Showing papers on "Internal wave published in 1978"

Waves in fluids

Abstract: Preface Prologue 1. Sound waves 2. One-dimensional waves in fluids 3. Water waves 4. Internal waves Epilogue Bibliography Notation list Author index Subject index.

On the response of a poro-elastic bed to water waves

Abstract: The problem of the response of a porous elastic bed to water waves is treated analytically on the basis of the three-dimensional consolidation theory of Biot (1941). Exact solutions for the pore-water pressure and the displacements of the porous medium are obtained in closed form for the case of waves propagating over the poro-elastic bed. The theoretical results indicate that the bed response to waves is strongly dependent on the permeability k and the stiffness ratio G/K’, where G is the shear modulus of the porous medium and K’ is the apparent bulk modulus of elasticity of the pore fluid. The earlier solutions for pore-water pressure by various authors are given as the limiting cases of the present solution. For the limits G/K′ → 0 or k→ ∞, the present solution for pressure approaches the solution of the Laplace equation by Putnam (1949). For the limit G/K′→ ∞, the present solution approaches the solution of the heat conduction equation by Nakamura et al. (1973) and Moshagen & Torum (1975).The theoretical results are compared with wave tank experimental data on pore-water pressure in coarse and fine sand beds which contain small amounts of air. Good agreement between theory and experiment is obtained.

Tsunamis -- the propagation of long waves onto a shelf

Abstract: The various aspects of the propagation of long waves onto a shelf (i.e., reflection, transmission and propagation on the shelf) are examined experimentally and theoretically. The results are applied to tsunamis propagating onto the continental shelf. A numerical method of solving the one-dimensional Boussinesq equations for constant depth using finite element techniques is presented. The method is extended to the case of an arbitrary variation in depth (i.e., gradually to abruptly varying depth) in the direction of wave propagation. The scheme is applied to the propagation of solitary waves over a slope onto a shelf and is confirmed by experiments. A theory is developed for the generation in the laboratory of long waves of permanent form, i.e., solitary and cnoidal waves. The theory, which incorporates the nonlinear aspects of the problem, applies to wave generators which consist of a vertical plate which moves horizontally. Experiments have been conducted and the results agree well with the generation theory. In addition, these results are used to compare the shape, celerity and damping characteristics of the generated waves with the long wave theories. The solution of the linear nondispersive theory for harmonic waves of a single frequency propagating over a slope onto a shelf is extended to the case of solitary waves. Comparisons of this analysis with the nonlinear dispersive theory and experiments are presented. Comparisons of experiments with solitary and cnoidal waves with the predictions of the various theories indicate that, apart from propagation, the reflection of waves from a change in depth is a linear process except in extreme cases. However, the transmission and the propagation of both the transmitted and the reflected waves in general are nonlinear processes. Exceptions are waves with heights which are very small compared to the depth. For these waves, the entire process of propagation onto a shelf in the vicinity of the shelf is linear . Tsunamis propagating from the deep ocean onto the continental shelf probably fall in this class.

Gravity wave generation, propagation, and dissipation in the thermosphere

Abstract: This is the first in a series of papers examining large-scale gravity waves in the thermosphere and their ability to transfer energy from high to low latitudes during magnetic disturbances. The gravity wave source is assumed to be either the Lorentz force of auroral electrojet currents or else a heat input due to energetic particle precipitation or to Joule heating. It is pointed out that the characteristic vertical width of the gravity wave source should usually lie between 2 and 4 pressure scale heights, placing constraints on the vertical wavelengths and horizontal velocities of the generated waves. A simplified analytic model of small-amplitude wave generation by a current source shows how wave energy production depends on the temporal and spatial dimensions of the source, on the electric field strength, and on the electron density enhancement. The steep thermospheric temperature gradient in the vicinity of the source altitude strongly influences the properties of upward and downward propagating waves compared with waves generated in an isothermal atmosphere. Waves produced by the Lorentz force of Hall currents, by the Lorentz force of Pedersen currents, and by Joule heating are influenced quite differently by this temperature gradient. Because upgoing waves above the source are combinations of waves originally launched upward and waves originally launched downward but reflected around 110 km altitude, the mean effective source altitude is about 110 km for the far field response in the thermosphere. Large-scale traveling ionospheric disturbances observable at middle latitudes are most likely produced primarily by Pedersen, rather than Hall, currents. The temperature structure of the thermosphere generally causes gravity wave packets to refract upward; waves traveling with a horizontal component of velocity faster than 250 m/s and with an initial downward component of group velocity will always be reflected upward in the lower thermosphere. The effects of viscosity, heat conduction, and Joule dissipation tend to filter out shorter-period and slower moving waves from observation points at some distance from the source, so that only long-period fast moving waves can reach low latitudes from an auroral source. For example, a wave with a 94-min period moving horizontally at 605 m/s is largely dissipated by the time it has traveled 4000 km from a typical auroral source. A numerical simulation using a fairly realistic thermospheric model illustrates many of the points described from analytic considerations.

