Showing papers on "Internal wave published in 1988"

Steep, steady surface waves on water of finite depth with constant vorticity

Abstract: Two-dimensional steady surface waves on a shearing flow are computed for the special case where the flow has uniform vorticity, i.e. in the absence of waves the velocity varies linearly with height. A boundary-integral method is used in the computation which is similar to that of Simmen & Saffman (1985) who describe such waves on deep water. Particular attention is given to the effects of finite depth with descriptions of waves of limiting steepness, waves with eddies beneath their crests and extremely high waves on high-speed flows.Many qualitative features of these waves are relevant to steep waves propagating in shallow water, or on a strong wind-induced drift current. An important practical point in the interpretation of wave measurements of wind driven waves is that mean kinetic energy and potential energy densities are unequal even for infinitesimal waves. This may mean that wave energy spectra deduced from surface-elevation measurements in the conventional way may sometimes be misleading.

A lee wave model for deep-sea mudwave activity

Abstract: Mudwaves, with wavelengths up to 6 km and heigths up to 100 m, are commonly found in the deep sea where steady, sediment-laden currents are present; their internal structure suggests that they have migrated with time. Lee waves appear to be generated in the density gradient above the sinusoidal mudwave topography; the near-bottom flow field associated with the lee waves creates a cross-wave asymmetry in bottom current velocity. A model of bottom flow and sedimentation rate for a transverse mudwave shows that prefernential deposition occurs on the upstream flanks and the bed forms migrate upstream. The flow conditions for such lee waves are common in the deep sea; therefore many mudwaves are probably active under present flow conditions. The model suggests that for a given wave, the ratio of downstream-upstream sedimentation rate varies primarily with flow velocity. Thus changes in this ratio, determined by seismic or sampling techniques, might be used to determine past variations in flow velocity.

Analysis of nonlinear internal waves in the New York Bight

Abstract: An analysis of the nonlinear-internal-wave evolution in the New York Bight was performed on the basis of current meter mooring data obtained in the New York Bight during the SAR Internal Wave Signature Experiment (SARSEX) The solitary wave theory was extended to include dissipation and shoaling effects, and a series of numerical experiments were performed by solving the wave evolution equation, with waveforms observed in the SARSEX area as initial conditions The results of calculations demonstrate that the relative balance of dissipation and shoaling effects is crucial to the detailed evolution of internal wave packets From an observed initial wave packet at the upstream mooring, the numerical evolution simulation agreed reasonably well with the measurements at the distant mooring for the leading two large solitons

Trapping of Low-Level Internal Gravity Waves

Abstract: The characteristics of internal gravity waves propagating on a layer of high stratification near the ground with a deeper, weakly stratified layer above are examined with the aid of a nonhydrostatic numerical model. Simulations are performed of a density current propagating into an environment with a typically observed thermodynamic structure and with no shear. These simulations indicate that the amplitude of the disturbance that forms ahead of the density current is limited considerably by the upward propagation of energy in the upper layer. To explain the large amplitude of observed gravity waves there must exist some additional mechanism, besides the weak stratification in the upper layer, to trap energy at low levels. A thorough examination of several observed gravity wave events suggested three commonly occurring mechanisms. The first mechanism, explored in a previous paper, occurs when winds in the upper layer oppose the wave motion. This reduces the Scorer parameter l2 = N2/(U − c)2 − U″/(...

The dependence of turbulent dissipation on stratification in a diffusively stable thermocline

Abstract: To relate the viscous dissipation rate ϵ in the thermocline to internal waves, we operated the multiscale profiler (MSP) in the eastern North Pacific. The location is well removed from fronts and strong currents, and below 0.6 MPa the water column is diffusively stable. Hence internal wave breakdown is the only known source of turbulence. We found that shear levels were in close agreement with the Garrett and Munk model of internal waves and that dissipation rates were low, . This is the first report of > (previous observations indicated ) and agrees with predictions by McComas and Muller (1981a) and by Henyey et al. (1986), both based on calculations of energy transfer within the internal wave spectrum.

