Download or read book GENERATION OF INTERNAL WAVES IN STRATIFIED FLUIDS written by Charles C. S. Song and published by . This book was released on 1973 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: Internal waves in exponentially stratified fluids confined between two parallel boundaries have been studied analytically and experimentally with both a fixed and a free upper surface. In the analytical model, waves were generated by vortex-like or source-like oscillatory disturbances. A modified image method was developed according to the principle of superposition using Hurley's elementary solutions for unbounded fluid. A basic image system which satisfies the wall boundary condition and is free of singularities in the flow field was found for every elementary vortex or source located anywhere in the field. An experiment was carried out in a channel filled with salt water of exponential density stratification. A rigid flat plate wave generator and a flexible rubber diaphragm anywhere in the field. An experiment was carried out in a channel filled with salt water of exponential density stratification. A rigid flat plate wave generator and a flexible rubber diaphragm wave generator located at mid-depth, both oscillating in a vertical direction, were used. Excellent agreement was obtained between the predicted and the measured wave length. The predicted wave shape and the measured wave shape were also in good agreement. Less complete agreement was obtained for the case of wave amplitude, however. (Modified author abstract).

Download or read book Internal Gravity Waves written by Bruce R. Sutherland and published by Cambridge University Press. This book was released on 2010-09-02 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of internal gravity waves provides many challenges: they move along interfaces as well as in fully three-dimensional space, at relatively fast temporal and small spatial scales, making them difficult to observe and resolve in weather and climate models. Solving the equations describing their evolution poses various mathematical challenges associated with singular boundary value problems and large amplitude dynamics. This book provides the first comprehensive treatment of the theory for small and large amplitude internal gravity waves. Over 120 schematics, numerical simulations and laboratory images illustrate the theory and mathematical techniques, and 130 exercises enable the reader to apply their understanding of the theory. This is an invaluable single resource for academic researchers and graduate students studying the motion of waves within the atmosphere and ocean, and also mathematicians, physicists and engineers interested in the properties of propagating, growing and breaking waves.

Download or read book Generation of Internal Waves in Stratified Fluids written by Chyi-sheng Hwang and published by . This book was released on 1973 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Internal Wave Generation by Convection written by Daniel Lecoanet and published by . This book was released on 2016 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: In nature, it is not unusual to find stably stratified fluid adjacent to convectively unstable fluid. This can occur in the Earth's atmosphere, where the troposphere is convective and the stratosphere is stably stratified; in lakes, where surface solar heating can drive convection above stably stratified fresh water; in the oceans, where geothermal heating can drive convection near the ocean floor, but the water above is stably stratified due to salinity gradients; possible in the Earth's liquid core, where gradients in thermal conductivity and composition diffusivities maybe lead to different layers of stable or unstable liquid metal; and, in stars, as most stars contain at least one convective and at least one radiative (stably stratified) zone. Internal waves propagate in stably stratified fluids. The characterization of the internal waves generated by convection is an open problem in geophysical and astrophysical fluid dynamics. Internal waves can play a dynamically important role via nonlocal transport. Momentum transport by convectively excited internal waves is thought to generate the quasi-biennial oscillation of zonal wind in the equatorial stratosphere, an important physical phenomenon used to calibrate global climate models. Angular momentum transport by convectively excited internal waves may play a crucial role in setting the initial rotation rates of neutron stars. In the last year of life of a massive star, convectively excited internal waves may transport even energy to the surface layers to unbind them, launching a wind. In each of these cases, internal waves are able to transport some quantity--momentum, angular momentum, energy--across large, stable buoyancy gradients. Thus, internal waves represent an important, if unusual, transport mechanism. This thesis advances our understanding of internal wave generation by convection. Chapter 2 provides an underlying theoretical framework to study this problem. It describes a detailed calculation of the internal gravity wave spectrum, using the Lighthill theory of wave excitation by turbulence. We use a Green's function approach, in which we convolve a convective source term with the Green's function of different internal gravity waves. The remainder of the thesis is a circuitous attempt to verify these analytical predictions. I test the predictions of Chapter 2 via numerical simulation. The first step is to identify a code suitable for this study. I helped develop the Dedalus code framework to study internal wave generation by convection. Dedalus can solve many different partial differential equations using the pseudo-spectral numerical method. In Chapter 3, I demonstrate Dedalus' ability to solve different equations used to model convection in astrophysics. I consider both the propagation and damping of internal waves, and the properties of low Rayleigh number convective steady states, in six different equation sets used in the astrophysics literature. This shows that Dedalus can be used to solve the equations of interest. Next, in Chapter 4, I verify the high accuracy of Dedalus by comparing it to the popular astrophysics code Athena in a standard Kelvin-Helmholtz instability test problem. Dedalus performs admirably in comparison to Athena, and provides a high standard for other codes solving the fully compressible Navier-Stokes equations. Chapter 5 demonstrates that Dedalus can simulate convective adjacent to a stably stratified region, by studying convective mixing near carbon flames. The convective overshoot and mixing is well-resolved, and is able to generate internal waves. Confident in Dedalus' ability to study the problem at hand, Chapter 6 describes simulations inspired by water experiments of internal wave generation by convection. The experiments exploit water's unusual property that its density maximum is at 4C, rather than at 0C. We use a similar equation of state in Dedalus, and study internal gravity waves generation by convection in a water-like fluid. We test two models of wave generation: bulk excitation (equivalent to the Lighthill theory described in Chapter 2), and surface excitation. We find the bulk excitation model accurately reproduces the waves generated in the simulations, validating the calculations of Chapter 2.

