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 Numerical Simulations of Internal Waves Around Bodies in Density Stratified Fluids written by Lap Yan Pao and published by . This book was released on 1990 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Environmental Stratified Flows written by Roger Grimshaw and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of flows in density-stratified fluids has been and remains now an important topic for scientific enquiry. Such flows arise in many contexts, ranging from industrial settings to the oceanic and atmospheric environments. It is the latter topic which is the focus of this book. Both the ocean and atmosphere are characterised by the basic vertical density stratification, and this feature can affect the dynamics on all scales ranging from the micro-scale to the planetary scale. The aim of this book is to provide a “state-of-the-art” account of stratified flows as they are relevant to the ocean and atmosphere with a primary focus on meso-scale phenomena; that is, on phenomena whose time and space scales are such that the density stratification is a dominant effect, so that frictional and diffusive effects on the one hand and the effects of the earth’s rotation on the other hand can be regarded as of less importance. This in turn leads to an emphasis on internal waves.
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 Internal Waves in the Ocean written by Marek Stastna and published by Springer Nature. This book was released on 2022-06-16 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a concise overview of nonlinear internal wave theory. It serves as a self-contained reference for both students of mathematics as well as scientific professionals by presenting the material in two parts, isolating the narrative analysis from the mathematical detail. This unique format allows the text to remain accessible to oceanographers and researchers outside of mathematics by presenting a range of relevant theories on their own terms. Conversely, it enables applied mathematicians to understand how the conversation between mathematics and sciences proceeds in a field that has developed through a combination of the two. In addition, the text is supplemented by hands-on Matlab software, as the book incorporates a collection of working codes that enable readers to reproduce all theoretical figures in the text, with modification potential to fit a range of applications including a number of mini-projects outlined throughout the text.
Download or read book Internal Gravity Waves written by Bruce 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 first comprehensive treatment of the theory for small and large amplitude internal gravity waves, with illustrative examples and exercises.
Download or read book Numerical Simulations of Internal Solitary and Solitary like Waves written by Chengzhu Xu and published by . This book was released on 2019 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Internal solitary and solitary-like waves (ISWs) are commonly observed in stably stratified fluids such as the Earth's atmosphere and oceans. As these waves interact with other physical processes and/or move through a varying background environment, they may change their form and possibly become unstable. In this thesis, we study ISWs using high-resolution direct numerical simulations and address three major topics: the interaction of ISWs with short waves, the onset of shear instability in ISWs, and the dynamics of ISWs in a shear background current induced by basin-scale standing internal waves. The first topic examines the behavior of short internal waves as they propagate through large-amplitude ISWs. A key finding is that for waves that are short in comparison to the ISW width, the interaction leads to an almost complete destruction of the short waves, but that longer waves are able to maintain their structure after the interaction. The destruction of short waves occurs primarily due to the velocity shear induced by the ISW, which alters the vertical structure of the short waves so that significant wave activity is found only on the upstream side of the ISW crest (i.e. the deformed pycnocline). These results suggest that through the interaction with waves of relatively smaller length scale, ISWs can provide a means to decrease the power observed in the short-wave band in the coastal ocean. The second topic focuses on the onset and growth of shear instability in ISWs, which is particularly important for the diapycnal mixing in open waters. The complexity of instability onset in ISWs is due to the finite length and the non-parallel structure of the wave-induced high-shear region. We examine large-amplitude ISWs with a flat crest and show that, depending on the ratio of the length of high shear region and the width of the wave, there are cases in which instability can occur spontaneously, cases in which its onset is Reynolds number dependent, and cases in which instability does not occur spontaneously but must be triggered by small, but finite amplitude noise. The amplitude of the noise has a crucial influence on the instability growth, regardless of its spatial structure. In the final topic we study the effect of a shear background current on the dynamics of ISWs by investigating the interaction of ISWs with basin-scale standing internal waves. The ISWs are generated using a lock-release mechanism, while the seiches are created using a tilted tank suddenly returned to the upright position, both of which are readily realizable in a laboratory. In most cases, the wave forms of ISWs in the simulations match those described by the fully nonlinear theory, implying that in laboratory experiments ISWs propagating in a shear background current can be generated in a similar manner. In some circumstances, however, the presence of a shear background current prevents the formation of ISWs, but enables the formation of a finite amplitude dispersive wave train, even when the pycnocline center is not close to the mid-depth.