An overview of the SAR Internal Wave Signature Experiment

Abstract: The SAR Internal Wave Signature Experiment (SARSEX) was conducted in the New York Bight in late summer 1984 to investigate synthetic aperture radar (SAR) imaging of oceanic internal waves. The experiment was designed to acquire adequate in situ data to test hydrodynamic theories for the interaction of surface waves and currents, as well as theories for radar imaging of internal wave surface manisfestations. This paper provides an overview of the experiment and highlights from results obtained to date. Excellent agreement has been found between measured and calculated surface wave modulations at wavelengths from 20 to 100 cm. Internal wave signatures in SAR images at X and L band were found to have comparable magnitudes. Calculated SAR intensity modulations were in reasonable agreement with observed modulations at both radar frequencies.

Atmospheric Tidal and Planetary Waves

Abstract: 1. Introduction.- 2. Basic Equations.- 2.1. Hydrodynamic and Thermodynamic Equations.- 2.2. Equations of the Mean Flow.- 2.3. Equations of the Eddies.- 2.4. Energy Balance.- 2.5. Vorticity and Divergence.- 2.6. Linearization.- 2.7. Eliassen-Palm Flux.- 2.8. Ertel Potential Vorticity.- 2.9. Diffusive Separation of Atmospheric Constituents.- 2.10. Spherical Harmonics.- 2.11. Hermite Functions.- 3. External Energy Sources.- 3.1. Solar Irradiance.- 3.2. Solar Heat Input into Upper Atmosphere.- 3.3. Solar Heat Input into Lower and Middle Atmosphere.- 3.4. Lunar Gravitational Tidal Energy.- 3.5. Solar Wind Energy.- 4. Internal Energy Sources and Sinks.- 4.1. Eddy Viscosity.- 4.2. Eddy Heat Conduction.- 4.3. Latent Heat.- 4.4. Newtonian Cooling.- 4.5. Rayleigh Friction.- 4.6. Ion Drag.- 4.7. Feedback between Large-Scale Eddies and Mean Flow.- 5. Horizontal Modal Structure.- 5.1. Separation of Variables.- 5.2. Eigenvalues of Laplace's Equations.- 5.3. Gravity Waves.- 5.4. Rossby-Haurwitz Waves.- 5.5. Kelvin Waves and Yanai Waves.- 5.6. Low Frequency Waves with Positive Eigenvalues.- 5.7. Class II Waves of Wavenumber m = 0.- 5.8. Diurnal Tides.- 5.9. Dynamo Action of Tidal Winds.- 5.10. Rossby Waves Migrating within Mean Zonal Flow.- 5.11. Influence of Zonal Mean Flow on Rossby-Haurwitz Waves.- 5.12. Solutions of Inhomogeneous Laplace Equations.- 6. Vertical Modal Structure.- 6.1. Characteristic Waves.- 6.2. Vertical Wavenumber.- 6.3. Particular Solutions.- 6.4. Boundary Conditions.- 6.5. Normal Modes.- 6.6. Height Structure of External Waves.- 6.7. Directly Driven Circulation Cells.- 6.8. Indirectly Driven Circulation Cells.- 6.9. Height Structure of Internal Waves.- 6.10. Impulsive Heat Input.- 6.11. Ray Tracing of Rossby Waves.- 6.12. Mode Conversion.- 6.13. Baroclinic Instability.- 7. Nonlinear Wave Propagation.- 7.1. Nonlinear Coupling between Rossby-Haurwitz Waves.- 7.2. Analytic Solutions for Weak Coupling of Rossby-Haurwitz Waves.- 7.3. Rossby-Haurwitz Wave Coupling in Realistic Mean Flow.- 7.4. Homogeneous and Isotropic Turbulence.- 7.5. Space-Time Analysis.- 7.6. Nonlinear Normal Mode Initialization.- 7.7. Lorenz Attractor.- 7.8. Logistic Difference Equation.- 7.9. Multiple Equilibria.- 8. Tidal Waves.- 8.1. Seasonal Tides within Lower and Middle Atmosphere (m = 0).- 8.2. Quasi-Stationary Seasonal Waves (m > 0).- 8.3. Climatic Mean Flow.- 8.4. Seasonal Tides within Upper Atmosphere.- 8.5. Migrating Solar Diurnal Tides within Lower and Middle Atmosphere.- 8.6. Migrating Solar Diurnal Tides within Upper Atmosphere.- 8.7. Nonmigrating Solar Diurnal Tides.- 8.8. Lunar Tides.- 8.9. Electromagnetic Effects of Tidal Waves.- 8.10. Energy and Momentum Deposition of Solar Diurnal Tides.- 9. Planetary Waves.- 9.1. Extratropical Transients.- 9.2. Southern Oscillation.- 9.3. Forty-Day Oscillations.- 9.4. Transients in the Tropical Middle Atmosphere.- 9.5. Fluctuations of Atmospheric Angular Momentum.- 9.6. Sudden Stratospheric Warmings.- 9.7. Thermospheric Response to Solar EUV Fluctuations.- 9.8. Thermospheric Storms.- 9.9. Solar Activity Effects within Middle and Lower Atmosphere.- 10. Epilogue.- References.

