Boundaries for the Kelvin-Helmholtz Instability (KHI) is investigated. We have focused our attention on the emission of magnetosonic waves from the Kelvin-Helmholtz (K-H) unstable shear flow boundaries of MHD plasmas. We have shown for the first time that the Kelvin-Helmholtz Instability is a mechanism for fast and slow MHD wave, i.e. magnetosonic wave, generation along MHD shear flow boundaries. Our results is significant in showing that the emission of MHD waves from an unstable MHD shear flow boundary is possible and these waves may provide a efficient mean of energy transportation in between two MHD media. The Kelvin - Helmholtz generated fast/slow waves are introduced in the context of the primary/secondary KHI. First, the primary and secondary K-H surface wave modes on the Earth's magnetopause are studied. The primary KHI is caused by fast MHD waves while the secondary KHI is caused slow MHD waves. The secondary KHI usually is possible at smaller shear flow speeds and have smaller growth rates than the primary KHI. The Earth's magnetopause is considered as an infinitely thin MHD shear flow boundary. Phase velocity diagrams are presented that allow us to identify the excited MHD waves that correspond to growing modes of the KHI under different conditions of the regions on both sides of the magnetopause boundary. The relation between the primary and the secondary KHI to magnetosonic wave interactions under different solar wind conditions is revealed through these diagrams. Using the observational values of the KHI relevant waves and the results of our study, general behavior of the primary and the secondary KHI relevant waves along the K-H unstable magnetopause is provided. A relation between the KHI waves and Negative Energy Waves (NEWs) is also shown. Following, the KHI of the Earth's magnetotail flow channels associated with bursty bulk flows (BBFs) is investigated. The BBF channel boundary is also considered as an infinitely thin MHD shear flow boundary and an inner boundary is assumed in the middle of the channel. MHD oscillations of the BBF channels in both kink and sausage modes are investigated for the KHI. Both the primary and the secondary KHI are found to cause the emission of magnetosonic waves along these boundaries. These instabilities are shown to be important for stopping the BBFs where the KHI removes energy from the flow. We have provided a model that can explain, for the first time, the generation mechanism for the observations of waves propagating towards both flanks of the Earth's magnetopause and emitted from BBF channels in the central magnetotail. Results shown in this section was published in Geophysical Research Letters and the paper was chosen as a spotlight paper with innovative ideas by American Geophysical Union. Then a finite width boundary layer is added and emission of magnetosonic waves due to KHI from superfast relative flows across MHD plasma boundaries are investigated. While previous studies have focused their attention on the most unstable KHI waves, we have shown that the most significant modes are not the fastest growing modes. In contrast, the KHI wave growth resulting in emission of magnetosonic waves, which usually does not efficiently take place for the fastest growing modes, is the main source of energy transport. With the results obtained, the processes of the KHI and magnetosonic wave emission along various MHD shear flow boundaries in the Earth's magnetosphere and the solar corona is discussed. We have concluded that while the KHI would be more favorable on the day-side magnetopause and Coronal Mass Ejection (CME) boundaries, emission of magnetosound would dominate along the nightside magnetopause, BBFs in the inner plasmasheet and Supra-Arcade Downflows (SADs) in the solar corona. Finally, nonlinear evolution of the KHI and emission of magnetosound due to the action of the KHI are investigated using the FLASH code which is provided by Flash Center at the University of Chicago. The same parameter space as the linear calculations for finite transition thickness is used to study the nonlinear KHI along MHD shear flow boundaries. Results obtained from the FLASH code were in very good agreement with the linear results. Emission of magnetosound from MHD shear flow boundaries in the linear stages of the KHI is confirmed.

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.

Stability of Parallel Flows provides information pertinent to hydrodynamical stability. This book explores the stability problems that occur in various fields, including electronics, mechanics, oceanography, administration, economics, as well as naval and aeronautical engineering. Organized into two parts encompassing 10 chapters, this book starts with an overview of the general equations of a two-dimensional incompressible flow. This text then explores the stability of a laminar boundary layer and presents the equation of the inviscid approximation. Other chapters present the general equations governing an incompressible three-dimensional flow, which requires the massive use of a computer. This book discusses as well the experimental studies on the oscillations of the boundary layer wherein the mean flow is affected by the presence of oscillations. The final chapter describes the concept of the stability of turbulent flows found in boundary layers, wakes, and jets. This book is a valuable resource for physicists, mathematicians, engineers, scientists, and researchers.

A groundbreaking new theory of the magnetosphere The magnetosphere is the region around Earth in which our planet's magnetic field exerts its influence to trap charged particles. Waves in this magnetosphere, known as magnetohydrodynamic (MHD) oscillations, are caused by interactions between these charged particles, Solar wind pulses, and the magnetic field. The predictable interval between these oscillations enables them to serve as tools for understanding the magnetospheric plasma which comprises the field. Magnetospheric MHD Oscillations offers a comprehensive overview of the theory underlying these waves and their periodicity. Emphasizing the spatial structure of the oscillations, it advances a theory of MHD oscillation that promises to have significant ramifications in astronomy and beyond. Magnetospheric MHD Oscillationsreaders will also find: Theorizing of direct relevance to current satellite missions, such as THEMIS and the Van Allen Probe In-depth discussion of topics including Alfven resonance, waveguides in plasma filaments, and many more Detailed appendices including key calculations and statistical parameters Magnetospheric MDH Oscillations is ideal for plasma physicists, theoretical physicists, applied mathematicians, and advanced graduate students in these and related subfields.

