Downloads & Free Reading Options - Results

We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify and point out the regime of validity of second-order fluid dynamics in relativistic shock phenomena. The transition from ideal to viscous shocks is demonstrated by varying the shear viscosity to entropy density ratio $\eta/s$. We also find that a good agreement between these two approaches requires a Knudsen number $Kn < 1/2$.

In this paper, we derive asymptotic models for the propagation of two and three-dimensional gravity waves at the free surface and the interface between two layers of immiscible fluids of different densities, over an uneven bottom. We assume the thickness of the upper and lower fluids to be of comparable size, and small compared to the characteristic wavelength of the system (shallow water regimes). Following a method introduced by Bona, Lannes and Saut based on the expansion of the involved Dirichlet-to-Neumann operators, we are able to give a rigorous justification of classical models for weakly and strongly nonlinear waves, as well as interesting new ones. In particular, we derive linearly well-posed systems in the so called Boussinesq/Boussinesq regime. Furthermore, we establish the consistency of the full Euler system with these models, and deduce the convergence of the solutions.

The paper presents a mathematical model for an industry inspired problem of vibration isolation applied to a cluster of elastic fluid-filled containers. We develop a systematic approach employing full fluid-solid interaction and Floquet-Bloch waves in periodic multi-scale systems. The analytical findings are accompanied by numerical simulations, including frequency response analyses and computations in the transient regime.

Inertial waves propagate in homogeneous rotating fluids, and constitute a challenging and simplified case study for the broader class of inertio-gravity waves, present in all geophysical and astrophysical media, and responsible for energetically costly processes as diapycnal and angular momentum mixing. However, a complete analytical description and understanding of internal waves in arbitrarily shaped enclosed domains, such as the ocean, or a planet liquid core, is still missing. In this work, the inviscid, linear inertial wave field is investigated by means of three dimensional ray tracing in spherical shell domains, having in mind possible oceanographic applications. Rays are here classically interpreted as representative of energy paths. But in contrast with previous studies, they are now launched with a non-zero initial zonal component allowing for a more realistic, localized forcing, and the development of azimuthal inhomogeneities. We find that meridional planes generally act in the shell geometry as attractors for ray trajectories. In addition, the existence of trajectories that are not subject to meridional trapping is here observed for the first time. Their dynamics was not captured by the previous purely meridional studies and unveils a new class of possible solutions for inertial motion in the spherical shell. Both observed behaviours shed some new light on possible mechanisms of energy localization, a key process that still deserves further investigation in our ocean, as well as in other stratified, rotating media.

We have recently proposed a new general concept of macroscopic quantum-type experiment. It amounts to transform a classical fluid into a quantum-type fluid by the application of a quantum-like potential, either directly in a stationary configuration, or through a retro-active loop to simulate the time evolution. In this framework, the amplitude of the quantum potential depends on a macroscopic generalization of the Planck constant, which can be changed during the experiment, therefore simulating a quantum to classical transition. The experiment is exemplified here by an application of this concept to gravity waves at the surface of an incompressible liquid in a basin of finite height, with particular emphasis on the quantized vortex. We construct a complex wave function with the height of the fluid in the basin as its square modulus and the velocity potential as its phase. This wave function is solution of a nonlinear Schrodinger equation typical of superfluids. The quantum potential is therefore defined here in terms of the square root of the fluid height. We suggest two methods for applying this quantum-like potential to the fluid: (i) by the action of a force on the surface (wind, blower, pressure, field, etc...); (ii) by a curvature of the basin ground. In this last case the ground profile yields the quantum potential itself, while usually only the quantum force is accessible, so that such an experiment is expected to provide one with a macroscopic model of a quantum-type vacuum energy. These results may also be relevant to the study of freak waves, which have already been described by nonlinear Schrodinger equations.

