Showing papers on "Internal wave published in 1983"

HF Doppler Measurements of Mesospheric Gravity Wave Momentum Fluxes

Abstract: Recent theoretical studies have emphasized the probable importance of internal gravity waves in balancing the momentum budget of the mesosphere. In this paper, we propose a method by which the vertical flux of horizontal momentum can be measured by ground based radars. The method uses two or more radar beams each offset from the vertical to measure the atmospheric motions by the Doppler technique. Provided there is horizontal homogeneity, the momentum flux is proportional to the difference of the variances of the Doppler velocities measured in each beam. The flux convergence and, hence, the associated body force acting on the atmosphere can be inferred by measuring the flux as a function of height. It is shown that mean wind components can also be measured by this method and, under certain circumstances, so can the horizontal wavelengths and phase velocities of the internal waves. Observations of the vertical flux of zonal momentum made with this technique using an HF radar located near Adelaide,...

Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid

Abstract: The evolution of unsheared grid-generated turbulence in a stably stratified fluid was investigated in a closed-loop salt-stratified water channel. Simultaneous single-point measurements of the horizontal and vertical velocity and density fluctuations were obtained, including turbulent mass fluxes central in understanding the energetics of the fluctuating motion. When the buoyancy lengthscale was initially substantially larger than the largest turbulent scales, the initial behaviour of the velocity and density fields was similar to that in the non-stratified case. With further downstream development, the buoyancy lengthscale decreased while the turbulence scale grew. Deviations from neutral behaviour occurred when these two lengthscales became of the same order, after the initially larger inertial forces associated with the initial kinetic energy had become weaker and buoyancy forces became important.Buoyancy forces produced anisotropy in the largest scales first, preventing them from overturning, while smaller-scale isotropic turbulent motions remained embedded within the larger-scale wave motions. These small-scale motions exhibited classical turbulent behaviour and scaled universally with Kolmogorov length and velocity scales. Eventually even the smallest scales of the decaying turbulence were affected by buoyancy, all isotropic motions disappeared, and Kolmogorov scaling failed. The turbulent vertical mass flux decreased to zero for this condition, indicating that the original turbulent field had been completely converted to random internal wave motions.The transition from a fully turbulent state to one of internal waves occurred rapidly in a time less than the characteristic time of the turbulence based on the largest-scale eddies found in the flow at transition. The dissipation rate for complete transition to a wave field was found to be of the order of et = 24.5νN2, where ν is the kinematic viscosity and N the Brunt-Vaisala frequency. This is in fairly good agreement with the value 30νN2 predicted by Gibson (1980, 1981).The present experiments have determined quantitative limits on the range of active turbulent scales in homogeneous stratified turbulence, in terms of an upper limit near the buoyancy lengthscale and a lower limit determined by viscosity in the usual way. This description has been used here to help explain and assimilate the results from the earlier stratified grid-turbulence experiments of Lin & Veenhuizen (1975) and Dickey & Mellor (1980). While some of the features of the present observations may be qualitatively seen in the numerical simulations of the problem of Riley, Metcalfe & Weissman (1981), there are fundamental differences, probably due in part to large differences in initial lengthscale ratios and in the limited range of scales attainable in numerical simulations. The present experiments may serve as a useful test case for future modelling and interpretation of the behaviour of turbulence in stratified flows observed in the oceans and atmosphere.

Internal Wave Wake of a Moving Storm. Part I. Scales, Energy Budget and Observations

Abstract: The ocean's baroclinic response to a steadily moving storm is analyzed using a numerical model for an inviscid, multi-layered fluid. This first part of a two-part study gives a detailed account of the response to a rapidly moving hurricane, while parameter dependence is examined in the second part. A central theme of both parts is the coupling between wind-forcing, the surface mixed layer, and the thermocline. The baroclinic response is made up of a geostrophic component and a three-dimensional wake of inertial-internal waves which is emphasized. These waves initially have large horizontal spatial scales set directly by the storm. Their along-storm track wavelength is the storm translation speed times the wave period, which is typically five percent less than the local inertial period. Their cross-track scale is the storm scale. If the storm is intense as it is here, finite amplitude effects soon produce a double inertial frequency wave and smaller spatial scales. An important qualitative result ...