Download or read book Laboratory experiments and numerical simulations of inertial waves in a rotating spherical shell written by Sandy Dahley and published by Cuvillier Verlag. This book was released on 2016-02-01 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geo- und astrophysikalisch motivierte Strömungen, wie sie in der Atmosphäre, in den Ozeanen oder im Inneren von Planeten auftreten, lassen sich in rotierenden Experimenten mit homogenen Fluiden untersuchen. In dieser Arbeit werden Untersuchungen zu Trägheitswellen und Wellenattraktoren in einer Kugelschale und einem rechteckigen Tank gezeigt. Viele geophysikalische Anwendungen mit planetaren Skalen motivieren den Einsatz von sphärischen Geometrien. Mit dem Kugelspaltexperiment, bestehend aus zwei rotierenden konzentrisch angeordneten Kugelschalen, werden die Anregung und Ausbildung verschiedener Wellenphänomene sowie der internen Grenzschichten untersucht. Durch eine Modulation der Rotationsgeschwindigkeit an der Innenkugel in Form einer Sinuskurve werden Wellen erzeugt, die an den gekrümmten Rändern des Modells mehrfach reflektiert werden und somit bestimmten Bahnen folgen. Für den Vergleich mit numerischen Untersuchungen werden unterschiedliche Visualisierungen und Messtechniken spezifiziert. Die numerische Simulation erlaubt dabei die Untersuchung in Parameterbereichen mit Instabilitäten, die für die experimentelle Untersuchung schwer zugänglich sind.
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 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 Solitary Waves in Fluids written by R. Grimshaw and published by WIT Press. This book was released on 2007 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited by R.H.J. Grimshaw, this book covers the topic of solitary waves in fluids.
Download or read book Mixing and Dispersion in Stably Stratified Flows written by P. A. Davies and published by Oxford University Press. This book was released on 1999 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stratified flows are important in determining how various atmospheric and environmental processes occur. The book investigates these processes and focuses on the methods by which pollutants are mixed and dispersed in natural and industrial environments.
Download or read book Numerical Simulation of Nonlinear Internal Solitary Wave Interactions with Submarine Topographic Features written by Michael Peter Lee and published by . This book was released on 2011 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximately 120 computer simulations were conducted to evaluate how a mode-1-type internal wave would interaction with a variety of submarine topographic (physiographic) obstacles likely to be found in a marine setting. A total of seven obstacle geometries were selected for evaluation - shelf, slope-shelf, extended slope, short-slope, reverse-shelf, a single (isolated) rectangular obstacle, and a single triangular obstacle. Internal waves of `depression' as well as `elevation' were formed using a two-layered, stratified numerical model based on the Navier-Stokes and continuity equations. The governing equations assumed Boussinesq conditions. Output data from the FORTRAN-based computer code were post-processed using MATLAB-based computer programs that calculated internal wave amplitudes and energies. These data were compared to published data associated with experimental wave tank studies and found generally to be in good agreement. Data from the numerical simulation trials were also used to generate figures illustrating various hydrodynamic features (pycnocline, streamlines, and velocity vectors) of an internal wave as it forms as well as when it interacts with different types of obstacle geometries. The types of features and processes observed included the formation of Kelvin-Helmholtz or K-H-like vortices and various stages of the classically-recognized wave-breaking progression ("wash-down," "breaking," "bore," and "surge"). When considering a stratified fluid system, it was confirmed that internal wave characteristics are influenced in large measure by the relative depths of the two fluids defining the system as well as the effects of viscous decay (damping). It was also confirmed that the nature of the interaction between an internal wave and a topographic obstacle is influenced by the magnitude of either the nonlinear parameter or the blocking parameter. The numerical simulation trials also allowed for the interrogation of the modeling domain to determine the nature of the stability conditions (static vs. dynamic) in time and space. In this regard, evaluation of both the Richardson number and the normalized density gradient provided additional insights into the hydrodynamics of the system when topographic obstacles are present. Three instability states were evaluated: K-H, buoyant, and static. This research contributes to a basic understanding of internal wave phenomena and includes some general conclusions regarding the effects of obstacle geometry on internal wave behavior and properties.