A deep intermediate nepheloid layer

Abstract: A weak, but very large, intermediate nepheloid layer has been observed on two occasions 8 months apart at a depth of about 2550 m adjacent to the continental slope off the Porcupine Bank. It extended along the slope for over 100 km with no trend in its intensity, and offslope to about 16 km or about 1.4 times the internal Rossby radius. Further offslope, maximum light scattering was found near the depths at which the M2 internal tide is “critical” on the slope. It is suggested that whilst transient nepheloid layers near the slope may temporarily dominate the nephel “signal”, the pattern of light scattering far from the slope is determined by more persistent processes such as the result of sediment erosion by the larger bottom currents associated with “critical” internal waves.

Run-up of internal waves on a gentle slope in a two-layered system

Abstract: This paper describes the dissipative phase of internal-wave run-up on uniform slopes of 0.030 and 0.054 rad as observed in a series of laboratory experiments. The waves were generated continuously at the interface of two miscible layers of differing density. As each wave in the perodic train propagated onto the slope, it steepened and developed into a solitary-like wave before finally overturning. Surrounding fluid was engulfed into the wave as it overturned and the resulting gravitational instability produced considerable turbulence and mixing. The broken wave took the form of a discrete bolus of dense fluid which propagated for some distance up the slope. Bulk parameters which characterize the nature of the bolus were defined and the dependence of these on the incident wave parameters and their behaviour during the run-up phase were examined.

Calculation of radar backscatter modulations from internal waves

Abstract: Calculations of microwave backscatter from the ocean surface using the small-perturbation method (first-order Bragg approximation), a modified Kirchhoff approximation, and a two-scale composite model derived from the modified Kirchhoff expression are described, and predictions of the modulation in the cross section induced by internal wave features are presented. The calculations demonstrate that the modified Kirchhoff approximation and the composite model yield equivalent cross sections if the cutoff wave number separating the long- and short-wavelength regions in the composite model is chosen to be roughly one-third the Bragg wave number. The interaction of internal waves and surface waves, assumed to modulate an equilibrium wind wave spectrum over wavelengths extending from about 0.1 to 10 m, results in significant perturbations to the L band (24 cm) and X band (3 cm) cross sections at incidence angles from 23° to 50°. These calculations indicate that the large modulations observed in X band synthetic aperture radar images of internal waves are due, at least in part, to the tilting of the X band Bragg scatterers by the internal-wave-modulated long-wavelength surface waves.

Long Internal Waves of Large Amplitude

Abstract: The results of an analytical investigation of the propagation of a strongly nonlinear, long internal gravity wave in a two-fluid system are presented. The governing equation is derived and shown to possess a steady-state solitary wavelike solution. The theory is tested experimentally by comparing measured and theoretical shapes of solitary waves.