Waves observed upstream of interplanetary shocks

Abstract: The properties of the waves that are present upstream of interplanetary, collisionless, quasi-parallel shocks are described. Two types of such waves have been detected, a higher frequency whistler mode wave and a lower frequency fast mode MHD wave. Both are typically circular or elliptically polarized right-hand waves which propagate along the ambient magnetic field with a 15 deg angle cone. The high frequency waves have sufficient group velocities to outrun the shock, and may be generated by cyclotron resonance with 100 eV to 1 keV shock electrons. The lower frequency waves must be generated locally by particles upstream of the shock, probably by 1-10 keV ions flowing away from the shock. Distinct changes in the spectra of upstream waves as a function of distance from the shock have been noted.

Internal mixing in stratified fluids

Abstract: Using experimental measurements, estimates are made of the efficiency of conversion of kinetic energy into potential energy through vertical mixing in a continuously stratified fluid. In the experiments kinetic energy was supplied continuously at a rate of e to a fundamental internal wave mode in a rectangularly bounded and initially linear stable stratification. Mixing resulted from the instability of this wave and its consequent ‘breaking’. Potential energy was gained by the system at rate , were found to have an average for seven runs of 0·24eM, with a standard deviation for the coefficient of 0·1, and no significant correlation with energy supply rate.These results, the first of their kind to correct for incidental losses, substantiate the values previously assumed in estimates of dissipation and vertical diffusion in the ocean and the atmosphere, and validate the assumption of similarity between buoyancy and mass transfer on which they are based. The efficiency value also agrees with the kinematic prediction for localized homogenization in small discrete volumes made in the companion paper (McEwan 1983). On the basis of that work it is inferred from the present results that the mixing efficiency is only weakly dependent upon Prandtl number provided that this is of order unity or greater.

Wave propagation through random media: Contributions from ocean acoustics

Abstract: Recent theoretical and experimental progress in understanding sound transmission through a random field of internal waves is reviewed. Some attempt is made to place this work in historical relation to similar efforts in radio-wave propagation through the ionosphere and light propagation through the atmosphere. It is emphasized that internal waves as a random medium possess several new features unfamiliar to those dealing with homogeneous isotropic turbulence. The effect of a background deterministic wave-speed variation (the ocean sound channel) is central to the theoretical treatment, which is based on a path-integral solution of the parabolic wave equation. A distinction is made between two sections of the saturated region and some emphasis is placed on the region of partial saturation. Comparison with experiment is discussed with examples from the two-point mutual coherence function of time, frequency, and vertical separation; the intensity correlation in time, frequency, and vertical separation; the spectra of phase and log intensity, pulse propagation, and the higher moments of intensity.

A numerical model of gravity wave breaking and stress in the mesosphere

Abstract: The goal of the study is to calculate numerically the deceleration and heating caused by breaking gravity waves. The effect of the radiative dissipation of the wave is included as vertical-wavelength-dependent Newtonian cooling. The parameterization for zonal deceleration is extended by breaking gravity waves (Lindzen, 1981) to include the turbulent diffusion of heat and momentum. After describing the numerical model, the numerical results are presented and compared with the parameterizations in a noninteractive model of the mean zonal wind. Attention is then given to the transport of constituents by gravity waves and the attendant turbulent zone. It is noted that if gravity wave breaking were not an intermittent process, gravity wave stresses would produce an adiabatic mesosphere with a zonal mean velocity close to the phase speed of the breaking wave.

A non-reflective upper boundary condition for limited-height hydrostatic models.

Abstract: A simple upper boundary condition for hydrostatic, Boussinesq models is derived from a linear internal wave theory, assuming a uniform stratification and no Coriolis effects. This condition is applied in a two-dimentional nonlinear model of the planetary boundary layer. The numerical implementation and some stability problems are discussed. A comparison of the results of numerical experiments using different vertical extensions with analytical solutions is used to show that the condition provides a satisfactory solution to the problems of radiation of upward propagating energy.