The Fission and Disintegration of Internal Solitary Waves Moving over Two-Dimensional Topography

Abstract: The propagation of long internal waves over two-dimensional topography is discussed. A two-dimensional version of the Korteweg-deVries equation is derived with variable coefficients which depend on the local fluid depth. The fission law for solitary waves propagating into shallower water for two density stratification models and the possible disintegration of a solitary wave into a dispersive packet are discussed on the basis of this equation.

The effect of internal waves on surface wind waves 2. Theoretical analysis

Abstract: A theoretical description is given of the behavior of a broadband, small-amplitude wind wave field in a perturbing internal wave velocity pattern. The theory includes the effect of the local wind. Specific predictions are made for the case of weak internal wave currents, and these predictions are compared with measurements. The theory predicts the magnitude of the mean square slope changes reasonably well, and it predicts the quadrant of the phases correctly. General features of the perturbed surface wave energy spectrum integrated in angle are also predicted reasonably well, and comparisons are made of the theoretical and measured local integrated spectrum at roughened areas and at slick areas.

The Instability of a Forced Standing Wave in a Viscous Stratified Fluid: A Laboratory Analogue of .the Quasi-Biennial Oscillation

Abstract: An experiment is described in which a standing internal wave is forced at the lower boundary of an annulus of salt-stratified water. At sufficiently large forcing amplitudes, the wave motion generates a strong mean azimuthal circulation which itself exhibits a long-period oscillation. Theoretical calculations, based on the wave-driven theory of the quasi-biennial oscillation of the tropical stratosphere (with suitable modifications), are performed and compared with the experimental results. Agreement is good and the study thus provides substantial confirmation of the fundamental principles of the theory.

Observations of Long Nonlinear Internal Waves in a Lake

Abstract: This paper describes observations of large-amplitude, long internal waves in Babine Lake. A unique feature of the observations is that they were taken simultaneously at several different points along the major axis. This permits study of the formation and subsequent development of individual waves as they travel along the lake. The waves typically begin as depressions on the thermocline at the south end following strong westerly winds directed along the lake's major axis. A bend in the southern part of the lake, together with the influence of surrounding mountains, can introduce a divergence in the longitudinal component of the wind stress which in turn produces a thermocline elevation. These two effects then combine to form a northward traveling surge. Subsequent modification of the waveform is interpreted in terms of nonlinear steepening and dispersion.

The Iwex spectrum

Abstract: We describe the analysis of current and temperature cross spectra from the trimoored internal wave experiment Iwex and present a spectral model for the fluctuations in the internal wave range. The model consists of internal waves contaminated by temperature and current fine structure and by current noise. Except for the inertial and tidal frequencies the distribution of wave energy is vertically symmetric and horizontally isotropic. The wave number spectrum is characterized by a bandwidth of about 20–10 equivalent modes (decreasing with frequency), by a power law at high wave numbers, and by a sharp peak at low wave numbers. The general features of this spectrum agree fairly well with the one proposed by Garrett and Munk (1975). The contaminations increase with frequency. Contamination by temperature fine structure is confirmed by independent measurements. The Iwex spectral model provides a consistent description of all observed cross spectra.

