Showing papers on "Internal wave published in 1993"

Nonlinear evolution of waves on a vertically falling film

Abstract: Wave formation on a falling film is an intriguing hydrodynamic phenomenon involving transitions among a rich variety of spatial and temporal structures. Immediately beyond an inception region, short, near-sinusoidal capillary waves are observed. Further downstream, long, near-solitary waves with large tear-drop humps preceded by short, front-running capillary waves appear. Both kinds of waves evolve slowly downstream such that over about ten wavelengths, they resemble stationary waves which propagate at constant speeds and shapes. We exploit this quasi-steady property here to study wave evolution and selection on a vertically falling film. All finite-amplitude stationary waves with the same average thickness as the Nusselt flat film are constructed numerically from a boundary-layer approximation of the equations of motion. As is consistent with earlier near-critical analyses, two travelling wave families are found, each parameterized by the wavelength or the speed. One family γ1 travels slower than infinitesimally small waves of the same wavelength while the other family γ2 and its hybrids travel faster. Stability analyses of these waves involving three-dimensional disturbances of arbitrary wavelength indicate that there exists a unique nearly sinusoidal wave on the slow family γ1 with wavenumber αs (or α2) that has the lowest growth rate. This wave is slightly shorter than the fastest growing linear mode with wavenumber αm and approaches the wave on γ1 with the highest flow rate at low Reynolds numbers. On the fast γ2 family, however, multiple bands of near-solitary waves bounded below by αf are found to be stable to two-dimensional disturbances. This multiplicity of stable bands can be interpreted as a result of favourable interaction among solitary-wave-like coherent structures to form a periodic train. (All waves are unstable to three-dimensional disturbances with small growth rates.) The suggested selection mechanism is consistent with literature data and our numerical experiments that indicate waves slow down immediately beyond inception as they approach the short capillary wave with wavenumber α2 of the slow γ1 family. They then approach the long stable waves on the γ2 family further downstream and hence accelerate and develop into the unique solitary wave shapes, before they succumb to the slowly evolving transverse disturbances.

Synthetic aperture radar interferometry applied to ship-generated internal waves in the 1989 Loch Linnhe experiment

Abstract: Interferometer synthetic aperture radar images collected during the 1989 Loch Linnhe experiment showed mean Doppler variations across the phase of ship-generated internal waves that corresponded to “velocity” variations of the order of 50 to 100 cm/s. The in situ current data, however, showed surface currents associated with the internal wave features of the order of 5 to 10 cm/s and virtually ruled out the existence of surface currents as large as the interferometer-inferred values. In this paper we show how the pixel-to-pixel phase difference measured by the Jet Propulsion Laboratory interferometer is related to the mean Doppler frequency of the backscattered field. Model calculations are used to show how this frequency can sometimes change by a large amount, even when rather small surface currents are present. In particular, for winds blowing roughly across the internal wave features, as was the case for the interferometer runs in Loch Linnhe, computations based on our wave-current interaction and time dependent scattering models show that changes in the mean Doppler frequency corresponding to large velocities can, in fact, be produced from the much smaller measured surface currents. We show that the larger interferometer velocity estimates are essentially due to the different modulation strengths of the surface Bragg waves advancing toward and receding from the radar. Thus for these crosswind conditions, care must be taken in converting the phase differences measured by the interferometer to a surface current image. When the wind is aligned more nearly along the internal wave propagation direction, the mean Doppler shifts (and the phase differences) are dominated mostly by advection, and interferometer current estimates are more accurate. C band computations predict that if the antenna spacing is small enough so that the fields from the two antennas remain correlated, then the C band interferometer current estimates will be better than those at L band.

Propagation and Structural Interpretation of Non-Plane Waves

Abstract: SUMMARY As a model for the 2-D horizontal propagation of seismic surface waves, we study the propagation of non-plane acoustic waves in homogeneous and inhomogeneous media. We find that their phase velocity depends not only on the medium but also on the local geometry of the wavefield, especially on the distribution of amplitudes around the point of observation. the phase velocity of a wave is therefore conceptually and in most cases numerically different from the phase velocity parameter in the wave equation, which is determined by the elastic properties of the medium. the same distinction must be made for seismic surface waves. Although it is a common observation that waves of the same period can propagate with different phase velocities over the same path, the fundamental character of this observation has apparently not been recognized, and the two phase velocities are frequently confused in the seismological literature. We derive a local relationship between the two phase velocities that permits a correct structural interpretation of acoustic waves in inhomogeneous media, and also of non-plane seismic surface waves in laterally homogeneous parts of the medium.