Measurements of wind velocity and pressure with a wave follower during Marsen

Abstract: Air pressure data are used in determining the rate of momentum transfer from wind to waves. On the basis of the wind velocity measurements, the wave-induced airflow and its coherence with waves are obtained for various wind velocities and phase speeds of the ocean waves. The pressure results suggest that momentum transfer to waves can be specified by a certain relation, which is given. The wind-velocity results suggest that the wave-induced airflow is much smaller than the mean wind speed. An empirical equation is proposed for the modulation of atmospheric transfer to short waves caused by the orbital velocity of long waves.

Nonlinear features of internal waves off Baja California as observed from the SEASAT imaging radar

Abstract: The synthetic aperture radar (SAR) on SEASAT has yielded well-defined images of quasi-periodic internal waves in the waters on the west side of Baja California. These waves occur in groupings separated by 15–23 km, each group having 2–20 striations with wavelengths of the order of 300 m or longer. They appear in water approximately 200 m deep, shoreward of several banks at the continental shelf edge whose depths are as shallow as 15 m. The wave surface signatures exhibit clear nonlinear features: higher-than-linear group velocities, and decreases in wavelength, crest length, and amplitude toward the rear of the packet. Environmental data for the area have been examined, and these show a well-developed mixed layer, low winds, and vigorous tidal action. Thus, stratification, wind speed, tidal current, and bottom topography apparently combine to establish proper conditions for tidal generation of internal waves. The images have been analyzed from the standpoint of nonlinear wave theory, and it is shown that the vertical displacement of an isopycnal surface can be estimated from a combination of SAR imagery, vertical density profiles, and simple theoretical expressions. Numerical examples are given.

Tidally generated high-frequency internal wave packets and their effects on plankton in Massachusetts Bay

Abstract: Tidally generated internal wave packets occur twice a day during late summer in Massachusetts Bay, U.S.A. The packets are formed at Stellwagen Bank and propagate into the Bay at about 60 cm sec-; they dissipate in shallow water at the western side of the Bay. The dominant waves in packets have lengths of about 300 m, periods of between 8 and 10 min, and amplitudes of up to 30 m. Overturning of the waves has been observed acoustically over Stellwagen Bank, in the deep (80 m) waters in the center of the Bay, and during dissipation in shallow water. The effects of the internal waves on the distribution of plankton were investigated in August 1977 using an instrument package (Longhurst-Hardy Plankton Recorder, in situ fluorometer, CTD) towed either at a constant depth or following an isotherm through wave packets. Phytoplankton and zooplankton appear to be carried passively up and down by the internal waves; the data were insufficient to resolve any active response by zooplankton to vertical displacements by the waves. Vertical distributions of the plankton were altered by overturning of waves and subsequent mixing. Patterns of horizontal distributions of plankton determined by constant-depth tows were dominated by the effects of internal wave vertical displacements. Isotherm-following tows removed much of the variability due to wave displacement, but problems of following rapidly moving isotherms introduced considerable smallerscale variability. Changes in zooplankton abundance on tow length scales (600-1200 m) were not correlated with temperature, salinity, or density; some significant correlations with chlorophyll fluorescence occurred when internal wave activity was present. Twice a day for several hours or more, phytoplankton were vertically displaced by as much as 30 m, with a period of about 10 min. The light level plant cells experienced varied from 0.1 to 26% of the ambient surface illumination. This rapid change in light should alter fluorescence yields of plant cells and affect continuous in situ measurements of chlorophyll fluorescence. The timing of internal wave packets varies with the semidiurnal tidal cycle and therefore interacts with the day-night cycle to significantly alter the light regime experienced by plant cells over a two-week period. This could affect the primary productivity of the Bay in the area affected by internal wave packets. The sporadic occurrence of internal wave overturning and mixing events in the deep waters of the Bay could enhance primary production by increasing nutrient input to the mixed layer. This effect should be greatly enhanced in the shallow waters where the internal waves 1. Scripps Institution of Oceanography, La Jolla, California, 92093, U.S.A. 2. Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, 02543, U.S.A. 3. Gulf Research and Development Company, P.O. Box 2038, Pittsburgh, Pennsylvania, 15230, U.S.A.