Download or read book Nonlinear Internal Waves in Lakes written by Kolumban Hutter and published by Springer Science & Business Media. This book was released on 2011-11-25 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Internal wave dynamics in lakes (and oceans) is an important physical component of geophysical fluid mechanics of ‘quiescent’ water bodies of the Globe. The formation of internal waves requires seasonal stratification of the water bodies and generation by (primarily) wind forces. Because they propagate in basins of variable depth, a generated wave field often experiences transformation from large basin-wide scales to smaller scales. As long as this fission is hydrodynamically stable, nothing dramatic will happen. However, if vertical density gradients and shearing of the horizontal currents in the metalimnion combine to a Richardson number sufficiently small (

Download or read book Numerical Simulations of Internal Waves in Stratified Fluids written by Andy K. O. Law and published by . This book was released on 1999 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Internal Wave Generation Over Rough Sloped Topography written by Lauren E. Eberly and published by . This book was released on 2012 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Internal waves exist everywhere in stratified fluids - fluids whose density changes with depth. The two largest bodies of stratified fluid are the atmosphere and ocean. Internal waves are generated from a variety of mechanisms. One common mechanism is wind forcing over re- peated sinusoidal topography, like a series of hills. When modeling these waves, linear theory has been employed due to its ease and low computational cost. However, recent research has shown that non-linear effects, such as boundary layer separation, may have a dramatic impact on wave generation. This research has consisted of experimentation on sloped, sinusoidal hills. As of yet, no experimental research has been done to characterize internal wave generation when repeated sinusoidal hills lie on a sloped surface such as a continental slope or a foothill. In order to perform this experiment, a laboratory was built which employed the synthetic schlieren method of wave visualization. Measurements were taken to find wind speed, boundary layer thickness, and density perturbation. From these data, an analysis was performed on wave propagation angle, wave am- plitude, and pressure drag. The result of the analysis shows that when wind blows across a series of sloped sinusoidal hills, fluid becomes trapped in the troughs of the hills resulting in a lower apparent forcing amplitude. The generated waves contain less energy than linear predictions. Ad- ditionally, the sloped hills produce waves which propagate at an angle away from the viewer. A necessary correction, which shifts from the reference frame of the observer to the reference plane of the waves is described. When this correction is applied, it is shown that linear theory may only be applied for low Froude numbers. At high Froude numbers, the effect of the boundary layer is great enough that the wave characteristics deviate significantly from linear theory predictions. The analyzed data agrees well with previous studies which show a similar deviation from linear theory.