The anatomy of the Antarctic polar front in the Drake Passage

Abstract: An intensive three-dimensional survey of the Antarctic Polar Front was made in the Drake Passage in March 1976. The front, which was imbedded within one of the high-velocity cores of the circumpolar current, is viewed as a water mass boundary demarking the northern extent of near-surface antarctic waters. Within the front, water masses are observed to intrude, one above the other, with characteristic vertical scales of 50–100 m. The intrusions are horizontally anisotropic, being elongated in the alongstream direction and constrained primarily to the upper 800 m of the front. The spatial and temporal persistence of the variability is examined through the analysis of continuous vertical profiles of horizontal velocity, temperature, salinity, and oxygen with discrete sampling of nutrients. Analysis of the velocity data showed the mean current flowing to the NNE with speeds of the order of 30–40 cm s−1 in the upper 600 m, with temporal variability over a 28-hour ‘yo-yo’ due primarily to internal gravity waves. The thermohaline variability was not internal wave induced but rather was associated with nearly isentropic advection of different water masses across the front. Cold fresh and warm salty intrusions did not conserve potential density, however, and double-diffusive transfers are strongly suggested as being crucial to an understanding of the dynamics of the intrusions. Applying a model (Joyce, 1977) for lateral mixing we estimate poleward temperature and salinity fluxes due to interleaving of 0.086°C cm s−1 and 0.069‰ cm s−1, respectively. If these values are typical, interleaving could play a significant role in large-scale balance of salt and, to a lesser extent, heat for the Southern Ocean.

On the existence theory for irrotational water waves

Abstract: This paper concerns steady plane periodic waves on the surface of an ideal liquid flowing above a horizontal bottom. The flow is irrotational. The volume flow rate is denoted by Q, the velocity potential by o, the period in o of the waves by 2L, and the maximum angle of inclination between the tangent to the surface and the horizontal by θm.Krasovskii (12) established that, at each fixed Q and L, there exist wave solutions for each value of θm strictly between zero and ⅙π. We establish that, at each fixed Q and L, there exist wave solutions for each value of qc strictly between c and zero. Here qc is the flow speed at the crest, andwhere g is the acceleration due to gravity. Krasovskii's set of solutions is included in the set that we obtain.

Measurements and models of fine structure, internal gravity waves, and wave breaking in the deep Ocean

Abstract: Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Earth and Planetary Sciences.

On the shape and breaking of finite amplitude internal gravity waves in a shear flow

Abstract: This paper is concerned with two important aspects of nonlinear internal gravity waves in a stably stratified inviscid plane shear flow, their shape and their breaking, particularly in conditions which are frequently encountered in geophysical applications when the vertical gradients of the horizontal current and the density are concentrated in a fairly narrow depth interval (e.g. the thermocline in the ocean). The present theoretical and experimental study of the wave shape extends earlier work on waves in the absence of shear and shows that the shape may be significantly altered by shear, the second-harmonic terms which describe the wave profile changing sign when the shear is increased sufficiently in an appropriate sense.In the second part of the paper we show that the slope of internal waves at which breaking occurs (the particle speeds exceeding the phase speed of the waves) may be considerably reduced by the presence of shear. Internal waves on a thermocline which encounter an increasing shear, perhaps because of wind action accelerating the upper mixing layer of the ocean, may be prone to such breaking.This work may alternatively be regarded as a study of the stability of a parallel stratified shear flow in the presence of a particular finite disturbance which corresponds to internal gravity waves propagating horizontally in the plane of the flow.

Finite amplitude solitary Alfvén waves

Abstract: Exact solitary Alfven waves are considered taking into account small, but finite β effects. The solitary waves consist of density humps whose amplitude has an upper limit.

Effect of internal gravity waves upon night airglow temperatures

Abstract: Large quasi-periodic fluctuations are observed simultaneously in the rotational temperature of the nightglow emission from both O 2 (¹Σ g ) and OH. The fluctuation amplitude usually is several times larger in the former and the O 2 (¹Σ g ) fluctuations often lead those of OH in phase. This behavior is consistent with that expected for internal gravity waves propagating upward over the ˜ 10 km vertical separation between the two emission layers. The most prominent periods are 1-2 hours and the full range of oscillation in temperature at 95 km sometimes approaches 100° K.

The Influence of Internal Waves on Deep-Water Drilling

Abstract: Internal waves were observed during drilling by the drillship Discoverer 534 in the Andaman Sea, offshore Thailand, in water depths ranging from 1,900 ft to more than 3,400 ft. An engineering analysis was conducted on measured internal wave data and simultaneous measured drillship response. Knowledge of internal waves will be required for designing production facilities in deep water.