Models of the oceanic internal wave field

Abstract: In recent years, considerable progress has been made in internal wave research by a fruitful combination of experiment and theory. Kinematical models of the wave field appear to be well established, and dynamical models are evolving toward a stage of understanding the energetics and the interrelations of the waves within the oceanic field of motion. This review presents kinematical models of the wave field in terms of vertically progressive waves (WKB waves) as well as standing modes. Some emphasis is attributed to critical layer effects. Spectral models have been successfully developed for the wave field in the main thermocline. This appears to be in a stationary universal state with respect to spectral shape and level, whereas the upper ocean wave field shows considerable temporal and regional variability. Several approaches for separating the internal wave contribution from turbulence and other contaminations in observations have been proposed. This problem is of particular relevance in the transition region between waves and small-scale turbulence at small vertical wavelengths. An accurate identification of reversible (wave induced) fine structure and irreversible fine structure is needed to determine the dissipation rate of the wave field and the mixing rates of the ocean. The search for dynamical relations of the wave field to environmental conditions has been extensive. The lack of dynamical correspondences between the wave spectrum and possible forcing fields in observations suggests that forcing is weak. Theoretical models of wave generation show that many mechanisms may contribute with equal efficiency. In concert with the observed low dissipation rates in the deep ocean, these results point toward the conclusion that there is no dominant source of energy but weak forcing by many different sources and weak dissipation. Under such conditions the interrelation between forcing and dissipation as well as the spectral form is controlled by internal transfer by wave-wave interactions which are very efficient in relaxing spectral distortions to the observed universal form.

The characteristics of breaking waves, bubble clouds, and near-surface currents observed using side-scan sonar

Abstract: An inverted 248 kHz two-component side-scan sonar mounted on the sea bed in a mean depth of 34 m has been used to detect the clouds of bubbles produced by breaking surface waves. The sonar has a range of about 150 m. The breaking waves appear on the sonograph records as short-lived intense echoes, and form patterns which can be explained in terms of the behaviour of groups of waves in which the highest are breaking. The bubble clouds are slightly elongated in the wave direction when they are first formed and, in winds of 5.1 m s−1, have lifetimes of up to about 5 min. Soon after a wave breaks, the horizontal motion of the fluid in which the bubbles are formed becomes similar to that of the surroundings, and the bubbles continue to be advected by the near-surface currents. The rate of drift of bubble clouds along the directions of the sonar beams allows the components of the currents to be measured. The sonographs show that large changes in currents can occur over horizontal distances of as little as 5 to 10 m when fronts are passing. The motion of the fronts through the water can be measured. The sonographs have been used to measure surface currents induced by internal waves. Bands of bubbles associated with Langmuir circulation can be detected in strong winds or when moderate winds are accompanied by heavy rain.

A statistical model of fluid-element motions and vertical diffusion in a homogeneous stratified turbulent flow

Abstract: The vertical displacements Z(t) of fluid elements passing through a source z = 0 at t = 0 in a horizontal mean flow with stably stratified statistically stationary turbulence (with buoyancy frequency N and velocity time-scale T), under the action of random pressure gradients and damping by internal wave motions, are investigated by a model Langevin-like equation, and by a general Lagrangian analysis of the displacements, of the density flux and of the energy of fluid elements. Solutions for the mean-square displacement Z”(t), the mean-square velocity 2, and the autoeorrelation of the velocity are calculated in terms of the spectrum @(s) of the pressure gradient. We use model equations for the momentum of fluid elements and for the exchange of density fluctuations between fluid elements, taking the elements’ diffusion timescale to be y-l times the buoyancy timescale W1, where y is a measurable parameter. In the case of moderate-to-strong stable stratification (i.e. NT 2 l), we find the following. (i) When there is no change of the fluid elements’ density (y = 0), the mean-square displacement z” of marked particles ceases to grow when t 2 8-l, and its asymptotic value is proportional to G/W, where the constant of proportionality, ?(a), is O(1) and a decreasing function of (NT)-l. This result is also shown to be a general consequence of the finite potential and kinetic energy in the stationary turbulence. (ii) If there is a small diffusive interchange of density between fluid elements (i.e. y 4 l), the marked particles’ mean-square displacement has a slow linear growth (i.e. (iii) Such molecular processes must also dilute the initial concentration of contaminants (e.g. dye or smoke) in those fluid dements that diffuse above the limit in (i). (iv) The mean-square fluctuation of density is proportional to the product of the asymptotic mean-square displacement of marked particles and the square of the mean density gradient (-9) (i.e. 7 = g2F = +P(a, y = 0) 9zzw’/N*). (v) The flux Fp of density in a turbulent flow can be expressed exactly as the sum of two terms, the first $(dF/dt) 9, being caused by thc growth of the displacements of fluid elements, and the second Z(p +p’) being caused by the mixing between fluid elements. In stable flows, it is shown that the second element is dominant, and Fp - yGNp,g while the first is smaller by O(y). Previous laboratory and field measurements of w2, Z2, p‘2 and K,(t) are discussed in some detail and shown to be consistent with this model.

