using a fully nonlinear, weakly nonhydrostatic two-layer theory that includes rotation. In the hydrostatic limit, the governing equations have periodic, nonlinear inertia–gravity solutions that are explored as models of the nonlinear internal tide. These long waves are shown to be robust to weak nonhydrostatic effects. Numerical solutions show that the disintegration of an initial sinusoidal linear internal tide is closely linked to the presence of these nonlinear waves. The initial tide steepens due to nonlinearity and sheds energy into short solitary waves. The disintegration is halted as the longwave part of the solution settles onto a state close to one of the nonlinear hydrostatic solutions, with the short solitary waves superimposed. The degree of d...

The relative importance of wind and ship waves in the littoral zone of a large lake

Abstract: Surface waves and their interactions with sediments and benthic organisms are the main hydrodynamic process affecting littoral ecosystems. Here, we present a long-term data set on surface-wave parameters, which was obtained from the analysis of measurements with a pressure sensor. The data set covers a time period of a year and allows for resolving waves with heights down to less than a centimeter and frequencies up to 0.8 Hz. Wind waves and three different types of ship waves were distinguished by their spectral properties. In Lake Constance, ship-generated waves are as important as wind-generated waves and contribute about 41% of the annual mean wave energy flux to shore. In summer, during the most productive time period, ship waves dominate the wave field in terms of the energy flux to shore and also in their frequency of occurrence. Ship waves cause a diurnal and a seasonal pattern in the frequency of occurrence and in the heights of surface waves, whereas in the case of wind waves these parameters do not vary significantly with season or between nighttime and daytime. In contrast to wind waves that occur only sporadically, ship waves propagate into the littoral zone very frequently at regular time intervals. The different pattern of occurrence of ship and wind waves results in a different pattern of disturbance in the littoral ecosystem.

Dynamics of the semi-diurnal and quarter-diurnal internal tides in the Bay of Biscay. Part 1: Barotropic tides

Abstract: A regional baroclinic model forced with several tidal constituents at different frequencies is used to investigate the internal tide of the Bay of Biscay. The regional ocean model is free surface, sigma-coordinate and it is implemented in order to accurately take into account the barotropic forcing, the strong bathymetry gradients and the temperature and salinity stratifications. In a previous paper, the barotropic component of the tides was studied in details and the boundary conditions of the three-dimensional model were extracted from the atlases. In the present paper, we focus on the baroclinic component of the tides and the simulations are validated against observations from the MINT94 experiment. The observed currents and stratification are accurately reproduced by the model. The internal tide pattern is consistent with the descriptions found in the literature. Combining wavelet and principal component analysis we extract the patterns of generation and propagation of the internal tide at the semi-diurnal and quarter-diurnal frequencies. Secondary internal wave generation areas are identified over the plain. The vertical displacements of isopycnal surfaces for the M4 internal tide are found to be locally half those induced by the semi-diurnal internal tide. A sensitivity study shows the impact of using a three-dimensional initial stratification over the direction of propagation and wavelengths of the internal tides.

Propagation of Wind Energy into the Deep Ocean through a Fully Turbulent Mesoscale Eddy Field

Abstract: The authors analyze the 3D propagation of wind-forced near-inertial motions in a fully turbulent mesoscale eddy field with a primitive equation numerical model. Although the wind stress is uniform, the near-inertial motion field quickly becomes spatially heterogeneous, involving horizontal scales much smaller than the eddy scales. Analysis confirms that refraction by the eddy relative vorticity is the main mechanism responsible for the horizontal distortion of the near-inertial motions, which subsequently triggers their vertical propagation. An important result is the appearance of two maxima of near-inertial vertical velocity (both with rms values reaching 40 m day−1): one at a depth of 100 m and another unexpected one much below the main thermocline around 1700 m. The shallow maximum, captured by the highest vertical normal modes, involves near-inertial motions with a spatial heterogeneity close to the eddy vorticity gradient field. These characteristics match analytical results obtained with Y...

Angular momentum transport by internal gravity waves - IV. Wave generation by surface convection zone, from the pre-main sequence to the early-AGB in intermediate mass stars

Abstract: Context. This is the fourth in a series of papers that deal with angular momentum transport by internal gravity waves in stellar interiors. Aims. Here, we want to examine the potential role of waves in other evolutionary phases than the main sequence. Methods. We study the evolution of a $3\,M_\odot$ Population I model from the pre-main sequence to the early-AGB phase and examine whether waves can lead to angular momentum redistribution and/or element diffusion at the external convection zone boundary. Results. We find that, although waves produced by the surface convection zone can be ignored safely for such a star during the main sequence, it is not the case for later evolutionary stages. In particular, angular momentum transport by internal waves could be quite important at the end of the sub-giant branch and during the early-AGB phase. Wave-induced mixing of chemicals is expected during the early-AGB phase.

