Stratified Flows is the second edition of the book Dynamics of Nonhomogenous Fluids. This book discusses the flow of a fluid of variable density or entropy in a gravitational field. In this edition, corrections have been made; unnecessary parts have been omitted; and new sections as well as notes on results related to the subject have been added. This book includes a general discussion of the effects of density or entropy and the structure of stratified flows; waves of small amplitude; the Eigenvalue problem; dependence of phase velocity on wavelength; wave motion; steady flows of finite amplitude; and types of solutions for steady flows. This edition also covers other topics such as hydrodynamic stability; flows in porous media; and the analogy between gravitational and electromagnetic forces. This text is recommended for those in the field of physics who would like to be familiarized with stratified flows and its related concepts.

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.

Diffusion-driven flow occurs when an object with a sloping surface is immersed in a stratified fluid, both of which are stationary in a stable configuration. The influence of this flow is examined on slow vertical fluid motion moving past an object, particularly for a cylinder and a sphere. Analytical solutions for streamfunction and density fields are presented, for which the governing equations are derived using perturbation theory. It is found that the solutions violate far-field flow conditions in a region surrounding the object. This difficulty is similar to that encountered for the Stokes' streamfunction in a homogeneous viscous flow. An analogous approach to the Oseen's method is followed here by introducing an "outer region", in which the dynamical balances are slightly different. In this thesis, the "outer solutions" (Oseen-type solutions) for viscous stratified fluid motion around the cylinder are successfully derived using the Fourier transform method. On the other hand, the "inner solutions" (Stokes-type solutions) are derived using a standard approach to solving differential equations. Results show that the outer solutions not only satisfy the conditions at a large radius but also match with the inner solutions at a small radius, based on the matched asymptotic expansions principle. In the case of the sphere, the exact outer solutions based on the same approach appear to be unavailable, but the fundamentals of the outer flow are presented; for instance, the governing equations and the relevant boundary conditions. Despite the unavailability of the exact outer solutions for the sphere, a numerical approach indicates that suitable outer solutions appear to exist. Previous studies have ignored the effect of the diffusion-driven flow on the viscous stratified flow past an object, but here the solutions reveal their relative importance in this parameter regime.