Observations of transport to surface waters from a plunging inflow to Lake Mead1

Abstract: Algae growing in the surface water of Las Vegas Bay, an arm of Lake Mead, may receive nutrients contained in the stream entering through Las Vegas Wash. The stream water is more dense than the lake water due to dissolved salts. Existing hydrodynamic theory predicts that the stream should form a submerged layer isolating the nutrients from the surface. The theory was tested by introducing dye into the stream during two 14-day experiments; salinity, temperature, and dye concentration were monitored in the inner portion of the bay. Significant dye concentrations were found in the surface waters during both experiments, and two modes of internal waves with amplitudes up to 6 m were observed. The wave motion provided the main mechanism for transport to the surface in the first experiment; in the second an additional mechanism was the creation and destruction of temporary thermoclines due to meteorological variation. An approximate nutrient balance shows that in each case about 10% of the entering nutrients were available to the surface water within the 14-day period of the experiments.

The effects of stable stratification on turbulent diffusion and the decay of grid turbulence

Abstract: Experiments are described in which a grid is towed horizontally along a large tank filled first with water and then with a stably stratified saline solution. The decay rates of the r.m.s. turbulent velocity components (w’, v’) perpendicular to the mean motion are measured by a ‘Taylor’ diffusion probe and are found to be unaffected by the stable stratification over distances measured from 5 to 47 mesh lengths (M) downstream, and over a range of Froude number U/NM of ∞ and 8·5 to 0·5, U being the velocity and N the buoyancy frequency. The Reynolds number Mw’/ν of the turbulence was about 103, where v is the kinematic viscosity. The vertical velocity fluctuations produced near the grid were reduced by the stratification by up to 30% when U/MN ≈ 0·5. Large-scale internal wave motion was not evident from the observations within about 50 mesh lengths of the grid.The turbulent diffusion from a point source located 4·7 mesh lengths downstream was studied. σy, σz, the horizontal and vertical plume widths, were measured by a rake of probes. σy was found to be largely unaffected by the stratification and grew like t½, while σz was found in all cases to reach an asymptotic limit σz∞ where 0·5 [les ] σz∞N/w’s [les ] 2, w’s being the r.m.s. velocity fluctuations at the source; the time taken for σz to reach its maximum was about 2N−1. These results are largely in agreement with the theoretical models of Csanady (1964) and Pearson, Puttock & Hunt (1983).

Experiments on solitary internal Kelvin waves

Abstract: Elementary calculations indicate that the effect of the Earth's rotation is likely to be important in the dynamics of most internal waves in oceans, lakes and the atmosphere. Here we present measurements of the structure and properties of one class of such waves, namely solitary internal Kelvin waves, in which the Coriolis force generated by wave motion in a stratified fluid is opposed by a pressure gradient and hence change in wave amplitude along its crest. We confirm that the wave speed is independent of the rate at which the system rotates and depends only on the stratification and maximum wave amplitude. However, rotation is shown to have a large effect on both the rate at which the amplitude varies with time and the cross-stream’ structure of the wave. In accordance with well-established theory, the amplitude transverse to the direction of propagation varies exponentially. This results in a decreasing wave speed with increasing distance from the wall, which in turn requires the wave front be curved backwards in order for the wave as a whole to propagate at a speed given by its maximum amplitude. Such a front curvature is not contained within the available theories. The rapid decay of wave amplitude is found to be due to the generation of inertial waves in the homogeneous fluid above and below the internal wave, and a reasonably successful scaling of this effect has been found. We also discuss the adjustment of the waves to geostropic balance and comment on applications of our results to natural systems.

