Instabilities of flows and transition to turbulence (Q2883346)

The monograph contains the following topics of hydrodynamics: 1. Classic linear hydrodynamic instability; 2. Receptivity and instability of different types; 3. Vortex-induced instability and bypass transition; 4. Transient growth and spatio-temporal instability; 5. Bifurcation and dynamical system theory of nonlinear instabilities for different flows; 6. Instability of mixed convection flows by restricted heat transfer; 7. Instability of three-dimensional flows; 8. Applications of instability and transition for flows past airfoils. These linear and nonlinear aspects of flow instabilities are studied by using analytic and computational (numerical simulation) means.NEWLINENEWLINE In the introductory Chapter 1, various types of instabilities are introduced and explained. Chapter 2 gives the basic equations of fluid mechanics together with a description of their equilibrium solutions (Couette flow between parallel plates, flow between concentric rotating cylinders, steady stagnation point flow, flow past a rotating disc); boundary layer theory; control volume analysis of boundary layers; numerical solution of the thin shear layer equation (Falkner-Skan similarity profile, Blasius profile); wave interaction; group velocity and energy flux; computing methods for unsteady flows etc. Chapter 3 provides a general introduction to the flow receptivity and flow instability, relevant to many engineering systems. Here the following problems are investigated: inviscid instability mechanism, viscous instability of parallel flows; receptibility analysis of shear layers (receptibility mechanism by a linearized approach: connection to stability theory, receptibility to wall excitation and impulse response, vibrating ribbon at the wall, receptibility to free stream excitation); direct simulation of receptibility to free stream excitation; nonparallel and nonlinear effects on instability and receptibility. Also, two important sections are included: properties of the Orr-Sommerfeld equation and boundary conditions, and the instability analysis employing the solution of the Orr-Sommerfeld equation.NEWLINENEWLINE Chapter 4 ``Bypass transition: theory, computations and experiments''NEWLINE explanes the bypass mechanisms. The disturbance energy equation arises by taking the divergence of Navier-Stokes equations in the rotational form, representing the irrotational component of the disturbance field. The rotational field of Navier-Stokes equations as governed by the vorticity transport equation yields the Orr-Sommerfeld equation obtained by linearization and parallel flow approximation. At the same time the unsteadiness during bypass transition is due to the shear noise term in the Poisson equation for the static pressure.NEWLINENEWLINE Chapter 5 ``Spatio-temporal wave front and transition'' consists of the following sections: transient energy growth; Bromwich contour integral method and energy-based receptivity analysis; spatio-temporal wave front obtained by the Bromwich contour integral method; nonlinear receptivity analysis: transition by the spatio-temporal front and bypass route. Chapter 6 is devoted to nonlinear multiple Hopf bifurcations and contains necessary means for the numerical investigation of dynamic bifurcations with applications to various problems (flow past a cylinder; Landau equation and flow instability; critical Reynolds number for a cylinder; proper orthogonal decomposition modes and nonlinear stability; Landau-Stuart-Eckhaus equation).NEWLINENEWLINE In Chapter 7, the author studies the effect of heat transfer on instability from both linear and nonlinear perspectives. Also, the mixed convection flow at low speed, modeled by the Boussinesq approximation, is studied. Here the main difficulty consists in the lack of available canonical equilibrium flows, even in the case of flows past a flat plate. A comparison with the results of \textit{W. Schneider} [Int. J. Heat Mass Transfer 22, 1401--1406 (1979; Zbl 0414.76066)] is given for a constant external flow past a horizontal flat plate. In conclusion, as a generalization of this similarity solution, the author discusses the absolute-convective instability of mixed forced-free convection boundary layers.NEWLINENEWLINE Chapter 8 examines the instabilities of three-dimensional flows. These are more complex as instabilities can occur not only for the streamwise component of the flow. Additional instabilities of the cross flow component of the velocity profile have to be considered. With the aim of aerospace applications, the author studies here various aspects of external instabilities which can occur in three-dimensional flows, taking into account the boundary layers effects. Chapter 9 is completely devoted to the analysis and design of natural laminar flow (NLF) airfoils and contains the following sections: airfoil nomenclature and their basic aerodynamic properties; pressure distribution and pressure recovery of some low drag airfoils; flapping of airfoils; effects of roughness and fixing transition; effects of vortex generator; section characteristics of various profiles; high speed NLF airfoils; direct simulation of bypass transitional flow past an airfoil.NEWLINENEWLINE In the final Chapter 9, various mechanisms of turbulence occurrence are discussed and compared.