High resolution numerical simulations of thermal convection in a rapidly rotating channel with gravity perpendicular to the rotation vector are described. The convecting columns are subject to a beta-effect resulting from cross-channel topographic vortex stretching. The symmetries of the problem allow many invariant wavenumber sets, and this property is associated with the existence of stable multiple-equilibria at modest supercriticality. The transition to chaotic behavior involves the production of intermittent unstable orbits off a two-torus in energy space. At very high Rayleigh number (of order 10(exp 6) to 10(exp 7)) the motion can be turbulent, depending on the size of beta. However, the turbulence is usually characterized by an almost-periodic formation of patches of small scale convection that cause regular pulsations in the accompanying strong zonal jets. The processes maintaining these flows may be related to those responsible for the zonal currents on Jupiter and for cyclic variability on the Sun.

The overall goal of the proposed work is to understand and model the interaction between waves and fine-grained sediment, in order to improve the accuracy of analysis and prediction of waves, currents, a suspended sediment distribution in the nearshore and in estuarine environments, where soft mud seabeds and fluid-mud layers are commonly found.

37 p. 28 cm

The goals of this project are to investigate the mechanisms for wave dissipation in the presence of bottom mud. These mechanisms are being examined via field measurements in the Gulf of Mexico, laboratory experiments of waves over a mud bottom, and numerical and theoretical analyses. Implementation of these various damping mechanisms into numerical models provides the ability to not only predict wave behavior over mud, but also to infer from the sea surface the nature of the bottom material.

An asymptotic method is developed for the study of gravity-capillary waves in a compressible viscous fluid with edge constraints in an inclined, straight channel. The Navier-Stokes equations subject to free surface and rigid bottom conditions are reduced to a sequence of elliptic boundary problems over a cross section of the channel. Their solutions are used to determine the wave speed and to construct the Burgers equation for the evolution of the gravity-capillary waves. The Burgers equation may become ill-posed when the Reynolds number exceeds some critical value. A criterion for the stability of the flow is then defined in terms of the critical Reynolds number. (Author)

A review of field and laboratory data indicated that bottom mud can appreciably damp surface water waves in coastal areas. The interactive feature is the ability of waves to fluidize bottom mud and sustain it in a fluidized state as long as the wave action continues. This report reviews iterative procedures and simple model approaches for studying the basics of the interaction between progressive water waves and a compliant mud bed in a shallow coastal environment. Possible applications include designing offshore structures-energy absorbing berms-as buffers against shoreline wave attack using dredged material. The mud is, assumed to be a continuum, and the suspension is assumed to have sediment and water phases. Constitutive relationships are developed to describe mud rheology. Mud can be highly rigid and weakly viscous or can be purely viscous fluid. Fluidization of the mud by waves proceeds as the space filling structure of the mud is broken and the stress between particles greatly diminished. An empirical relationship with which to estimate the depth of fluidization is presented. Models for water waves over mud are first presented, then compared to laboratory data. Field data are used to make example applications of the models. Berms,

A review of field and laboratory data indicated that bottom mud can appreciably damp surface water waves in coastal areas. The interactive feature is the ability of waves to fluidize bottom mud and sustain it in a fluidized state as long as the wave action continues. This report reviews iterative procedures and simple model approaches for studying the basics of the interaction between progressive water waves and a compliant mud bed in a shallow coastal environment. Possible applications include designing offshore structures-energy absorbing berms-as buffers against shoreline wave attack using dredged material. The mud is, assumed to be a continuum, and the suspension is assumed to have sediment and water phases. Constitutive relationships are developed to describe mud rheology. Mud can be highly rigid and weakly viscous or can be purely viscous fluid. Fluidization of the mud by waves proceeds as the space filling structure of the mud is broken and the stress between particles greatly diminished. An empirical relationship with which to estimate the depth of fluidization is presented. Models for water waves over mud are first presented, then compared to laboratory data. Field data are used to make example applications of the models. Berms,

We describe the effect of vibration on a confined volume of fluid which is density stratified due to its compressibility. We show that internal gravity-acoustic waves can be parametrically destabilized by the vibration. The resulting instability is similar to the classic Faraday instability of surface waves, albeit modified by the compressible nature of the fluid. It may be possible to observe experimentally near a gas-liquid critical point.