The Application of Internal-Wave Dissipation Models to a Region of Strong Mixing

Abstract: Several models now exist for predicting the dissipation rate of turbulent kinetic energy, ϵ, in the oceanic thermocline as a function of the large-scale properties of the internal gravity wave field. These models are based on the transfer of energy toward smaller vertical scales by wave-wave interactions, and their predictions are typically evaluated for a canonical internal wave field as described by Garrett and Munk. Much of the total oceanic dissipation may occur, however, in regions where the wave field deviates in some way from the canonical form. In this paper simultaneous measurements of the internal wave field and ϵ from a drifting ice camp in the eastern Arctic Ocean are used to evaluate the efficacy of existing models in a region with an anomalous wave field and energetic mixing. By explicitly retaining the vertical wavenumber bandwidth parameter, β*, models can still provide reasonable estimates of the dissipation rate. The amount of data required to estimate β*, is, however, substanti...

Internal waves produced by the turbulent wake of a sphere moving horizontally in a stratified fluid

Abstract: The internal gravity wave field generated by a sphere towed in a stratified fluid was studied in the Froude number range 1.5 < F < 12.7, where Fis defined with the radius of the sphere. The Reynolds number was sufficiently large for the wake to be turbulent (Re~[380,30000]). A fluorescent dye technique was used to differentiate waves generated by the sphere, called lee waves, from the internal waves, called random waves, emitted by the turbulent wake. We demonstrate that the lee waves are well predicted by linear theory and that the random waves due to the turbulence are related to the coherent structures of the wake. The Strouhal number of these structures depends on F when F 5 4.5. Locally, these waves behave like transient internal waves emitted by impulsively moving bodies.

On the propagation of ideal, linear Alfvén waves in radially stratified stellar atmospheres and winds

Abstract: The propagation of Alfven waves through isothermal, radially stratified, spherically symmetrical models of stellar atmospheres and winds is discussed. The transmission coefficient for the waves is calculated as a function of frequency, magnetic field base intensity, surface gravity and atmospheric temperature. When a wind is present, the wave energy flux is no longer conserved, but the conservation of the wave-action flux (Heinemann & Olbert 1980) allows the definition of an analogous transmission coefficient, giving the relative amount of waves reaching the super-Alfvenic regions of the wind. It is shown that for high-frequency waves the transmission coefficient for static and wind models is identical, while for low-frequency waves the presence of a wind enhances the transmission considerably

On slow‐mode waves in an anisotropic plasma

Abstract: The properties of small-amplitude waves propagating in a homogeneous anisotropic plasma are investigated using an MHD double-polytropic model that incorporates the CGL double-adiabatic model in one extreme and the isothermal model in the other. It is found that the properties of fast and intermediate mode waves remain qualitatively the same as in ordinary MHD but that, in certain parameter regimes, three inversions occur for slow-mode waves: (1) their phase speed exceeds that of intermediate waves; (2) they behave like fast-mode waves in that, across them, the plasma density and magnetic field increase or decrease together; (3) rarefaction waves rather than compression waves steepen.

Transient Development of Perturbations in Stratified Shear Flow

Abstract: Transient development of perturbations in inviscid stratified shear flow is investigated. Use is made of closed form analytic solutions that allow concise identification of optimally growing plane-wave solutions for the case of an unbounded flow with constant shear and stratification. For the case of channel flow, variational techniques are employed to determine the optimally growing disturbances. The maximum energy growth attained over a specific time interval decreases continuously with increasing stratification, and no special significance attaches to Ri = 0.25. Indeed, transient growth can be substantial even for Ri = O(1). A general lower bound on the energy growth attained by an optimal perturbation in a stratified flow over a given time interval is the square root of the growth attained by the corresponding perturbation in unstratified flow. Enhanced perturbation persistence is found for mean-flow stratification lying in the range Ri between 0.1 and 0.3. Small but finite perturbations in mean flow with Ri less than 0.4 produce regions with locally negative total density gradient, which are expected to overturn. Although the perturbations are of wave form, buoyancy fluxes mediate transfer between perturbation kinetic and potential energy during transient development, thus implying that buoyancy flux is not a determinative diagnostic for distinguishing between waves and turbulence in stratified flows.

