Initial-Value Problems in Stratified Shear Flows

Initial-Value Problems in Stratified Shear Flows
Author: Jerre Eugene Bradt
Publisher:
Total Pages: 149
Release: 1979
Genre: Boundary value problems
ISBN:

The question of the stability of steady state solutions in geophysical fluid flows is addressed through qualitative analysis and quantitative examples. The inviscid linear stability theory of stratified shear flows and the solution of the stability problem using normal modes and Fourier-Laplace transforms are discussed. Two numerical examples are used to illustrate the relationship of various physical parameters to the stability of the system and to trace the development of the instability of the instability for short, intermediate and long times. The examples are (1) two layer fluid of infinite extent with application to the air-sea interface and (2) a two-layer fluid having a free surface and finite depth with application to a salt wedge estuary. The initial-value problem is solved using a power series expansion for short times, superposition of modes for intermediate times and asymptotic analysis for long times. The asymptotic expansion applicable in non-conservative systems is compared with the approximate solution using ray techniques, which are valid in conservative systems, and analytic continuation of the eigenvalues into the complex wavenumber plane. (Author).

Initial-value Problems and Stability in Shear Flows

Initial-value Problems and Stability in Shear Flows
Author:
Publisher:
Total Pages: 21
Release: 1991
Genre:
ISBN:

It is the plan of this presentation of outline three major topics of the novel analysis. (1) Use of exact solutions in solving initial-value problems; (2) detailed linear example that illustrates the relevant of the early period and possible instability; (3) Lagrangian mechanics and the link to computational fluid dynamics.

Stability and Transition in Shear Flows

Stability and Transition in Shear Flows
Author: Peter J. Schmid
Publisher: Springer Science & Business Media
Total Pages: 561
Release: 2012-12-06
Genre: Science
ISBN: 1461301858

A detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. It presents analytical results and numerical simulations, linear and selected nonlinear stability methods. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It is equally of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Stability theory has seen a rapid development over the past decade, this book includes such new developments as direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem.

Wave Interactions and Fluid Flows

Wave Interactions and Fluid Flows
Author: Alex D. D. Craik
Publisher: Cambridge University Press
Total Pages: 340
Release: 1988-07-07
Genre: Mathematics
ISBN: 9780521368292

This up-to-date and comprehensive account of theory and experiment on wave-interaction phenomena covers fluids both at rest and in their shear flows. It includes, on the one hand, water waves, internal waves, and their evolution, interaction, and associated wave-driven means flow and, on the other hand, phenomena on nonlinear hydrodynamic stability, especially those leading to the onset of turbulence. This study provide a particularly valuable bridge between these two similar, yet different, classes of phenomena. It will be of value to oceanographers, meteorologists, and those working in fluid mechanics, atmospheric and planetary physics, plasma physics, aeronautics, and geophysical and astrophysical fluid dynamics.

Hydrodynamic Instability and Transition to Turbulence

Hydrodynamic Instability and Transition to Turbulence
Author: Akiva M. Yaglom
Publisher: Springer Science & Business Media
Total Pages: 611
Release: 2012-12-18
Genre: Technology & Engineering
ISBN: 9400742371

This book is a complete revision of the part of Monin & Yaglom's famous two-volume work "Statistical Fluid Mechanics: Mechanics of Turbulence" that deals with the theory of laminar-flow instability and transition to turbulence. It includes the considerable advances in the subject that have been made in the last 15 years or so. It is intended as a textbook for advanced graduate courses and as a reference for research students and professional research workers. The first two Chapters are an introduction to the mathematics, and the experimental results, for the instability of laminar (or inviscid) flows to infinitesimal (in practice "small") disturbances. The third Chapter develops this linear theory in more detail and describes its application to particular problems. Chapters 4 and 5 deal with instability to finite-amplitude disturbances: much of the material has previously been available only in research papers.

NRL Report

NRL Report
Author:
Publisher:
Total Pages: 28
Release: 1979
Genre: Naval research
ISBN:

Rotating Thermal Flows in Natural and Industrial Processes

Rotating Thermal Flows in Natural and Industrial Processes
Author: Marcello Lappa
Publisher: John Wiley & Sons
Total Pages: 666
Release: 2012-07-25
Genre: Science
ISBN: 1118342380

Rotating Thermal Flows in Natural and Industrial Processes provides the reader with a systematic description of the different types of thermal convection and flow instabilities in rotating systems, as present in materials, crystal growth, thermal engineering, meteorology, oceanography, geophysics and astrophysics. It expressly shows how the isomorphism between small and large scale phenomena becomes beneficial to the definition and ensuing development of an integrated comprehensive framework. This allows the reader to understand and assimilate the underlying, quintessential mechanisms without requiring familiarity with specific literature on the subject. Topics treated in the first part of the book include: Thermogravitational convection in rotating fluids (from laminar to turbulent states); Stably stratified and unstratified shear flows; Barotropic and baroclinic instabilities; Rossby waves and Centrifugally-driven convection; Potential Vorticity, Quasi-Geostrophic Theory and related theorems; The dynamics of interacting vortices, interacting waves and mixed (hybrid) vortex-wave states; Geostrophic Turbulence and planetary patterns. The second part is entirely devoted to phenomena of practical interest, i.e. subjects relevant to the realms of industry and technology, among them: Surface-tension-driven convection in rotating fluids; Differential-rotation-driven (forced) flows; Crystal Growth from the melt of oxide or semiconductor materials; Directional solidification; Rotating Machinery; Flow control by Rotating magnetic fields; Angular Vibrations and Rocking motions; Covering a truly prodigious range of scales, from atmospheric and oceanic processes and fluid motion in "other solar-system bodies", to convection in its myriad manifestations in a variety of applications of technological relevance, this unifying text is an ideal reference for physicists and engineers, as well as an important resource for advanced students taking courses on the physics of fluids, fluid mechanics, thermal, mechanical and materials engineering, environmental phenomena, meteorology and geophysics.