Cartesian-grid methods in combination with immersed-body and volume-of-fluid methods are ideally suited for simulating breaking waves around ships. A surface panelization of the ship hull is used as input to impose body-boundary conditions on a three-dimensional cartesian grid. The volume-of-fluid portion of the numerical algorithm is used to capture the free-surface interface, including the breaking of waves. The numerical scheme is implemented on a parallel computer. Various numerical issues are discussed, including implementing exit boundary conditions, conserving mass using a novel regridding algorithm, improving resolution through the use of stretched grids, minimizing initial transients, and enforcing hull boundary conditions on cartesian grids. Numerical predictions are compared to experimental measurements of ship models moving with forward speed, including model 5415 and model 5365 (Athena). The ability to model forced-motions is illustrated using a heaving sphere moving with forward speed.

In differentially rotating discs with no self-gravity, density waves cannot propagate around the corotation, where the wave pattern rotation speed equals the fluid rotation rate. Waves incident upon the corotation barrier may be super-reflected (commonly referred to as corotation amplifier), but the reflection can be strongly affected by wave absorptions at the corotation resonance/singularity. The sign of the absorption is related to the Rossby wave zone very near the corotation radius. We derive the explicit expressions for the complex reflection and transmission coefficients, taking into account wave absorption at the corotation resonance. We show that for generic discs, this absorption plays a much more important role than wave transmission across the corotation barrier. Depending on the sign of the gradient of the specific vorticity of the disc the corotation resonance can either enhance or diminish the super-reflectivity, and this can be understood in terms of the location of the Rossby wave zone relative to the corotation radius. Our results provide the explicit conditions (in terms of disc thickness, rotation profile and specific vorticity gradient) for which super-reflection can be achieved. Global overstable disc modes may be possible for discs with super-reflection at the corotation barrier.

In differentially rotating discs with no self-gravity, density waves cannot propagate around the corotation, where the wave pattern rotation speed equals the fluid rotation rate. Waves incident upon the corotation barrier may be super-reflected (commonly referred to as corotation amplifier), but the reflection can be strongly affected by wave absorptions at the corotation resonance/singularity. The sign of the absorption is related to the Rossby wave zone very near the corotation radius. We derive the explicit expressions for the complex reflection and transmission coefficients, taking into account wave absorption at the corotation resonance. We show that for generic discs, this absorption plays a much more important role than wave transmission across the corotation barrier. Depending on the sign of the gradient of the specific vorticity of the disc the corotation resonance can either enhance or diminish the super-reflectivity, and this can be understood in terms of the location of the Rossby wave zone relative to the corotation radius. Our results provide the explicit conditions (in terms of disc thickness, rotation profile and specific vorticity gradient) for which super-reflection can be achieved. Global overstable disc modes may be possible for discs with super-reflection at the corotation barrier.

We report experimental observations of traveling waves in a pure fluid with a free surface situated in a long container submitted to a horizontal temperature gradient perpendicular to its large extension. Above a critical value of the gradient and depending on the height of liquid $ h, $ a source of waves is created in the container for small value of $ h, $ while the system exhibits stationary patterns for larger values of $ h. $ The spatio-temporal properties of the waves are studied and compared to theoretical predictions. Email contact: [email protected]

A compact sampling tool mechanism that can operate at various temperatures, and transport and sieve particle sizes of powdered cuttings and soil grains with no moving parts, has been created using traveling surface acoustic waves (SAWs) that are emitted by an inter-digital transducer (IDT). The generated waves are driven at about 10 MHz, and it causes powder to move towards the IDT at high speed with different speeds for different sizes of particles, which enables these particles to be sieved. This design is based on the use of SAWs and their propelling effect on powder particles and fluids along the path of the waves. Generally, SAWs are elastic waves propagating in a shallow layer of about one wavelength beneath the surface of a solid substrate. To generate SAWs, a piezoelectric plate is used that is made of LiNbO3 crystal cut along the x-axis with rotation of 127.8 along the y-axis. On this plate are printed pairs of fingerlike electrodes in the form of a grating that are activated by subjecting the gap between the electrodes to electric field. This configuration of a surface wave transmitter is called IDT. The IDT that was used consists of 20 pairs of fingers with 0.4-mm spacing, a total length of 12.5 mm. The surface wave is produced by the nature of piezoelectric material to contract or expand when subjected to an electric field. Driving the IDT to generate wave at high amplitudes provides an actuation mechanism where the surface particles move elliptically, pulling powder particles on the surface toward the wavesource and pushing liquids in the opposite direction. This behavior allows the innovation to separate large particles and fluids that are mixed. Fluids are removed at speed (7.5 to 15 cm/s), enabling this innovation of acting as a bladeless wiper for raindrops. For the windshield design, the electrodes could be made transparent so that they do not disturb the driver or pilot. Multiple IDTs can be synchronized to transport water or powder over larger distances. To demonstrate the transporting action, a video camera was used to record the movement. The speed of particles was measured from the video images.