A Simple Model for the Shear-induced Decay of an Internal Solitary Wave

Abstract: Internal solitary waves (ISWs) are a common feature of the coastal zone and marginal seas, especially close to shelf breaks, and are observed to mix the water column at the depth of maximum density gradient. For a two-layer system separated by a thin interface with a finite density gradient, the Richardson number in the interface fails below 1/4 if, in the simplest case, the ISW amplitude exceeds 2(hH1)1/2, where h is the interface thickness and H1 the thickness of the upper layer. Assuming that mixing then thickens the interface and that the potential energy for this comes from the ISW, we derive formulas for the damping rate of the ISW. The model is generalized to allow for a stratified upper layer; a Richardson number of less than 1/4 now requires that the displacement of the base of the upper layer exceeds 0.82 times the thickness of the layer. The ISW damping rate is sensitive to the ratio of the mixing depths above and below the base of the upper layer but can be plausibly matched to field ...

A survey of low frequency waves at Jupiter: The Ulysses encounter

Abstract: We report the results of a survey of low-frequency (LF) plasma waves detected during the Ulysses Jupiter flyby. In the Jovian foreshock, two predominant wave periods are detected: 10(exp 2)-s and 5-s, as measured in the spacecraft frame. The 10(exp 2)-s waves are highly nonlinear propagate at large angles to vector-B(sub 0) (typically 50 deg), are steepened, and sometimes have attached whistler packets. For the interval analyzed the 10(exp 2)-s waves had mixed right-and left-hand polarizations. We argue that these are all consistent with being right-hand magnetosonic waves in the solar wind frame. The 10(exp 2)-s waves with attached whistler are similar to cometary waves. The trailing portions are linearly polaraized and the whistler portions circularly polarized with amplitudes decreasing linearly with time. The emissions are generated by approximately 2-keV protons flowing from the Jovian bow shock/magnetosheath into the upstream region. The instability is the ion beam instability. Higher Z ions were considered as a source of the waves but have been ruled out because of the low sunward velocities needed for their resonance. The 5-s waves have delta vector-B/B(sub 0 approximately = 0.5, are compressive and are left-hand polarized in the spacecraft frame. Local generation by three different resonant interactions were considered and have been ruled out. One possibility is that these waves are whistler mode by-products of the steepened lower-frequency magnetosonic waves. Mirror mode structures were detected throughout the outbound magnetosheath passes. For these structures, the theta(sub kB) values were consistently in the range of 80 deg to 90 deg, exceptionally high values.

Characteristics of gravity waves in the mesosphere observed with the middle and upper atmosphere radar: 2. Propagation direction

Abstract: We studied the characteristics of dominant component of gravity waves (λz ∼ 10 km) in the vertical profile of the wind velocities observed in the mesosphere (at around 70–75 km) with the middle and upper atmosphere (MU) radar in the four observation campaigns (June 1987, July 1990, October 1986, and January/February 1991) and the monthly mesosphere observations carried out 4–5 days a month in December 1985 to December 1988. By assuming linear dispersion relations of gravity waves, both vertical and horizontal propagation directions of gravity waves were determined. Most of the dominant waves propagated upward, except that they sometimes propagated downward mainly in summer. A typical vertical wavelength and intrinsic period of the dominant gravity waves were 4–15 km and 4–15 hours, respectively. The mean values of the vertical wavelength, horizontal wavelength, and intrinsic periods were 8.2 km, 1200 km, and 10.2 hours, respectively, which did not show significant seasonal variations. Most of the waves were found to be dissipated by the eddy diffusion of 15–100 m2/s, which does not agree with MF radar observations (10- to 120-min observed periods) but is rather consistent with sodium lidar observations (36–300 m2/s). The mean horizontal phase velocity was 33 m/s. The horizontal propagation direction was generally eastward throughout a year except for the westward propagation in early winter (November to December). This suggests that the dominant gravity waves are less sensitive to a change in the mean zonal wind direction in the middle atmosphere than the short-period gravity waves (2 hours to 5 min). Momentum flux carried by the dominant gravity waves was estimated to be 0.5–1 m2/s2, which was generally smaller than the momentum flux of gravity waves with periods ranging from 8 hours to 5 min. The amplitude of the momentum flux of the dominant gravity waves had an autumn maximum, while the momentum flux with periods of 8 hours to 5 min had equinoctial minima. Thus in September and October the momentum flux due to the dominant gravity waves became significant. We further pointed out that the possibility that / depends on the wave periods, and therefore the major frequency component of is not easily determined from simple dispersion relation only.