Sediment resuspension mechanisms associated with internal waves in coastal waters

Abstract: [1] Large-amplitude, vertically trapped internal waves can induce sizable velocities and trigger hydrodynamic instabilities in the bottom boundary layer, thereby contributing to the resuspension of sediments and the maintenance of sediment concentration in the water column. We discuss numerical simulations of several different situations in which the boundary layer in the wave footprint undergoes hydrodynamic instability, with a resultant increase in the incidence of spatiotemporal structures that could facilitate sediment resuspension. For the case of internal solitary waves we provide bounds in parameter space separating regions in which internal waves can be expected to efficiently resuspend sediment from those in which the boundary layer in the wave footprint is both laminar and stable. A notable finding is that the onset of instability is a strong function of the background current. The Lagrangian transport of passive particles due to the instability is explored, and some quantitative measures of the efficiency of the particle transport process are provided. We subsequently discuss the evolution of the power spectra of the bottom shear stress with time and find that while the general characteristics of the instability are robust, lowering either the Reynolds number or the strength of the background current leads to an increase in the typical length scales associated with the mature instability. Finally, we discuss instabilities during the internal wave generation process and alternative instability mechanisms when the bottom is not flat.

Internal Solitary Waves Induced by Flow Over a Ridge: With Applications to the Northern South China Sea

Abstract: [1] The generation of internal solitary waves by barotropic tides over a ridge is studied in a nonhydrostatic numerical model under idealized oceanographic settings. The experiments examine the effects of ridge width, barotropic tidal strength, and stratification on wave generation. The barotropic tidal flow produces internal wave beams emitting from the ridge top if the slope of the ridge exceeds a critical value equal to the slope of the wave beam. Reflection and refraction of a wave beam in an upper ocean waveguide associated with a strong shallow thermocline produce horizontally propagating internal tides. When the local Froude number over a ridge is not small, lee waves generated on the ridge convert enough energy from the barotropic tides to the internal tides to form tidal bores and solitary waves. Increasing stratification at ridge depths enhances the generation of internal waves, particularly at the diurnal periods. In the Luzon Strait, the slope of the wave beam decreases in spring and summer as stratification at the ridge depths increases, favoring the generation of internal tides. Without the presence of a strong shallow thermocline, internal solitary waves are not observed east of the Luzon Strait. In the northern South China Sea, internal solitary waves are likely observed from April to July when a strong shallow thermocline is present. A deep mixed layer in winter suppresses the production of internal solitary waves.

Mesoscale Eddy–Internal Wave Coupling. Part I: Symmetry, Wave Capture, and Results from the Mid-Ocean Dynamics Experiment

Abstract: Vertical profiles of horizontal velocity obtained during the Mid-Ocean Dynamics Experiment (MODE) provided the first published estimates of the high vertical wavenumber structure of horizontal velocity. The data were interpreted as being representative of the background internal wave field, and thus, despite some evidence of excess downward energy propagation associated with coherent near-inertial features that was interpreted in terms of atmospheric generation, these data provided the basis for a revision to the Garrett and Munk spectral model. These data are reinterpreted through the lens of 30 years of research. Rather than representing the background wave field, atmospheric generation, or even near-inertial wave trapping, the coherent high wavenumber features are characteristic of internal wave capture in a mesoscale strain field. Wave capture represents a generalization of critical layer events for flows lacking the spatial symmetry inherent in a parallel shear flow or isolated vortex.

Turbulent dissipation on the margins of the South China Sea

Abstract: [1] Measurements of turbulence along the continental slope, shelfbreak, and shelf of the northern South China Sea are presented from a 10-day measurement program during April 2005. The shelfbreak region was characterized by a deep stratification that appears to be typical of the late winter-monsoon. This appears to shift the wave field at the shelfbreak from the soliton-like depression anomalies observed in previous years to a more complex wave field, supporting high-frequency waves in both upper and lower depth-intervals of the water column. On average, 30% of the depth-integrated turbulent dissipation occurs within 10 m of the bottom, where baroclinic energy is preferentially dissipated. Dissipation levels, reaching 50 mW/m2, are an order of magnitude larger than those attainable through frictional dissipation of the local barotropic tide, and an order of magnitude larger than levels typical in the open ocean.