The understanding of large and rare waves in the ocean is becoming more important as these rare events are turning into more common observances. In order to design a marine structure or vehicle to withstand such a potentially devastating phenomenon, the designer must have knowledge of extreme waves with return periods of 50 and 100 years. Based on satellite radar altimeter data, researchers have successfully predicted extreme significant wave heights with the return periods of 50 and 100 years. This thesis extends their research further by estimating the most probable extreme wave heights and other wave statistics based on spectral analysis. The same technique used for extreme significant wave height prediction is applied to extrapolation of corresponding mean wave periods, and they are used to construct two parameter spectra representing storm sea conditions. The prediction of the most probable extreme wave heights as well as other statistical data is based on linear theory and short term order Statistics. There exists sufficient knowledge of second order effects on wave generation, and it could be applied to a logical progression of the simulation approach in this thesis. However, because this greatly increases computation time, and the kinematics of deep sea spilling breakers are not yet fully understood for which substantial new research is required, the nonlinear effects are not included in this thesis. Spectral analysis can provide valuable statistical information in addition to extreme wave height data, and preliminary results show good agreement with other prediction methods including wave simulation based on the Pierson-Moskowitz spectrum.

Research investigations involving the basic understanding and applications of nonlinear wave motion and related studies of inverse scattering and numerical simulation have been carried out with a number of significant results obtained. During this period, four papers were published in journals and three preprints were written. Some of these contributions are outlined in this report. (AN)

The purpose of this article is to present a T-matrix formalism for elastic wave scattering by multilayered regions with solid-fluid interfaces. Here the layers are not necessarily consecutively enclosing and thus in some regions there may be several different scatterers. We are using the Green's dyadic in an integral representation although the T-matrix can be obtained without using and Green's dyadic.

The properties of the nonlinear frequency shift (NFS) especially the fluid NFS from the harmonic generation of the ion-acoustic wave (IAW) in multi-ion species plasmas have been researched by Vlasov simulation. The pictures of the nonlinear frequency shift from harmonic generation and particles trapping are shown to explain the mechanism of NFS qualitatively. The theoretical model of the fluid NFS from harmonic generation in multi-ion species plasmas is given and the results of Vlasov simulation are consistent to the theoretical result of multi-ion species plasmas. When the wave number $k\lambda_{De}$ is small, such as $k\lambda_{De}=0.1$, the fluid NFS dominates in the total NFS and will reach as large as nearly $15\%$ when the wave amplitude $|e\phi/T_e|\sim0.1$, which indicates that in the condition of small $k\lambda_{De}$, the fluid NFS dominates in the saturation of stimulated Brillouin scattering especially when the nonlinear IAW amplitude is large.

A new type of wave in a magnetized fluid dielectric

The presence of a thin non-homogeneous layer at the interface of an elastic and a fluid medium can alter the energy exchange between the two media. In this report the effect of the transition layer upon the propagation of one-dimensional longitudinal waves is analyzed. The motion of the lower boundary of the elastic layer is assumed known and the energy radiation into the fluid is obtained.

This study contains a mathematical analysis of constrained-layer damping (CLD) in plates of infinite extent, with an emphasis on the physical understanding of some special features, including fluid loading. Previous work is expanded to cover extensional waves. Some essential aspects of fluid loading may be understood by applying thin-plate theory. Therefore, thin-plate theory of extensional waves in a fluid-loaded plate was developed as a counterpart to that for flexural waves. The description and examples of CLD follow three models: the first is an extension of Kerwin's 1959 model, the second a hybrid model for which the base plate is treated by exact elasticity theory, and finally a fully exact model for all three layers. Examples and comparisons are given.