Broadening of interfacial solitary waves

Abstract: Progressing interfacial gravity waves are considered for two fluids of differing densities confined in a channel of finite vertical extent and infinite horizontal extent. An integrodifferential equation for the unknown shape of the interface is derived. This equation is discretized and the resulting algebraic equations are solved using Newton’s method. It is found that, for a range of heights and densities of the two fluids, the system supports a branch of solitary waves. Progression along the branch produces a broadening of the wave. With increased broadening both the amplitude and the wave speed approach limiting values. The results are in good agreement with analytical studies and indicate the existence of internal surges.

Turbulent mixing at a shear-free density interface

Abstract: The interaction of a sharp density interface with oscillating-grid-induced shear-free turbulence was experimentally investigated. A linear photodiode array was used in conjunction with laser-induced fluorescence to measure the concentration of dye that was initially only in the less dense layer. A laser-Doppler velocimeter was used to measure the vertical velocity in and above the density interface at a point where the dye concentration was also measured. Potential refractive-index-fluctuation problems were avoided using solutes that provided a homogeneous optical environment across the density interface. Internal wave spectra, amplitudes and velocities, as well as the vertical mass flux were measured. The results indicate that mixing occurs in intermittent bursts and that the gradient (local) Richardson number remains constant for a certain range of the overall Richardson number R_j, defined in terms of an integral lengthscale, buoyancy jump and turbulence intensity. The spectra of the internal waves decay as f^(−3) at frequencies below the maximum Brunt-Vaisala frequency. These findings give support to a model for oceanic mixing proposed by Phillips (1977) in which the internal waves are limited in their spectral density by sporadic local instabilities and breakdown to turbulence. The results also indicate that, for a certain R_j range, the thickness of the interfacial layer (normalized by the integral lengthscale of the turbulence) is a decreasing function of R_j. At sufficiently high R_j the interfacial thickness becomes limited by diffusive effects. Finally, we discuss a simple model for entrainment at a density interface in the presence of shear-free turbulence.

Further support for the hypothesis that internal waves can cause shoreward transport of larval invertebrates and fish

Abstract: In areas of mesotides (tidal range 2 to 4 m) and narrow continental shelves (~30 km) internal waves can transport (Le., convey from one place to another) the larvae of coastal organisms shoreward. Research reported here was in an area of microtides (tidal range 80 km), the South Atlantic Bight. Half of the sampled sets of internal waves were aligned parallel to shore and probably originated at the shelf break. The higher densities oflarvae and flotsam in the slicks over these internal waves (convergence zones) than in the rippled water between slicks (divergence zones) indicates that these waves were transporting larvae and flotsam shoreward. All nontransporting internal waves were aligned at a sharp angle to shore and may have formed over shoals oriented perpendicular to shore. To further test the hypothesis that internal waves can transport larvae, surface plankton were col­ lected from the waters over, in front, and behind a set of internal waves. The density of PortulIU8 spp. megalopae was significantly higher in waters in front of the set than behind. The average densities of a variety of larval fish and invertebrates were significantly higher over the internal waves than in front of the set of waves. These data indicate that internal waves can cause shoreward transport of larvae and flotsam. Precompetent larval fish were not carried shoreward by this set of waves while competent stages (Le., juvenile through postflexion) were transported shoreward.

Finite-amplitude solitary waves at the interface between two homogeneous fluids

Abstract: Numerical solutions are presented for finite‐amplitude interfacial waves. Only symmetric waves are calculated. Two cases are considered. In the first case the waves are free‐surface solitary waves propagating on a basic flow with uniform vorticity. Large‐amplitude waves of extreme form are calculated for a range of values of the basic vorticity. In the second case the waves are propagating on the interface between two homogeneous fluids of different densities, which are otherwise at rest. Again large‐amplitude waves of extreme form are calculated for a range of values of the basic density ratio. In particular, in the Boussinesq limit when the density ratio is nearly unity, solitary waves of apparently unlimited amplitude can be found.