Generation of internal waves in Massachusetts Bay

Abstract: Observations of stratified tidal flow over a submarine ridge indicate that the large amplitude and asymmetry of the topography are critical in determining the type of flow response. The observations consist of hydrographic, current meter, and echo-sounding data and are used as a basis for inferring the generation mechanism of previously observed trains of internal waves. The flow response on ebb and flood tide is categorized according to the Froude number classification of sill flows proposed by Farmer and Smith (1980a). The calculated Froude numbers, response length scale, and duration differ markedly between the two phases of the tide due to the asymmetry of the bank. The development of two features in the acoustic imagery related to wave formation is followed.

The stability of internal solitary waves

Abstract: A theory is developed relating to the stability of solitary-wave solutions of the so-called Benjamin-Ono equation. This equation was derived by Benjamin (5) as a model for the propagation of internal waves in an incompressible non-diffusive heterogeneous fluid for which the density is non-constant only within a layer whose thickness is much smaller than the total depth. In his article, Benjamin wrote in closed form the one-parameter family of solitary-wave solutions of his model equation whose stability will be the focus of attention presently.

Turbulent Dissipation Over the Continental Slope Off Vancouver Island

Abstract: Thirteen profiles of the rate of viscous dissipation of turbulent kinetic energy &epsi¯ were made over the continental slope off Vancouver Island between 12 and 14 May 1980 in conjunction with CTD and moored current-meter observations. Systematic variability was observed in the vertical but not in the horizontal direction. Above 200 m depth numerous salt-stabilized temperature inversions were seen and dissipation rates were significantly larger than below 200 m. Dissipation rates below 200 m are the lowest ever reported and coincide with a low level of energetics revealed by the current meter moorings. Comparison with the Garrett-Munk internal wave spectrum indicates an e-folding decay time of internal wave energy of ∼50 days at depths below 200 m.

Ship waves and lee waves

Abstract: Dynamics analogous to those of surface ship waves on water of finite depth are noted for the three-dimensional trapped lee wave modes produced by an isolated obstacle in a stratified fluid. This vertical trapping of wave energy is modeled by uniform upstream flow and stratification, bounded above by a rigid lid, and by a semiinfinite fluid of uniform stability whose wind velocity increases exponentially with height, representing the atmosphere. While formal asymptotic solutions are produced, limited quantitative usefulness is obtained through them because of the limitations of the approximations and the infinity of modes in the solution. Time-dependent numerical models are accordingly developed for both surface ship waves and internal and atmospheric ship waves, yielding a variety of results.

Overhanging interfacial gravity waves of large amplitude

Abstract: Methods to investigate the existence of overhanging gravity waves of permanent form at the interface between two uniform fluids of different density are discussed. Numerical results which demonstrate their existence are presented.

A conjecture relating oceanic internal waves and small‐scale processes

Abstract: A scheme is suggested providing an overall account of vertical wavenumber spectra of velocity and temperature in the ocean. The account ranges from vertical scales of hundreds of metres to scales of millimetres. Larger scales are dominated by quasi‐random shear refraction of internal waves. Smaller scales are dominated by parallel cascades of kinetic and potential energy. In contrast to previous ideas, the present scheme suggests that vertical mass flux p'w’ plays no dynamically significant role at any length scale. Efficiency of vertical mixing must be very small. Small‐scale spectra are assumed to be in equilibrium with respect to variance production, transfer and dissipation; no significant “fossilization” is expected.