This research has been primarily concerned with the excitation and detection of inertial waves in a fluid contained in a rotating cylindrical cavity during spin-up of the fluid from rest. Application of this work is to the study of fluid filled projectiles and their stability in free flight. It is well known that a projectile containing fluid will be subject to instability if its nutational frequency is near one of the eigenfrequencies of the contained fluid. Our work has centered on finding these time dependent eigenfrequencies for a fluid which completely fills a cylindrical cavity. Also of interest in the application of our work is the rate at which these waves decay once they are excited during the spin-up period. Included in our experimental work was a study of decay rates for several inertial waves during spin-up from rest. (Author)

A theoretical investigation is presented of the nonlinear effects in reflection and refraction of plane finite-amplitude acoustic waves at an initially plane interface between two lossless fluids. In the first part, the terms in the equations of motion for a homogeneous, thermoviscous fluid with a single relaxation mechanism are rank ordered to determine the most important nonlinear and dissipation terms. The equations are then combined to form a general wave equation that includes the most important effects of nonlinearity and dissipation. In the second part, the terms in the boundary conditions between two lossless fluids are rank ordered to include the most important nonlinear effects. Subject to these boundary conditions, a solution of the lossless form of the aforementioned wave equation is obtained by way of second order perturbation expansion. The lossless form of the wave equation and the lossless boundary conditions are expanded, and the O (epsilon) and O (epsilon- sq) systems are solved in terms of a modified velocity potential. The analysis is performed for oblique incidence, and the boundary condition at the source is arbitrary. Effects examined include the finite displacement of the interface and the variation of the direction of the normal to the interface, both of which are caused by the motion of the interface as it responds to the incident sound. In the third part, two different modified forms of Snell's law for the special case of simple wave flow are derived: one by matching the trace velocities at the interface and one by matching the variation of the pressure along the interface. It is shown, however, that to O(epsilon-sq), both reduce to ordinary Snell's law and a condition necessary for simple wave flow.

Collisionless regime kinetic models for coherent nonlinear Alfven wave dynamics are studied using fluid moment equations with an approximate closure anzatz. Resonant particle effects are modelled by incorporating an additional term representing dissipation akin to parallel heat conduction. Unlike collisional dissipation, parallel heat conduction is presented by an integral operator. The modified derivative nonlinear Schrodinger equation thus has a spatially nonlocal nonlinear term describing the long-time evolution of the envelope of parallel-propagating Alfven waves, as well. Coefficients in the nonlinear terms are free of the 1/(1-beta) singularity usually encountered in previous analyses, and have very a simple form which clarifies the physical processes governing the large amplitude Alfvenic nonlinear dynamics. The nonlinearity appears via coupling of an Alfvenic mode to a kinetic ion-acoustic mode. Damping of the nonlinear Alfven wave appears via strong Landau damping of the ion-acoustic wave when the electron-to-ion temperature ratio is close to unity. For a (slightly) obliquely propagating wave, there are finite Larmor radius corrections in the dynamical equation. This effect depends on the angle of wave propagation relative to B_0 and vanishes for the limit of strictly parallel propagation. Explicit magnetic perturbation envelope equations amenable to further analysis and numerical solution are obtained. Implications of these models for collisionless shock dynamics are discussed.

The influence of various kinetic effects (e.g. Landau damping, diffusive and collisional dissipation, and finite Larmor radius terms) on the nonlinear evolution of finite amplitude Alfvenic wave trains in a finite-beta environment is systematically investigated using a novel, kinetic nonlinear Schrodinger (KNLS) equation. The dynamics of Alfven waves is sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field. Numerical solution for the case with Landau damping reveals the formation of dissipative structures, which are quasi-stationary, S-polarized directional (and rotational) discontinuities which self-organize from parallel propagating, linearly polarized waves. Parallel propagating circularly polarized packets evolve to a few circularly polarized Alfven harmonics on large scales. Stationary arc-polarized rotational discontinuities form from obliquely propagating waves. Collisional dissipation, even if weak, introduces enhanced wave damping when beta is very close to unity. Cyclotron motion effects on resonant particle interactions introduce cyclotron resonance into the nonlinear Alfven wave dynamics.