The effect of internal waves on surface wind waves 1. Experimental measurements

Abstract: Internal waves were generated by a ship using the ‘dead water’ effect in areas where the water contains a strong near-surface density gradient. The effects of these internal waves on wind waves were examined. The principal measurements were slope statistics of the wind waves and horizontal currents in the internal waves. The effects on the wind waves were always observable from an aircraft; however, in measurements made only along the ship's track the effects of the internal waves were not always readily distinguishable from other factors that influence the wind wave field. By using statistical techniques, relationships have been established between the wind waves, the internal waves, and the wind velocity. The principal finding is that the wind wave field is relatively more sensitive to internal wave currents at low wind speeds than at high wind speeds. Numerical values are given.

Some effects of the air-water interface on gravity waves

Abstract: New rates of decay are presented for temporally-attenuated gravity waves in deep water, allowance being made for the energy dissipated in the Stokes interfacial boundary layer in the air. This decay-rate, involving air drag, may then be used to deduce a new “free-surface” boundary condition for the problem of the mass transport velocity due to progressive waves; for shallow-water waves, two specific velocity profiles are calculated, and indicate large differences in comparison with the corresponding profiles of Longuet-Higgins (1953) for a vacuum-water interface.

A Note on the Stability of Steady Inviscid Helical Gas Flows

Abstract: A necessary condition for linear stability of steady inviscid helical gas flows is found by the generalized progressing-wave expansion method The criterion obtained is compared with the known Richardson number criteria giving sufficient conditions for stability

The nature of gravity wave ducting in the thermosphere

Abstract: It has been widely held that the steep temperature gradient in the lower thermosphere can support one or more surface modes of long-period gravity wave propagation, thereby acting as a ducting mechanism. This paper shows that such a ducting mechanism in fact does not operate in the earth's thermosphere. It is shown that the thermospheric gravity modes computed by Francis [1973] can instead be explained by internal waves undergoing total reflections in the lower thermosphere and weak partial reflections in the upper thermosphere due to viscosity and heat conduction effects. This ducting mechanism is, however, so weak that the usefulness of the concept of ducted thermospheric gravity modes appears to be limited. An alternative concept of freely propagating waves appears to have more practical applications.

Acceleration waves and second sound in a perfect fluid

Abstract: The evolutionary behaviour of acceleration waves of arbitrary shape in a perfect fluid is investigated. The theory employed allows two coupled mechanical and temperature acceleration waves to propagate with finite wavespeeds. New results are described for waves entering isothermal regions but where the exterior flow velocity is non-zero.

Internal wave solitons

Abstract: A numerical solution of the Benjamin–Ono equation for internal waves shows soliton behavior. Two and three Lorentzian solitons pass through one another unscathed. An initial Lorentzian with larger than soliton amplitude decays into solitons, with velocities predicted by the five conservation laws.

Radiation damping of inertial oscillations in the upper ocean

Abstract: Turbulent motions within the wind-mixed layer, which is advected by near-surface inertial oscillations, excite internal gravity waves in the underlying ocean layers. Momentum transport in the radiated wave field results in a drag force on the inertial currents. Because the magnitude of the inertial currents is large compared with the turbulence intensity, the resultant rate of dissipation of inertial oscillation energy is approximately equal to the energy flux in the radiated wave field. Using linear internal wave theory, asymptotic results are derived for the energy flux in terms of the Brunt-Vaisala frequency N below the mixed layer, the magnitude U0 of the inertial current, the integral length scale l of the mixed-layer turbulence and the mean-square displacement 〈ζ20〉 of the base of the mixed layer. For representative conditions, we estimate an energy flux of 1-10 erg/cm2 s into relatively short (wavelength of order 2πU0/N) high frequency (of order, but less than, N) internal waves. The resultant decay times for inertial oscillation energy range from a day to a week or so, in agreement with reported observations on the decay of inertial oscillations in the upper ocean. The estimated energy flux is comparable in magnitude to estimates for other internal wave generation mechanisms, indicating that, in addition to being a significant sink of inertial energy, this process may locally represent a significant source of internal wave energy in the open ocean.