Statistics of Shear and Turbulent Dissipation Profiles in Random Internal Wave Fields

Abstract: Because breaking internal waves produces most of the turbulence in the thermocline, the statistics of ϵ, the rate of turbulent dissipation, cannot be understood apart from the statistics of internal wave shear. The statistics of ϵ and shear are compared for two sets of profiles from the northeast Pacific. One set, PATCHEX, has internal wave shear close to the Garrett and Munk model, but the other set, PATCHEX north, has average 10-m shear squared, 〈S210〉, about four times larger than the model. The 10-m, shear components, Sx and Sy, were measured between 1 and 9 MPa and referenced to a common stratification by WKB scaling. The scaled components, Sˆx and Sˆy, are found to be independent and normally distributed with zero means, as assumed by Garrett and Munk. This readily leads to analytic forms for the probability densities of Sˆ210 and Sˆ410. The observed probability densities of Sˆ210 and Sˆ410 are close to the predicted forms, and both are strongly skewed. Moreover, σlnSˆ210 and σlnSˆ410 are c...

Energetics of the Internal Tide on Northern Georges Bank

Abstract: This paper discusses the energetics of the internal waves generated by the tide on the northern edge of Georges Bank in the outer Gulf of Maine–-a region of strong tidal flow, a density/temperature front, and abrupt topography. A series of bank-edge cross sections in early July 1988, using the towed vertically profiling Batfish, shows that during off-bank flow a large internal hydraulic jump develops over the bank slope. This disturbance propagates on bank during the reverse phase of the tide, evolving into two internal solitonlike features that impinge upon the frontal zone separating stratified bank-edge water from the homogeneous water on bank. Thermistor chain data from the bank edge show that two internal wave packets per tidal cycle are characteristic of the region during this time of year. The available potential energy plus kinetic energy of the internal disturbances, estimated using the Batfish and thermistor chain data, is found to be 35 J m−3 in a plug of fluid 60 m deep and 4 km long ...

Solitary waves in the atmosphere

Abstract: The weakly nonlinear theory for internal solitary waves is reviewed, and theoretical results of the vertical and horizontal structure of temperature, vertical displacements, and vertical and horizontal perturbations to the wind field associated with steadily propagating solitary waves are presented in two idealized atmospheric configurations. One configuration is representative of solitary waves observed in the lower troposphere and the other of solitary waves that occupy the entire troposphere. The important results of the theory are presented in a form that can be readily used by observationalists. The results obtained are then analyzed using actual rawinsonde data for two well-documented observations of atmospheric solitary waves, which are analogous to the two idealized configurations. The importance and difficulties of properly identifying the waveguide within which the solitary wave is confined are discussed. The fundamental role of a critical level in ducting the disturbances and thus in defining the thickness of the waveguide is illustrated in the example dealing with the solitary wave occupying the entire troposphere. Together, these two examples illustrate the decisions and compromises that must be made in applying the theory to the real atmosphere.

Pulsed phytoplankton supply to the rocky subtidal zone: influence of internal waves.

Abstract: Hydrographic measurements indicate that the thermocline and the phytoplankton-rich chlorophyll maximum layer are vertically displaced over a rocky pinnacle in the central Gulf of Maine by internal waves with maximum amplitudes of 27 m. Such predictable downwelling events are linked to rapid, 2- to 3-fold increases in chlorophyll a, an indicator of phytoplankton concentration, in pulses of warm water recorded 4 cm above the bottom (29-m depth). The 1.5-5.6 degrees C temperature fluctuations had an average period of 10.6 min and were generated on both ebb and flood tides. Local lee waves and the arrival of solitons propagated from Georges Bank are hypothesized to explain the timing of the internal waves. Because internal waves and chlorophyll maxima are pervasive features of stratified temperate seas, this mechanism of food coupling should be common in other rocky subtidal habitats.