On the theory of electromagnetic induction in the Earth by ocean currents

Abstract: of the electrical conductivity structure of the earth. TM modes are closely associated with the Coriolis force deflection of water currents and with coastline effects that limit the source currents to the ocean basin. PM modes are induced by nondivergent electric currents that are fully contained within the ocean. Surface gravity waves and a Kelvin wave are examined in detail. The Kelvin wave result of Larsen (1968) is reevaluated, and because the upper lithosphere was modeled as an insulator, significant errors in his magnetic induction values, caused by neglect of the TM mode, are revealed. The sensitivity of the TM mode magnetic field to lithospheric electrical conductivity suggests the use of tidal induced electromagnetic fields to probe the earth's conductivity structure. Electromagnetic fields are induced in the earth by exter- nal, ionospheric and magnetospheric, current systems and have long been used to investigate the electrical conduc- tivity structure of the earth by the geomagnetic depth sounding or magnetotelluric methods. An additional natural source, the dynamo interaction of ocean currents with the ambient geomagnetic field, is important in the world oceans. Since the crust and mantle of the earth are electrical conductors that couple to the ocean both conduc- tively and inductively, observations of low-frequency elec- tromagnetic fields in the ocean contain information about both the electrical conductivity of the earth and the circu- lation of the oceans. Electromagnetic fields produced by ocean flows are dis- cussed by Cox et al. (1971), Sanford (1971), and Larsen (1973). Solutions of the Maxwell equations for surface gravity waves were obtained by Weaver (1965) for an infinitely deep ocean and were extended to long waves in a finite depth ocean by Larsen (1971). The surface and internal wave problem was also investigated by Podney (1975), who presented a general method for solving fluid induction problems using a magnetic vector potential when the flow is incompressible. All of these studies indicate that the induced electromagnetic fields are small, amount- ing to fractions of a/xV/m or a few nanoteslas (nT) near the sea surface. At lower frequencies, tidal signals have been detected in both seafloor- and island-based elec- tromagnetic data (Larsen, 1968). Low-frequency, meso- scale and large-scale, ocean-induced electromagnetic fields are discussed by Cox (1980, 1981), who emphasized the influence of shallow electrical conductivity structure on the observed fields.

Mixing processes in lakes: mechanisms and ecological relevance

Abstract: In Lake Baldegg, Switzerland (surface area 5.3 km2, maximum depth 66 m) the analysis of data from moored instrument systems (atmospheric boundary layer, lake temperature distribution, bottom currents) was correlated to the long-term development of vertical mixing as seen from profiles of natural isotopes (radon-222, tritium and helium-3) and chemical species. The investigation shows: 1. Vertical mixing coefficients below 25 m are small. Consequently the vertical concentration distribution of sediment emanating species in the deep hypolimnion is controlled by the bottom topography. 2. Renewal of deep hypolimnic water is significant even during stratification. 3. Weakly damped internal waves characterize the internal dynamics during stratification. 4. Horizontal bottom currents play an important role in the hypolimnion mixing and can be correlated to internal waves during stratification.

A Statistical Dynamical Theory of Strongly Nonlinear Internal Gravity Waves

Abstract: A statistical dynamical closure theory describing the interaction of strongly (and weakly) nonlinear two-dimensional internal waves in the presence of viscous dissipation and thermal conduction is derived By applying renormalization methods originally formulated for quantum and classical statistical field theory, closures similar to the Direct Interaction and eddy-damped quasi-normal procedures of turbulence are derived These methods are applied directly to the strongly nonlinear primitive field equations in Eulerian variables, thus avoiding the small amplitude assumptions inherent in the resonant interaction formalism Propagator renormalization techniques provide formulas for the nonlinear internal wave frequency and spectral width in terms of the energy spectrum The commonly used multiple time and space scale analysis is replaced by an analysis of the two-point correlation functions in terms of sum and difference variables This permits the systematic development of a Landau equation This

Wave and turbulence structure in a disturbed nocturnal inversion

Abstract: Acoustic sounder and tower data obtained at the Boulder Atmospheric Observatory (BAO) are used to examine several features of the wave and turbulence structure associated with a disturbed nocturnal inversion. General features, including mean fields and Richardson number, for the case selected for this study are presented. Spectral analysis of the tower data reveals a separation of energy into wavelike and turbulent fluctuations. Analysis of the heat flux, however, shows upward counter-gradient fluxes in the vicinity of a low-level jet and near the top of the inversion. Cospectral analysis shows that the major contribution to the upward heat flux occurs at frequencies that would normally be considered characteristic of waves. In some cases, the upward flux is associated with a phase shift between vertical velocity w and fluctuating temperature θ different from the quadrature relation that would be expected of internal waves. Time series analysis reveals that these unexpected positive fluxes occur in relatively short bursts. Analysis of time series of θ and w in other cases, as well as inspection of acoustic sounder records, shows that sometimes such upward fluxes can result from a combination of wave motion and horizontal temperature advection. In this case the advection is associated with a shallow cold front.