Download or read book A Numerical Investigation of Turbulence driven and Forced Generation of Internal Gravity Waves in Stratified Mid water written by Ammar Mohammed Abdilghanie and published by . This book was released on 2011 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Natural and externally-forced excitation of internal gravity waves in a uniformly stratified fluid have been thoroughly investigated by means of highly resolved large eddy simulations. The first part of the thesis focuses on the generation of high frequency internal gravity waves by the turbulent wake of a towed sphere in a uniformly stratified fluid. We have used continuous wavelet transforms to quantify relevant wavelength and frequencies and their spatial and temporal dependence in the near field of the wake. The dependence on Reynolds number and Froude number of the internal wave field wavelengths, frequencies and isopycnal displacements are reported for the first time. The initial wavelengths and decay rates show a dependence on both parameters that can not be explained on the basis of impulsive mass source models. The results also clearly identify Reynolds number as the main driver for the observed selection of a narrow range of wave phase- line-tilt-angles and shed some light on the coupling of the waves and turbulent wake region at high Reynolds number. Finally, the potential for nonlinear interactions, instability and breaking of the waves increases with both Reynolds and Froude numbers. The results of this part of the thesis motivate future theoretical investigations into the underlying generation mechanisms and improved parametrization of the role of small scale processes, such as high frequency internal gravity waves, in large scale circulation models in the ocean and atmosphere. In the second half of the thesis, we have focused on the generation of an internal gravity wavepacket by a vertically localized transient forcing. We have found that the unique combination of strong vertical localization and large wave amplitude, typically not considered in the literature, lead to the formation of strong horizontal mean flow inside the wave forcing region that nonlinearly grows at the expense of a depleted and structurally modified emerging internal wave packet. A novel theoretical analysis is developed which can explain the underlying mechanism for the formation of the mean flow. By appealing to scaling arguments, based on a one way wave-mean flow interaction, we quantify the mean flow dependence on the input parameters. By means of a phase averaging procedure, we offer additional insight on mean flow reduction through horizontal localization of a wavepacket. Finally, mean flow containment techniques that allow the generation of a well-defined wavepacket that preserves its structure near the source and during the propagation towards a remote interaction region are proposed and tested. The efficiency of the techniques is tested in a simulation of internal gravity wave-shear flow interaction near a critical level. The simulations qualitatively agree with previous numerical investigations of such flow.
Download or read book Environmental Stratified Flows written by Vincenzo Armenio and published by Springer Science & Business Media. This book was released on 2007-03-07 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the theory of stratified flows, from basic concepts to recent developments in environmental fluid mechanics. State-of-the-art numerical techniques suited for stratified flows are given, along with results of recent research in the areas of environmental stratified flows. The book offers a unified view of stratified turbulent flows, from small-scale mixing to large-scale environmental phenomena, including detailed discussion on interaction between turbulence and internal gravity waves.
Download or read book Numerical Simulation of Water Waves written by Jianhua Tao and published by Springer Nature. This book was released on 2020-03-30 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the numerical simulation of water waves, which combines mathematical theories and modern techniques of numerical simulation to solve the problems associated with waves in coastal, ocean, and environmental engineering. Bridging the gap between practical mathematics and engineering, the book describes wave mechanics, establishment of mathematical wave models, modern numerical simulation techniques, and applications of numerical models in engineering. It also explores environmental issues related to water waves in coastal regions, such as pollutant and sediment transport, and introduces numerical wave flumes and wave basins. The material is self-contained, with numerous illustrations and tables, and most of the mathematical and engineering concepts are presented or derived in the text. The book is intended for researchers, graduate students and engineers in the fields of hydraulic, coastal, ocean and environmental engineering with a background in fluid mechanics and numerical simulation methods.