Submesoscale Dynamics near a Seamount. Part 1. Measurements of Ertel Vorticity

Abstract: The prevailing view that submesoscale fluctuations (horizontal wavelengths less than a few kilometers and vertical wavelengths less than a few hundred meters) are dominated by internal gravity waves is tested by measuring Ertel's potential vorticity, Π = (f + ∇ × V) · ∇B, where the buoyancy B = −gδρ/ρo. Unlike geostrophic or nonlinear Ertel vorticity-carrying motions, internal waves have no Ertel vorticity fluctuations. Velocity and temperature profile surveys beside Ampere Seamount reveal appreciable Ertel enstrophy, and thus a significant non-internal-wave component, on horizontal wavelengths of 6–15 km and vertical wavelengths of 50–380 m. The twisting terms are negligible and the relative vorticities less than 0.2f, so the anomalies are in geostrophic balance. It is unlikely that the anomalies arise from stirring of the large-scale isopycnal gradients of stretching and planetary Ertel vorticity as this would require stirring lengths of thousands of kilometers. The most likely source appears t...

Topographic Waves Generated by a Transient Wind

Abstract: The concept of linear mountain waves is generally equated with steady-state stationary waves. This essentially means that the absolute horizontal phase velocity of mountain waves is zero and that their momentum flux profile is independent of height and time in the absence of dissipation and zero-level wind. This paper investigates the generation of linear unsteady mountain gravity waves. The incident flow is transient, starting from zero at a given time and returning to zero after a finite time. The topography is a single horizontal harmonic. The unsteadiness of the waves is due partly to the temporal change of their phase velocity, which takes place during their propagation in the time-dependent mean flow. When the wind ceases, most of the waves present have a phase velocity nearly opposite to the maximum wind. For this reason, mountain waves can propagate through levels of zero mean wind. The transient structure of the wave field also comes from the temporal change of the amplitude of the groun...

Statistical and dynamical analysis of internal waves on the continental shelf of the Middle Atlantic Bight from space shuttle photographs

Abstract: The internal waves on the continental shelf on the Middle Atlantic Bight seen on Space Shuttle photographs taken during the STS-40 mission in June 1991 are measured and analyzed. The internal wave field in the sample area has a three-level structure which consists of packet groups, packets, and solitons. An average packet group wavelength of 17.5 km and an average soliton wavelength of 0.6 km are measured. Finite-depth theory is used to derive the dynamic parameters of the internal solitons: the maximum amplitude of 5.6 m, the characteristic phase speed of 0.42 m/s, the characteristic period of 23.8 min, the velocity amplitude of the water particles in the upper and lower layers of 0.13 m/s and 0.030 m/s respectively, and the theoretical energy per unit crest line of 6.8 x 10 exp 4 J/m. The frequency distribution of solitons is triple-peaked rather than continuous. The major generation source is at 160 m water depth, and a second is at 1800 m depth, corresponding to the upper and lower edges of the shelf break.

On the irreversibility of internal-wave dynamics due to wave trapping by mean flow inhomogeneities. Part 1. Local analysis

Abstract: The propagation of guided internal waves on non-uniform large-scale flows of arbitrary geometry is studied within the framework of linear inviscid theory in the WKB-approximation. Our study is based on a set of Hamiltonian ray equations, with the Hamiltonian being determined from the Taylor-Goldstein boundary-value problem for a stratified shear flow. Attention is focused on the fundamental fact that the generic smooth non-uniformities of the large-scale flow result in specific singularities of the Hamiltonian. Interpreting wave packets as particles with momenta equal to their wave vectors moving in a certain force field, one can consider these singularities as infinitely deep potential holes acting quite similarly to the ‘black holes’ of astrophysics. It is shown that the particles fall for infinitely long time, each into its own ‘black hole‘. In terms of a particular wave packet this falling implies infinite growth with time of the wavenumber and the amplitude, as well as wave motion focusing at a certain depth. For internal-wave-field dynamics this provides a robust mechanism of a very specific conservative and moreover Hamiltonian irreversibility.This phenomenon was previously studied for the simplest model of the flow non-uniformity, parallel shear flow (Badulin, Shrira & Tsimring 1985), where the term ‘trapping’ for it was introduced and the basic features were established. In the present paper we study the case of arbitrary flow geometry. Our main conclusion is that although the wave dynamics in the general case is incomparably more complicated, the phenomenon persists and retains its most fundamental features. Qualitatively new features appear as well, namely, the possibility of three-dimensional wave focusing and of ‘non-dispersive’ focusing. In terms of the particle analogy, the latter means that a certain group of particles fall into the same hole.These results indicate a robust tendency of the wave field towards an irreversible transformation into small spatial scales, due to the presence of large-scale flows and towards considerable wave energy concentration in narrow spatial zones.