The influence of various kinetic effects (e.g. Landau damping, diffusive and collisional dissipation, and finite Larmor radius terms) on the nonlinear evolution of finite amplitude Alfvenic wave trains in a finite-beta environment is systematically investigated using a novel, kinetic nonlinear Schrodinger (KNLS) equation. The dynamics of Alfven waves is sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field. Numerical solution for the case with Landau damping reveals the formation of dissipative structures, which are quasi-stationary, S-polarized directional (and rotational) discontinuities which self-organize from parallel propagating, linearly polarized waves. Parallel propagating circularly polarized packets evolve to a few circularly polarized Alfven harmonics on large scales. Stationary arc-polarized rotational discontinuities form from obliquely propagating waves. Collisional dissipation, even if weak, introduces enhanced wave damping when beta is very close to unity. Cyclotron motion effects on resonant particle interactions introduce cyclotron resonance into the nonlinear Alfven wave dynamics.

This research has been primarily concerned with the excitation and detection of inertial waves in a fluid contained in a rotating cylindrical cavity during spin-up of the fluid from rest. Application of this work is to the study of fluid filled projectiles and their stability in free flight. It is well known that a projectile containing fluid will be subject to instability if its nutational frequency is near one of the eigenfrequencies of the contained fluid. Our work has centered on finding these time dependent eigenfrequencies for a fluid which completely fills a cylindrical cavity. Also of interest in the application of our work is the rate at which these waves decay once they are excited during the spin-up period. Included in our experimental work was a study of decay rates for several inertial waves during spin-up from rest. (Author)

Analysis of scattering and radiation of acoustic waves from an axisymmetric structure in an infinite fluid medium is presented. It is shown that the use of a basis function, consistent with the one used for axisymmetric pressure on the finite surface, yields accurate results and uses fewer finite surface elements than does piston-type analysis. (Author)

Isothermal interfacial zones are investigated starting from a local energy which can be considered as the sum of two terms: one corresponding to a medium with a uniform composition equal to the local one and a second one associated with the non-uniformity of the fluid. In an extended van der Waals theory, the volume internal energy is proposed with a gradient expansion depending not only on the gradient of density but also on the gradient of entropy. We obtain the equation of conservative motions for non-homogeneous fluids near its critical point. For such a medium, it is not possible to obtain shock waves. The waves are tangential to the interface and the wave celerity is expressed depending on thermodynamic conditions at the critical point.

Theory of finite amplitude waves in fluid-filled elastic tubes, including wave distortion, shock wave propagation, and Korotkoff sounds

Fluid dynamic limit to compressible Euler equations from compressible Navier-Stokes equations and Boltzmann equation has been an active topic with limited success so far. In this paper, we consider the case when the solution of the Euler equations is a Riemann solution consisting two rarefaction waves and a contact discontinuity and prove this limit for both Navier-Stokes equations and the Boltzmann equation when the viscosity, heat conductivity coefficients and the Knudsen number tend to zero respectively. In addition, the uniform convergence rates in terms of the above physical parameters are also obtained. It is noted that this is the first rigorous proof of this limit for a Riemann solution with superposition of three waves even though the fluid dynamic limit for a single wave has been proved.

We study the generation of 2D turbulence in Faraday waves by investigating the creation of spatially periodic vortices in this system. Measurements which couple a diffusing light imaging technique and particle tracking algorithms allow the simultaneous observation of the three-dimensional fluid motion and of the temporal changes in the wave field topography. Quasi-standing waves are found to coexist with a spatially extended fluid transport. More specifically, the destruction of regular patterns of oscillons coincides with the emergence of a complex fluid motion whose statistics are similar to that of two-dimensional turbulence. We reveal that a lattice of oscillons generates vorticity at the oscillon scale in the horizontal flow. The interaction of these vortices explain how 2D turbulence is fueled by almost standing waves. Remarkably, the curvature of Lagrangian trajectories reveals a "footprint" of the forcing scale vortices in fully developed turbulence. 2D Navier-Stokes turbulence should be considered a source of disorder in Faraday waves. These findings also provide a new paradigm for vorticity creation in 2D flows.