Download or read book Spectra of Internal Waves and Turbulence in Stratified Fluids Part I General Discussion and Indications from Measurements in Stably Stratified Atmosphere and Ocean written by Yih-Ho Pao and published by . This book was released on 1969 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified spectral description of internal waves and turbulence in stably stratified atmosphere and ocean is proposed. We envisage that the fluctuating motions in a free atmosphere with scales smaller than the synoptic scale consist of internal waves and turbulence. At low wavenumbers, internal waves predominate; this range of wavenumbers may be called the internal wave subrange. The internal waves can be identified from the characteristics of velocity-scalar co-spectra and quadrature-spectra, as shown recently by Pao in a laboratory experiment. When the internal waves are sufficiently strong and distinct, the different harmonics of internal waves may present themselves in the auto-spectra of velocity and temperature, where the peaks and valleys are clearly identifiable. This, we believe, explains the presence of peaks and valleys in some velocity auto-spectra of clear air turbulence measured in strongly stratified regions of the atmosphere. At intermediate wavenumbers (buoyant subrange), the buoyancy effect is still strong but the turbulent scrambling process becomes important; the higher-order harmonics of internal waves are no longer distinct and cannnot be detected in the auto-spectra. (Author).

Download or read book Wake Collapse in a Stratified Fluid written by Carlton Louis Hindman and published by . This book was released on 1974 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical and analytical study of internal waves in stratified fluids written by Ren Liu and published by . This book was released on 1989 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Viscous internal waves in density stratified fluids written by Uri Rudi Klement and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Tidally Generated Internal Waves from Asymmetric Topographies written by Kyle Jeffrey Hakes and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Internal waves are generated in stratified fluids, like the ocean, where density increases with depth. Tides are one of the major generation mechanisms of internal waves. As the tides move water back and forth over underwater topography, internal waves can be generated. The shape of the topography plays a major part in the properties of the generated internal wave and the type of wave and energy is known for multiple symmetric topographies, such as Gaussian or sinusoidal. In order to further understand the effects topographic shape plays, the effect of asymmetry on internal waves is investigated.

Download or read book Some Aspects of Wave Motion in Stably Stratified Fluids written by Russ Erik Davis and published by . This book was released on 1967 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Wake Collapse and Subsequent Generation of Internal Waves in a Density Stratified Medium written by Jin Wu and published by . This book was released on 1968 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: An experimental technique was developed to model a two-dimensional mixed region collapsing in a continuously density-stratified medium. The process of this mixed region can be divided into three stages. Empirical formulae were derived to describe the process of the first two stages, during which densimetric effects determine the modeling criterion. The collapse process in the final stage is complicated by viscous effects including mixing at the thin wake tip. The pattern of the internal waves generated by the initial impulsive collapse of the mixed region was studied; it can be represented by moving rays connecting either wave crests or troughs. These rays move away from the collapse center and at the same time decrease their slopes. A simpler steady state wave pattern generated by an oscillating plunger was also studied. Taken together, these experimental results are interpreted to show that the energy density of the initial impulsive collapse is skewed toward higher frequencies and that it is peaked at 8/10 of the Brunt-Vaisala frequency. The mechanism underlying the moving ray patterns is explained. (Author).

Download or read book Nonlinear Water Waves written by Kiyoshi Horikawa and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-linear behaviour of water waves has recently drawn much attention of scientists and engineers in the fields of oceanography, applied mathematics, coastal engineering, ocean engineering, naval architecture, and others. The IUTAM Symposium on Non-linear Water Waves was organized with the aim of bringing together researchers who are actively studying non-linear water waves from various viewpoints. The papers contained in this book are related to the generation and deformation of non-linear water waves and the non-linear interaction between waves and bodies. That is, various types of non-linear water waves were analyzed on the basis of various well-known equations, experimental studies on breaking waves were presented, and numerical studies of calculating second-order non-linear wave-body interaction were proposed.

Download or read book Some Two dimensional Internal Waves in a Stratified Fluid written by T. N. Stevenson and published by . This book was released on 1968 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Waves in Fluids written by Sir M. J. Lighthill and published by Cambridge University Press. This book was released on 2001-11-15 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive textbook in which the author describes the science of waves in liquids and gases. Drawing on a subject of enormous extent and variety, he provides his readers with a thorough analysis of the most important and representative types of waves including sound waves, shock waves, waterwaves of all kinds, and the so-called internal waves (inside atmospheres and oceans) due to intensity stratification. Emphasis throughout is on the most generally useful fundamental ideas of wave science, including the principles of how waves interact with flows. This standard work on one of the great subdivisions of the dynamics of fluids is lucidly written and will be invaluable to engineers, physicists, geophysicists, applied mathematicians or any research worker concerned with wave motions or fluid fllows. It is especially suitable as a textbook for courses at the final year undergraduate or graduate level.