Rapid generation of high‐frequency internal waves beneath a wind and wave forced oceanic surface mixed layer

Abstract: [1] High-frequency internal waves generated by Langmuir motions over stratified water may be an important source of turbulent mixing below the surface mixed layer. Large eddy simulations of a developing mixed layer and inertial current are employed to investigate this phenomena. Uniform surface wind stress and parallel Stokes drift wave forcing rapidly establishes a turbulent mixed-layer flow, which (as the inertial motion veers off the wind) generates high-frequency internal waves in the stratified fluid below. The internal waves evolve such that their vector phase velocity matches the depth-averaged mixed-layer velocity that rotates as an inertial oscillation. The internal waves drain energy and momentum from the mixed layer on decay time-scales that are comparable to those of near-inertial oscillations. The high-frequency waves, which are likely to be trapped in the transition layer, may significantly contribute to mixing there and thus provide a potentially important energy sink for mixed-layer inertial motions.

Resonant Generation of Internal Waves on a Model Continental Slope

Abstract: We study internal wave generation in a laboratory model of oscillating tidal flow on a continental margin Waves are found to be generated only in a near-critical region where the slope of the bottom topography matches that of internal waves Fluid motion with a velocity an order of magnitude larger than that of the forcing occurs within a thin boundary layer above the bottom surface The resonant wave is unstable because of strong shear; Kelvin-Helmholtz billows precede wave breaking This work provides a new explanation for the intense boundary flows on continental slopes

Observations on the wavenumber spectrum and evolution of an internal wave attractor

Abstract: Reflecting internal gravity waves in a stratified fluid preserve their frequency and thus their angle with the gravitational direction. At boundaries that are neither horizontal nor vertical, this leads to a focusing or defocusing of the waves. Previous theoretical and experimental work has demonstrated how this can lead to internal wave energy being focused onto ‘wave attractors’ in relatively simple geometries. We present new experimental and theoretical results on the dynamics of wave attractors in a nearly two-dimensional trapezoidal basin. In particular, we demonstrate how a basin-scale mode forced by simple mechanical excitation develops an equilibrium spectrum. We find a balance between focusing of the basin-scale internal wave by reflection from a single sloping boundary and viscous dissipation of the waves with higher wavenumbers. Theoretical predictions using a simple ray-tracing technique are found to agree well with direct experimental observations of the waves. With this we explain the observed behaviour of the wave attractor during the initial development, steady forcing, and the surprising increase of wavenumber during the decay of the wave field after the forcing is terminated.

Near-inertial parametric subharmonic instability

Abstract: New analytic estimates of the rate at which parametric subharmonic instability (PSI) transfers energy to high-vertical-wavenumber near-inertial oscillations are presented. These results are obtained by a heuristic argument which provides insight into the physical mechanism of PSI, and also by a systematic application of the method of multiple time scales to the Boussinesq equations linearized about a 'pump wave' whose frequency is close to twice the inertial frequency. The multiple-scale approach yields an amplitude equation describing how the 2 fo-pump energizes a vertical continuum of near-inertial oscillations. The amplitude equation is solved using two models for the 2 fo-Pump: (i) an infinite plane internal wave in a medium with uniform buoyancy frequency; (ii) a vertical mode one internal tidal wavetrain in a realistically stratified and bounded ocean. In case (i) analytic expressions for the growth rate of PSI are obtained and validated by a successful comparison with numerical solutions of the full Boussinesq equations. In case (ii), numerical solutions of the amplitude equation indicate that the near-inertial disturbances generated by PSI are concentrated below the base of the mixed layer where the velocity of the pump wave train is largest. Based on these examples we conclude that the e-folding time of PSI in oceanic conditions is of the order of ten days or less.

Impacts of tidal currents and Kuroshio intrusion on the generation of nonlinear internal waves in Luzon Strait

Abstract: [1] The analysis of remotely sensed images shows that two kinds of nonlinear internal solitary waves (ISWs) in the forms of single ISW and groups of ISWs are commonly seen in Luzon Strait (LS), with larger occurrence during spring tides A 2-D numerical model with idealized topography is then used to investigate the generation processes of ISWs in LS The model results confirm that the ISWs are likely generated during spring tides with strong tidal currents The results further suggest that the ISWs can be generated by two mechanisms: the evolution of depression and the internal mixing disturbance Our simulations also show that the Kuroshio intrusion to LS or South China Sea through LS increases the occurrence of generating internal mixing and groups of ISWs Both remotely sensed images and numerical simulations suggest the existence of a distance between the actual locations where ISWs are generated and where the strongest flow occurs

Mid‐depth internal wave energy off the Iberian Peninsula estimated from seismic reflection data

Abstract: Energy levels of internal waves are estimated from seismic reflection data. Three legacy seismic sections from 1993 and 1997 obtained off the Iberian Peninsula have been analyzed for acoustic reflections within the water column. The reflections are aligned continuously for up to several kilometers over large parts of the sections and in the depth interval from 200 to 2000 m. Depth variations of these reflections are thought to be caused by the background internal wave field. From the variations we derive horizontal wave number spectra of normalized internal wave displacement. The general slope of the power density spectra is remarkably consistent for all sections and agrees well with model spectra for internal waves. Significant differences within the sections can be found when sufficiently large subsections are averaged. The spatial variation of the energy level indicates increasing internal wave activity with shallower water depths as well as near a subsurface eddy.