We study the generation of 2D turbulence in Faraday waves by investigating the creation of spatially periodic vortices in this system. Measurements which couple a diffusing light imaging technique and particle tracking algorithms allow the simultaneous observation of the three-dimensional fluid motion and of the temporal changes in the wave field topography. Quasi-standing waves are found to coexist with a spatially extended fluid transport. More specifically, the destruction of regular patterns of oscillons coincides with the emergence of a complex fluid motion whose statistics are similar to that of two-dimensional turbulence. We reveal that a lattice of oscillons generates vorticity at the oscillon scale in the horizontal flow. The interaction of these vortices explain how 2D turbulence is fueled by almost standing waves. Remarkably, the curvature of Lagrangian trajectories reveals a "footprint" of the forcing scale vortices in fully developed turbulence. 2D Navier-Stokes turbulence should be considered a source of disorder in Faraday waves. These findings also provide a new paradigm for vorticity creation in 2D flows.

We unveil the generation of universal morphologies of fluid interfaces by radiation pressure whatever is the nature of the wave, acoustic or optical. Experimental observations reveal interface deformations endowed with step-like features that are shown to result from the interplay between the wave propagation and the shape of the interface. The results are supported by numerical simulations and a quantitative interpretation based on the waveguiding properties of the field is provided.

This research has been primarily concerned with the excitation and detection of inertial waves in a fluid contained in a rotating cylindrical cavity during spin-up of the fluid from rest. Application of this work is to the study of fluid filled projectiles and their stability in free flight. It is well known that a projectile containing fluid will be subject to instability if its nutational frequency is near one of the eigenfrequencies of the contained fluid. Our work has centered on finding these time dependent eigenfrequencies for a fluid which completely fills a cylindrical cavity. Also of interest in the application of our work is the rate at which these waves decay once they are excited during the spin-up period. Included in our experimental work was a study of decay rates for several inertial waves during spin-up from rest. (Author)

Nonlinear, spatially localized structures of traveling convection rolls are investigated in quantitative detail as a function of Rayleigh number for two different Soret coupling strengths (separation ratios) with Lewis and Prandtl numbers characterizing ethanol-water mixtures. A finite-difference method was used to solve the full hydrodynamic field equations numerically. Structure and dynamics of these localized traveling waves (LTW) are dominated by the concentration field. Like in the spatially extended convective states ( cf. accompanying paper), the Soret-induced concentration variations strongly influence, via density changes, the buoyancy forces that drive convection. The spatio-temporal properties of this feed-back mechanism, involving boundary layers and concentration plumes, show that LTW's are strongly nonlinear states. Light intensity distributions are determined that can be observed in side-view shadowgraphs. Detailed analyses of all fields are made using colour-coded isoplots, among others. In the frame comoving with their drift velocity, LTW's display a nontrivial spatio-temporal symmetry consisting of time-translation by half an oscillation period combined with vertical reflection through the horizontal midplane of the layer. A time-averaged concentration current is driven by a phase difference between the waves of concentration and vertical velocity in the bulk of the LTW state. The associated large-scale concentration redistribution stabilizes the LTW and controls its drift velocity into the quiescent fluid by generating a buoyancy-reducing concentration "barrier" ahead of the leading LTW front. The selection of the width of the LTW's is investigated and comparisons with experiments are presented.