Estimates of Potential Vorticity at Small Scales in the Ocean

Abstract: The trimoored design of the current meter army of the Internal Wave Experiment (IWEX) is exploited to calculate time series of relative vorticity, horizontal divergence, vortex stretching and (linen) potential vorticity at five different levels in the vertical. Potential vorticity characterizes the vortical mode of motion which coexists with the (internal) gravity mode (which does not carry potential vorticity). The amplitudes, and the space- and time-scales of the vortical mode, or potential vorticity field, are determined by spectral analysis. The observed variance of potential vorticity (enstrophy) is 10−6 s−2, implying a Rossby number of order 10, the energy 2 × 10−4 m2 s−2 and the inverse Richardson number 0.7. The observed frequencies are interpreted as Doppler frequencies. A low frequency “steppy” potential vorticity field is advected vertically past the sensors by internal gravity waves. The advected potential vorticity field is characterized by a vertical wavenumber smaller than 0.2 m−1 ...

Kinetic Energy Transfer between Internal Gravity Waves and Turbulence

Abstract: We describe a reliable method for distinguishing the mean, wave and turbulence fields when internal waves with changing amplitude perturb the turbulent boundary layer. By integrating the component wave and turbulence kinetic energy budgets through the turbulent layer, we show that only mechanism trasnferring energy between wave and turbulent fields is the work done by the periodic part of the turbulent stress against the wave rate of strain. When these components are π/2 out of phase. the net energy transfer is zero. Eight wave-turbulence interaction events of differing stability are analyzed and interpreted using rapid distortion theory. When density stratification is approximately steady, the phase relationship does not change from π/2 However, periodicity in the stratification changes the phase angle and leads to strong energy transfer from wave to turbulence.

The generation of internal waves by tidal flow over Stellwagen Bank

Abstract: The generation mechanism of internal waves by tidal flow over Stellwagen Bank in Massachusetts Bay is qualitatively clarified. First, in order to demonstrate the continuous generation process of internal waves, a numerical simulation is carried out for the hydrographic condition during a field study by Chereskin (1983). The resulting internal waveforms agree well with the acoustic images obtained at several stages of the tidal flow. Next, the generation mechanism for these internal waves is analyzed via a physical interpretation of the calculated result. This analysis is made by use of characteristics which describe the propagation of the first- and second-mode internal waves. It is shown that each mode internal wave with an upstream phase propagation is efficiently amplified while being carried downstream toward the location where the maximum tidal flow becomes critical: with the decrease of the tidal flow, the internal wave thus amplified begins to propagate upstream. In previous studies, these internal waves were interpreted as quasi-steady lee waves. The present analysis, however, provides a satisfactory explanation for the time-dependent features that are shown in numerical simulation. This indicates that the internal waves over the bank are transient waves formed in response to a time-varying tidal flow, and not quasi-steady lee waves.

Studies of internal gravity waves at Halley Base, Antarctica, using wind observations

Abstract: At Halley Base, which is situated on the Brunt Ice Shelf in Antarctica, internal gravity waves are frequently observed in the stably stratified atmospheric boundary layer. In this paper, time series of wind speed and direction at a height of 8 m, observed from three meteorological masts, are used to determine some of the physical properties of the waves, such as their wavelengths, phase speeds and directions of propagation. The relationship of the results to various theories of the generation of internal gravity waves is considered. It is shown that the waves do not usually propagate in the direction of the surface wind; typically the direction of propagation is rotated about 45° clockwise from the wind vector. The waves most frequently propagate from a direction of about 135°, which is perpendicular both to the Hinge Line (line where the ice shelf meets the land) and to the ridges in the ice shelf, suggesting a topographic influence. It is shown that the waves obey a dispersion relation similar to that for neutral, trapped internal gravity waves.

A comparison of measured surface wave spectral modulations with predictions from a wave-current interaction model

Abstract: Predictions from a wave-current interaction model based on a wave action balance equation are compared with measured surface wave modulations induced by internal waves. The comparison involves relative modulations of the surface wave spectrum at wavelengths ranging from 0.2 to 1.0 m for wind speeds of 3.5 and 7 m/s. Good agreement is found between measurements and predictions for interactions with eight internal waves in two wave packets encountered during the Synthetic Aperture Radar Internal Wave Signature Experiment.