Download or read book Far field Evolution of Turbulence emitted Internal Waves and Reynolds Number Effects on a Localized Stratified Turbulent Flow written by Qi Zhou and published by . This book was released on 2015 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, internal waves (IWs) and turbulence in the stably stratified ocean are studied via a series of numerical simulations. First of all, internal wave beams that are representative of high-mode internal tide originated from the ocean topography and constituent element of turbulence-emitted IWs are studied via direct numerical simulations (DNS), with an emphasis on their reflection at the sea surface as modelled by a free-slip rigid lid. Nonlinear effects due to wave-wave interaction, such as mean flow and harmonics, are investigated; in particular, the amplitude of the wave-driven Eulerian mean flow is found to match the theoretical prediction of an inviscid weakly nonlinear theory. The IW beams can also degrade at late time of reflection due to parametric subharmonic instability. Subsequent particle tracking is performed based the DNS dataset, in an attempt to examine the mass transport driven by the reflecting IW beams. These fully nonlinear computations reveal a horizontal dispersion of ocean tracers with a dispersivity scaling with O(A4), where A is the steepness of the IW beam, while small-amplitude analysis accurate to O(A2) suggests an exact cancellation of Eulerian mean flow due to wave-wave interaction and the wave-driven Stokes drift. The second topic of the dissertation investigates the manifestation of submerged-turbulence-emitted IWs at the sea surface and the correlation between the IW characteristics to turbulent source of IW. The turbulent wake of a sphere of diameter D towed at speed U is investigated using three-dimensional implicit largeeddy simulations, in a linearly stratified Boussinesq fluid with buoyancy frequency N and kinematic viscosity [nu]. Six simulations are performed at Reynolds numbers Re [congruent to] U D/[nu] [set membership] {5 x 103, 105 } and Froude numbers Fr [congruent to] 2U/(N D) [set membership] {4, 16, 64}, with the wave-emitting wake located at a fixed distance of 9D below the surface. As the wake evolves for up to O(300) units of buoyancy time scale 1/N, IW characteristics, such as horizontal wavelength [lamda]H and wave period T, are sampled at the sea surface via wavelet transforms of surface horizontal divergence signals. The statistics of amplitudes and orientations of IW-induced surface strains are also reported. The normalized mean observable wavelength [lamda]H /D at the sea surface decays in time as (N t)[-]1, which is due to the waves' dispersion, the dominant process in the far-field, and is in agreement with a linear propagation model that is independent of the wake Re and Fr. This agreement suggests that, within the Re range considered, the most energetic waves impacting the surface originate from the early-time wake that is adjusting to buoyancy. Questions remain about the efficiency of late-time buoyancy driven stratified turbulence in radiating waves with ^considerable energy content. The most energetic wavelength [lamda]H, when normalized by D, is found to scale as Fr 1/3 and decrease with Re, which causes the arrival time (in N t units) of the strongest waves at the surface to scale as Fr [-]1/3 and ^increase with Re. This wavelength [lamda]H is also found to correlate with the vertical integral scale, V, of the wake turbulence. IW-driven phenomena at the surface that are of interest to an observer, such as the local enrichment of surfactant and the transport of ocean surface tracers, are also discussed. The local enrichment ratio of surfactant scales linearly with the steepness of IWs that reach the surface and often exceeds a possible visibility threshold. The nonlinear Lagrangian drifts of ocean tracers create a local divergence in lateral mass transport right above the wake centreline, an effect that intensifies strongly with increasing Fr. The final portion of the dissertation focuses on massively-parallel, implicit large-eddy simulations of stratified towed-sphere wakes at Re = 4 x 105, a previously unattained Reynolds number of such flow. The analyses focus on the vortical structures within the wake, evolution of mean flow, turbulent length scales and turbulent viscosities. The key finding is that, the wake Reynolds number Re has a significant impact on the evolution of the dynamically critical buoyancy Reynolds number, R, i.e., as Re increases, the R at a given dimensionless time N t is higher, and thus the transition from the inviscid regime at R> 1 to the viscous regime at R