Stratification and mixing on sloping boundaries

Abstract: [1] In lakes as well as in the ocean vertical transport is, to a large extent, controlled by localized mixing along the boundaries of the respective basin. Direct measurements of turbulent mixing and density stratification in the bottom-boundary layer of a large and deep lake reveal the importance of cross-slope advection near sloping boundaries for local and basin-scale vertical transport. The periodic, internal wave driven, occurrence of up- and downslope directed currents results in periodic heating and cooling of the boundary layer. Cooling of the boundary layer during periods of up-slope flow is associated with unstable stratification and turbulent diffusivities exceed those observed during periods of down-slope flow by almost one order of magnitude. The periodic replacement of water in this layer with water from the interior of the basin maintains vertical density gradients and thus enhances the overall efficiency of the boundary mixing.

Experiments on mixing and dissipation in internal solitary waves over two triangular obstacles

Abstract: A series of laboratory experiments was undertaken in a stratified two-layer fluid to investigate the energetics of the interaction between an internal solitary wave (ISW) and triangular obstacles, as well as to determine the partitioning of ISW energy and its subsequent dynamics. The ISW energy was dissipated as a result of internal breaking and turbulent mixing induced by wave instability. Tests involving different combinations of triangular obstacles in various heights and intervals and ISW of different amplitudes were performed. The wave features resulting from the interaction of an ISW and double obstacles were found to differ from those of single obstacle. The incident energy of an ISW was either reflecting back from the obstacles, dissipated through turbulent mixing, or transmitted over the double obstacles. Reduction in wave energy increased as the intervals between obstacles reduced. For two obstacles in different heights, energy dissipation was greater in the case with a higher obstacle ahead of a lower one. However, the overall performance was dependent on the relative height of the obstacles, relative water depth of the upper and bottom layer, in addition to the intervals between the obstacles.

Quasi-Steady Katabatic Winds on Slopes in Wide Valleys: Hydraulic Theory and Observations

Abstract: Theoretical and field observational studies on mean velocity and temperature fields of quasi-steady nocturnal downslope (katabatic) flows on sloping surfaces are reported for the case of very wide valleys in the presence of weak synoptic winds. Because of the lateral constraints on the flow, Coriolis effects are considered negligible. The layer-averaged equations of Manins and Sawford were used for the analysis. It is shown that (i) in the absence of significant turbulent entrainment into the current (i.e., at large Richardson numbers Ri h cos /U 2 ) the downslope flow velocity U is related to the slope length (LH), slope angle (), and the buoyancy jump between the current and the background atmosphere ( )a sU u(LH sin) 1/2 , where u is a constant and h is the flow depth; (ii) on very long slopes h is proportional to Lh(tan) 1/2 ; and (iii) under highly stable conditions (i.e., Ri 1) the katabatic flow exhibits pulsations with period T0 2/N sin, where N is the buoyancy frequency of the background atmosphere. These predictions are verified principally using observations made during the Vertical Transport and Mixing Experiment (VTMX) conducted in Salt Lake City, Utah, in October 2000. By assuming the flow follows a straight line trajectory to the nearest ridgeline a good agreement was found between the predictions and observations over appropriate Richardson number ranges. For Ri 1.5, u 0.2, although u was a decreasing function of Ri at lesser stabilities. Oscillations with period T0 are simply alongslope (critical) internal-wave oscillations with a slope-normal wavenumber, which are liable for degeneration into turbulence during their reflection. These critical internal waves may be responsible, at least partly, for weak sustained turbulence often observed in complex-terrain nocturnal boundary layer flows.

Diurnal and semidiurnal internal tide energy flux at a continental slope in the South China Sea

Abstract: [1] Barotropic (surface) and baroclinic (internal) tides were measured at four mooring sites during a field investigation of acoustic propagation characteristics and physical oceanography in the northern South China Sea. The mooring positions were in a line moving up the shallow portion of a continental slope at water depths between 350 and 85 m. Using time series of temperature and velocity, at several depths, 1-month series of semidiurnal and diurnal species internal tidal energy flux vectors were computed for three sites, with a 14-day series computed for the fourth (shallow) site. The internal tides had a temporal signature that was not in complete accord with the barotropic tides, showing an enhancement of diurnal internal tides with respect to semidiurnal. Bathymetric slope, barotropic tidal fluid particle trajectories, and scale of generation site versus internal tide wavelength are investigated as possible causes of the differing response of the species.