Double reflection of capillary/gravity waves by a non-uniform current : A boundary layer theory

Abstract: When a train of gravity waves encounters an opposing current, the wavelength is shortened and the waves may be reflected. If capillarity is included, the shortened waves may be reflected for a second time and experience further shortening. By this process the initially long gravity waves can be damped by viscosity quickly without breaking. In this paper a boundary-layer approximation is obtained close to the reflection points, and is matched to the ray approximations outside. This is then applied to the propagation of a wavepacket. Damping is accounted for in the ray solution and the result is compared to the undamped solution. The case where the two reflection points coalesce is also considered. It is found that as the separation between the reflection points decreases, the wavepacket appears to remain longer in the region of reflections relative to the width of this region.

Elliptical instabilities of stratified, hydromagnetic waves

Abstract: The stability of a uniformly-rotating, electrically-conducting, stratified fluid is discussed under conditions of slight tidal straining. The ensuing steady flow consisting of elliptical streamlines and magnetic field lines is linearly unstable through the resonant coupling of two free waves of the system. New families of linear waves consisting of modified Poincare, “slow” hydromagnetic and, in the case of axial stratification, internal evanescent waves are isolated upon a rotating fluid bearing an axial current. All possible resonant couplings between these waves are examined. Stable radial stratification is found to be a destabilizing influence on some elliptical couplings and always so for slow hydromagnetic waves. Internal evanescent waves can be stimulated elliptically in the case of axial stratification and typically possess boundary-layer structure. In all cases studied, including in the presence of a central core, the preferred mode of disturbance is a tipping over, or spinover, of the b...

The evolution of thermocline waves from an oscillatory disturbance

Abstract: The way in which energy propagates away from a two-dimensional oscillatory disturbance in a thermocline is considered theoretically and experimentally. It is shown how the St. Andrew's-cross-wave is modified by reflections and how the cross-wave can develop into thermocline waves. A linear shear flow is then superimposed on the thermocline. Ray theory is used to evaluate the wave shapes and these are compared to finite-difference solutions of the full Navier-Stokes equations.

Coupling processes in the lower and middle atmosphere

Abstract: Large-Scale Dynamics. Planetary Waves and Tides. Gravity Waves: Sources, Saturation Processes, Spectra and Transports. Turbulence and Small-Scale Processes.

The Strait of Gibraltar Model: internal tide, diurnal inequality and fortnightly modulation

Abstract: A three-dimensional, general ocean circulation model is applied to the Strait of Gibraltar. The model is driven at the open boundaries by the observed barotropic diurnal and semidiurnal tidal transport. The initial density distribution is a lock-exchange in which half of the basin is the Atlantic water and the other half the Mediterranean water. The model is run over a 15 day spring-neap cycle, and the results are compared quantitatively with data obtained from the Gibraltar Experiment. The model and data are well correlated (γ2>0.9) for the mean velocity and salinity over all moored current measurements. The predicted semidiurnal interface amplitudes of 33 and 15 m on the sill and at the eastern end are also comparable with the observed amplitudes of 40 m and 15 m. The model indicates that the diurnal tidal current has significant effect on the generation and propagation of semidiurnal internal tide. The diurnal inequality is distinct at the eastern end in both the surface current and the arrival time of internal tidal surge. The model also indicates that the semidiurnal S2 component contributes to a fortnightly cycle in the tidally averaged interface depth and vertical shear variations. The interface is deeper and the vertical shear is larger in neap tide than in spring tide. The predicted diurnal inequality and fortnightly cycle are consistent with the observational evidence.