The growth of a turbulent patch in a stratified fluid

Abstract: The behaviour of a turbulent region generated within a linearly-stratified fluid by an external energy source has been studied experimentally. A monoplanar grid that generated small-amplitude oscillations was used as the energy source. The results show that the mixed layer initially grows rapidly, as in an unstratified fluid, but when its physical vertical size becomes rf ∼ (K1/N)½, at a time tf ≈ 4.0 N−1, where N is the buoyancy frequency and K1 is the ‘action’ of the grid, the buoyancy forces become dominant and drastically reduce further vertical growth of the patch. While the patch size remains at rf, a well-defined density interfacial layer is formed at the entrainment interface. An important feature of the interfacial layer is the presence of internal waves, excited by the mixed-layer turbulence. If the grid oscillations are continuously maintained, the interfacial waves break and cause turbulent mixing, thereby increasing the size of the patch beyond rf at a very slow rate. Theoretical estimates are made for the growth characteristics and are compared with the experimental results.

Joint Canada‐U.S. Ocean Wave Investigation Project: An overview of the Georgia Strait Experiment

Abstract: An overview of the Georgia Strait Experiment ( Joint Canada-U.S. Ocean Wave Investigation Project, or JOWIP), 1983, is presented containing a list of participants, objectives, procedures, and main results. JOWIP was designed to provide quantitative comparisons between surface measurements and remote SAR imagery of internal waves and narrow V surface ship wakes. First-order Bragg modeling gives factor of 3 accuracy for L band internal wave modulation; the composite model and possibly nonlinear surface wave-internal wave interaction theory are required at X band. Narrow V wakes were imaged in Dabob Bay, Washington, under low-wind conditions at L band. Surface slopes in the Kelvin wakes are not large enough to produce specular reflections even at a radar incidence angle of 23°. Modulations along the V arms are strongly evident and have the same wavelength as the transverse Kelvin wake component. These results and others are described in detail in other papers in this same issue.

Gravity Waves Generated during Frontogenesis.

Abstract: Gravity waves forced by nonhydrostatic and nongeostrophic processes within a frontal zone are discussed. In particular, stationary waves immediately above and below the surface front are considered. The waves that appear above the front are horizontally stationary with respect to the front, but are vertically propagating. The vertical wavelength here is given by 2πυ/N, since the waves are nearly hydrostatic. The horizontal wavelength of the waves above the front is determined by standing waves that set up below the Front. These waves corrugate the frontal surface, and these corrugations, in turn, determine the horizontal scale of the waves above the front. The waves under the front are standing and are trapped between the earth's surface and the frontal zone which, due to its conditions of flow reversal and small Ri, is assumed to be a reflector of gravity waves. The horizontal scale of the standing waves is determined by their vertical wavelength and the slope of the frontal surface. These waves...

The Linear Stability of Nonlinear Mountain Waves: Implications for the Understanding of Severe Downslope Windstorms

Abstract: Two-dimensional vertically propagating steady state internal waves launched by the flow of stratified unboundedfluid over an obstacle of finite height are subjected to a linear stability analysis. Solution of the associatednonseparable boundary value problem reveals an abrupt change in the stability of small amplitude fluctuationswhen the obstacle is sufficiently high to cause streamlines to locally overturn. In addition to the convedvemode which is expected on the basis of even the simplest physical reasoning, a deep resonant mode is alsodiscovered. This resonant mode is, in fact, the dominant form of instability at small supercnticality, and it istrapped in the cavity between the ground and the level of maximum steepening of the streamlines, in which itgrows at the expense of the kinetic energy of the sheared flow which constitutes the finite-amplitude mountainwave. This trapped mode is instrumental in the transition which takes place in breaking mountain waves thatresults in the Occurrence of ...