This book presents the fundamentals and advanced research on the global stability analysis of the shear flows. The contents investigate the results of global stability analysis for different configurations of internal and external shear flows. The topics covered are global stability analysis of converging-diverging channel flows, axisymmetric boundary layer developed on a circular cylinder, cone and inclined flat-plate boundary layer, and wall jets. It further explains the effect of divergence, convergence, transverse curvature, and pressure gradients on the global stability of the different configurations of shear flows. The book is a valuable reference for beginners, researchers, and professionals working in the field of aerodynamics and marine hydrodynamics.

In the 1990s it was rigorously revealed by the hydrodynamic community non-normal nature of operators of the modal analysis of linear processes in shear flows - so, called "shear flow non-normality". The non-normality ensures finite-time, or transient, growth of perturbations in spectrally stable shear flows that is essentially anisotropic in spectral space and, in turn, leads to anisotropy of nonlinear processes in spectral space - the dominant nonlinear process turns out to be not a direct/inverse, but a transverse cascade, that is, a transverse/angular redistribution of perturbation harmonics in spectral space. The investigation of the linear transient growth and nonlinear transverse cascade in magnetohydrodynamic (MHD) unbounded constant shear flows - their special nature, interplay and consequences - is the goal of the present thesis. Initially, in Chapter 2, is investigated in detail the transient linear dynamics in the form of overreflection of pseudo- and shear-Alfv ́en waves (P-AWs and S-AWs) in spectrally stable MHD plane constant shear flow. We show that: (1) the linear coupling of counter-propagating waves determines the overreflection, (2) counter-propagating P-AWs are coupled with each other, while counter-propagating S-AWs are not coupled with each other, but are asymmetrically coupled with P-AWs; S-AWs do not participate in the linear dynamics of P-AWs, (3) the transient growth of S-AWs is somewhat smaller compared with that of P-AWs, (4) the linear transient processes are highly anisotropic in wave number space, (5) the waves with small streamwise wavenumbers exhibit stronger transient growth and become more balanced. Further, in the thesis is investigated MHD turbulence in spectrally stable two dimensional (2D) plane shear flows (Chapter 3) and three dimensional (3D) Keplerian disk flows, threaded by a non-zero azimuthal (Chapter 4) and vertical (Chapter 5) net magnetic flux. In order to gain a deeper insight into the underlying dynamical balances and sustaining mechanism, we performed a set of numerical simulations in the shearing box model and based on the simulation data, analyzed in detail the turbulence dynamics in Fourier space. 2D MHD plane shear flow, considered in Chapter 3, is spectrally stable, so the turbulence is subcritical by nature and hence it can be energetically supported just by a transient growth mechanism due to shear flow non-normality. We focus on analysis of the character of nonlinear processes and the underlying self-sustaining scheme of the turbulence, i.e., on the interplay between linear transient growth and nonlinear processes, in the spectral plane. The study, being concerned with a new type of energy-injecting process for turbulence - the transient growth - represents an alternative to the main trends of magnetohydrodynamic (MHD) turbulence research. In the case of Keplerian disk flows with a net azimuthal field, classical exponential/modal instabilities are absent and linear growth of perturbations (shearing waves) has a transient nature, also referred to as nonmodal growth. Particularly, in the case of disk flows with azimuthal field and rotation, magnetorotational instability (MRI), being only available source of energy for turbulence, has transient nature and by itself, cannot ensure a long-term sustenance of the perturbations, i.e. is imperfect in this sense. A necessary positive nonlinear feedback is required to regenerate new transiently growing modes. In other words, the role of nonlinearity becomes crucial: it lies at the heart of the sustenance of turbulence. The detailed analysis of the dynamics in apextral/Fourier space, allows to demonstrate existence of the positive feedback. Specifically, main novelties of the findings are the following: I. The nonmodal growth process is strongly anisotropic in Fourier space that, in turn, leads to anisotropy of nonlinear processes in this space. As a result, the main nonlinear process appears to be not an usual direct/inverse, but rather a new type of transverse/angular redistribution of perturbation modes in Fourier space, when their wavevector mainly changes orientation during nonlinear mode interactions - nonlinear transverse cascade. II. Both the linear nonmodal growth and nonlinear transverse cascade mainly operate at large length scales, comparable to the box/system size. Consequently, the central, small wavenumber area of Fourier space, is crucial in the turbulence sustenance process and is called the vital area. III. The turbulence is sustained by a subtle interplay of the linear nonmodal growth (transient MRI in the case of Keplerian disks) and the nonlinear transverse cascade. Analyzing this interplay, it is revealed the basic subcycle of the sustenance scheme that clearly shows synergy of the linear and nonlinear processes in the self-organization of the magnetized flow system. In the case of net vertical field, there is exponential growth of axisymmetric channel modes, and hence no deficit in energy supply. Due to this, the role of the transverse cascade in the turbulence sustenance is not as crucial as in the case of the azimuthal field. But it still shapes the dynamics, sets the saturation level, and determines the overall"design" of the net vertical field MRI-turbulence. In particular, it accounts for the transfer of energy among the "building blocks" of this turbulence: the axisymmetric channel mode, zonal flow, to a broad spectrum of nonaxisymmetric (parasitic) modes. The analyzed refined interplay of linear and nonlinear processes should be relevant to the understanding of subcritical turbulence in other sheared and magnetized complex environmental and engineering flows (e.g., sheared E×B plasma fusion flows)