Circulation, Hydrographic Structure and Mixing at Tidal Fronts: The View from Georges Bank [and Discussion]

Abstract: The steep slope on the northern side of Georges Bank and its location in the Fundy-Maine tidal system result in a persistent summertime frontal system comprising a tidal-mixing front and a stratified tide-topography interaction at the Bank edge. Recent field studies have provided a high-resolution description of the circulation, hydrographic structure and mixing in the region. Frontal features include an along-front residual jet, a surface convergence zone, regular variations in frontal structure and position over the tidal period and tidal modulation cycle, large-amplitude internal waves, and strong spatial and temporal variations in small-scale turbulence. The observations suggest that the magnitude of cross-front and vertical exchange in frontal regions can be site-specific depending on the relative importance of the underlying physical processes.

Influence of density stratification and bottom depth on vertical mode structure functions in the tropical Pacific

Abstract: Vertical mode structure functions are computed over the entire tropical Pacific Ocean (30°N to 30°S) by using the Levitus temperature-salinity climatological file and a National Oceanic and Atmospheric Administration bathymetry file and over a few selected areas of the Pacific by using a more accurate conductivity-salinity temperature depth (CTD-STD) file. At every 1° grid point of the tropical Pacific, phase speeds of the first five modes are estimated from the Levitus density profiles and the actual bottom depth. They range from 305 to 195 cm s−1 for mode 1 to 65 to 40 cm s−1 for mode 5. Because of the coarse vertical resolution in the Levitus profiles, the corresponding phase speeds are underestimated by about 8% compared to phase speeds calculated with CTD-STD profiles. In order to estimate the relative importance of density stratification and bottom depth on vertical mode structure functions, two sets of modes are calculated. The first set is calculated with the Levitus density profiles truncated or extended to a mean basin bottom depth (3570 m) at every grid point. The resulting modes are representative of the influence of density stratification on modal calculations. The second set is computed with a mean basin density profile and the actual bottom depth at every grid point. This set represents the influence of bottom depth. Phase speed comparison between these two sets of modes and the original modes indicates that for the first two modes, the bottom depth contribution is an order of magnitude less than the density contribution. For modes 3 and 4, the bottom depth contribution increases, and for mode 5 it is almost equal to the density contribution. The relative importance of deep density stratification and upper layer stratification on vertical mode structure functions is evaluated by using the more accurate CTD-STD file. This study is restricted to a few small areas with enough deep profiles, taken within a few days, to ensure proper statistical results. Vertical modes are calculated first with complete vertical density profiles and then with the same profiles truncated at a certain depth and replaced below by a mean density profile (obtained from 159 CTD-STD deep profiles in the tropical Pacific). Statistical comparison reveals that meaningful computation of the first five vertical modes can be obtained in the tropics by using precise density information in the first 600 m and mean density information below.

Trapped modes of internal waves in a channel spanned by a submerged cylinder

Abstract: A horizontal channel of infinite length and depth and of constant width contains inviscid, incompressible, two-layer fluid under gravity. The upper layer has constant finite depth and is occupied by a fluid of constant density p*. The lower layer has infinite depth and is occupied by a fluid of constant density p > p*. The parameter E = @/p*)- 1 is assumed to be small. The lower fluid is bounded internally by an immersed horizontal cylinder which extends right across the channel and has its generators normal to the sidewalls. The free, time-harmonic oscillations of fluid, which have finite kinetic and potential energy (such oscillations are called trapped modes), are investigated. Trapped modes in homogeneous fluid above submerged cylinders and other obstacles are well known. In the present paper it is shown that there are two sets of frequencies of trapped modes for the two-layer fluid. The frequencies of the first finite set are close to the frequencies of trapped modes in the homogeneous fluid (when p* = p). They correspond to the trapped modes of waves on the free surface of the upper fluid. The frequencies of the second finite set are proportional to e, and hence, are small. These latter frequencies correspond to the trapped modes of internal waves on the interface between two fluids. To obtain these results the perturbation method for a quadratic operator family was applied. The quadratic operator family with bounded, symmetric, linear, integral operators in the space L,( - co, + co) arises as a result of two reductions of the original problem. The first reduction allows to consider the potential in the lower fluid only. The second reduction is the same as used by Ursell (1987).