Observations of Strong Mid-Pacific Internal Tides above Horizon Guyot

Abstract: Large semidiurnal current and isotherm oscillations were observed by one current meter continuously for 9 months in the waters above Horizon Guyot, a seamount located in the central Pacific. The M2 tides dominated the current-meter record. The M2 current ellipse was oriented along 142°; the semi-major amplitude was 7.6 cm s−1 and the currents rotated in a clockwise direction. The M2 isotherm deflection amplitude was 20 m. The M2 currents observed above the guyot were two to three times larger than M2 currents either observed in or predicted for this region of the mid-Pacific. Evidence suggests that the semidiurnal tide was predominantly an internal tide that was generated at the guyot. The observed internal tide had a narrow bandwidth and a constant amplitude and phase for 9 months, and had characteristics similar to a vertically propagating, rather than a vertically standing, internal wave.

Towed thermistor chain observations of fronts in the subtropical North Pacific

Abstract: A thermistor chain was towed 1400 km through the eastern North Pacific subtropical frontal zone in January 1980. The observations resolve surface layer temperature features with horizontal wavelengths of 0.2–200 km and vertical scales of 10–70 m. The dominant features, which have horizontal wavelengths of 10–100 km, amplitudes of 0.2°-1.0°C, and random orientation, likely arise from baroclinic instability. Associated with them is a plateau below 0.1 cpkm in the horizontal temperature gradient spectrum. Strong temperature fronts O(1°–2°C/3–10 km) are observed near 33°N, 31°N, and 27°N. Temperature variability is partially density compensated by salinity, with the fraction of compensation increasing northward. There is evidence of vertical mixing during high winds. Temperature at 15-m depth is roughly normally distributed around the climatological surface mean, with a standard deviation of approximately 0.5°C. The standard deviation would correspond to an adiabatic meridional displacement of 80–100 km in the mean gradient. Horizontal temperature gradient at 15-m depth has maximum values in excess of 0.25°C/100 m and kurtosis near 80. In the band 0.10–1 cpkm, the 15-m gradient spectrum is inversely proportional to wave number, consistent with predictions from geostrophic turbulence theory, while the spectrum at 70-m depth has additional variance that is consistent with Garrett-Munk internal wave displacements.

A general method for determining upstream effects in stratified flow of finite depth over long two-dimensional obstacles

Abstract: A procedure for determining the flow which results from introducing a long two-dimensional obstacle of finite height into a unidirectional, two-dimensional, stable, but otherwise arbitrary stratified shear flow of finite depth is described. The method is based on a generalization of the known results for two-layer flows, described in Baines (1984). The flow is assumed to be hydrostatic with negligible mixing, and the stratified flow is represented by an arbitrary number of discrete layers, so that the model is hydraulic in character. The procedure involves the calculation of the changes to the steady-state flow resulting from successive increases in the height of the topography from zero. For a given initial flow, introduction of an obstacle only alters the flow in its vicinity for obstacle heights hm less than a height hc, where the flow is critical (implying zero wave speed) at the obstacle crest for some particular internal wave mode. Increasing the obstacle height further causes the flow to adjust to maintain a critical condition at the obstacle crest, and this causes disturbances with the structure of the critical mode to be propagated upstream. These may take the form of an upstream hydraulic jump or of a time-dependent rarefaction (implying a disturbance which becomes increasingly spread out with time), or both, depending on the nonlinear dispersive properties of the system. Their passage past a given upstream location results in a permanent change to the local velocity and density profiles. As the obstacle height is further increased these processes will continue until the flow becomes critical just upstream of the obstacle, or a fluid layer becomes blocked. For greater obstacle heights the above phenomena may be repeated with other modes. A numerical procedure which implements these processes has been developed, and examples of applicatons to two- and three-layer systems are given.

The energetics of the interaction between short small-amplitude internal waves and inertial waves

Abstract: The interaction between a wave packet of small-amplitude short internal waves, and a finite-amplitude inertial wave field is described to second order in the short-wave amplitude. The discussion is based on the principle of wave action conservation and the equations for the wave-induced Lagrangian mean flow. It is demonstrated that as the short internal waves propagate through the inertial wave field they generate a wave-induced train of trailing inertial waves. The contribution of this wave-induced mean flow to the total energy balance is described. The results obtained here complement the finding of Broutman & Young (1986) that the short internal waves undergo a net change in energy after their encounter with the inertial wave field.