After a brief discussion of some undesirable features of a number of different partial differential equations often employed in the existing literature on water waves, a relatively simple restricted theory is constructed by a direct approach which is particularly suited for applications to problems of fluid sheets. The rest of the paper is concerned with a derivation of a system of nonlinear differential equations (which may include the effects of gravity and surface tension) governing the two-dimensional motion of incompressible inviscid fluids for propagation of fairly long waves in a nonhomogeneous stream of water of variable initial depth, as well as some new results pertaining to hydraulic jumps. The latter includes an additional class of possible solutions not noted previously. (Author)

This research has been primarily concerned with the excitation and detection of inertial waves in a fluid contained in a rotating cylindrical cavity during spin-up of the fluid from rest. Application of this work is to the study of fluid filled projectiles and their stability in free flight. It is well known that a projectile containing fluid will be subject to instability if its nutational frequency is near one of the eigenfrequencies of the contained fluid. Our work has centered on finding these time dependent eigenfrequencies for a fluid which completely fills a cylindrical cavity. Also of interest in the application of our work is the rate at which these waves decay once they are excited during the spin-up period. Included in our experimental work was a study of decay rates for several inertial waves during spin-up from rest. (Author)

This research has been primarily concerned with the excitation and detection of inertial waves in a fluid contained in a rotating cylindrical cavity during spin-up of the fluid from rest. Application of this work is to the study of fluid filled projectiles and their stability in free flight. It is well known that a projectile containing fluid will be subject to instability if its nutational frequency is near one of the eigenfrequencies of the contained fluid. Our work has centered on finding these time dependent eigenfrequencies for a fluid which completely fills a cylindrical cavity. Also of interest in the application of our work is the rate at which these waves decay once they are excited during the spin-up period. Included in our experimental work was a study of decay rates for several inertial waves during spin-up from rest. (Author)

This research has been primarily concerned with the excitation and detection of inertial waves in a fluid contained in a rotating cylindrical cavity during spin-up of the fluid from rest. Application of this work is to the study of fluid filled projectiles and their stability in free flight. It is well known that a projectile containing fluid will be subject to instability if its nutational frequency is near one of the eigenfrequencies of the contained fluid. Our work has centered on finding these time dependent eigenfrequencies for a fluid which completely fills a cylindrical cavity. Also of interest in the application of our work is the rate at which these waves decay once they are excited during the spin-up period. Included in our experimental work was a study of decay rates for several inertial waves during spin-up from rest. (Author)

41 p. 28 cm

Thesis (Degree of Ocean E. & M.S. in Ocean. Eng.)--Massachusetts Institute of Technology, 1976

Thesis (Degree of Ocean E. & M.S. in Ocean. Eng.)--Massachusetts Institute of Technology, 1976

Plane inertial waves are generated using a wavemaker, made of oscillating stacked plates, in a rotating water tank. Using particle image velocimetry, we observe that, after a transient, the primary plane wave is subject to a subharmonic instability and excites two secondary plane waves. The measured frequencies and wavevectors of these secondary waves are in quantitative agreement with the predictions of the triadic resonance mechanism. The secondary wavevectors are found systematically more normal to the rotation axis than the primary wavevector: this feature illustrates the basic mechanism at the origin of the energy transfers towards slow, quasi two-dimensional, motions in rotating turbulence.

The present work deals with dynamics of gravitational collapse with cylindrical symmetry as developed by Misner and Sharp. The interior collapsing anisotropic cylindrical perfect fluid is matched to an exterior vacuum cylindrically symmetric space-time due to Einstein--Rosen using the Darmois matching conditions. It is found that the radial pressure of the anisotropic perfect fluid is non-zero on the boundary surface and is related to the components of shear viscosity. As a result, there is formation of gravitational waves outside the collapsing matter.

Special features of surface gravity waves in deep fluid flow with constant vertical shear of velocity is studied. It is found that the mean flow velocity shear leads to non-trivial modification of surface gravity wave modes dispersive characteristics. Moreover, the shear induces generation of surface gravity waves by internal vortex mode perturbations. The performed analytical and numerical study provides, that surface gravity waves are effectively generated by the internal perturbations at high shear rates. The generation is different for the waves propagating in the different directions. Generation of surface gravity waves propagating along the main flow considerably exceeds the generation of surface gravity waves in the opposite direction for relatively small shear rates, whereas the later wave is generated more effectively for the high shear rates. From the mathematical point of view the wave generation is caused by non self-adjointness of the linear operators that describe the shear flow.