Hydrodynamic Stability Theory

1987 ◽  
Vol 54 (1) ◽  
pp. 250-250
Author(s):  
A. Georgescu ◽  
J. T. Stuart
Keyword(s):  
Hydrodynamic Stability ◽  
Stability Theory ◽  
Hydrodynamic Stability Theory

scholarly journals A space–time variational approach to hydrodynamic stability theory

2013 ◽  
Vol 469 (2155) ◽  
pp. 20130036 ◽  
Author(s):  
Masayuki Yano ◽  
Anthony T. Patera
Keyword(s):  
Hydrodynamic Stability ◽  
Stability Theory ◽  
Stokes Equations ◽  
Solution Space ◽  
Finite Amplitude ◽  
Space Time ◽  
Reynolds Number Flow ◽  
Linear Framework ◽  
Moderate Reynolds Number ◽  
Hydrodynamic Stability Theory

We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a space–time variational formulation and associated generalized singular value decomposition of the (linearized) Navier–Stokes equations. We first introduce a linear framework applicable to a wide variety of stationary- or time-dependent base flows: we consider arbitrary disturbances in both the initial condition and the dynamics measured in a ‘data’ space–time norm; the theory provides a rigorous, sharp (realizable) and efficiently computed bound for the velocity perturbation measured in a ‘solution’ space–time norm. We next present a generalization of the linear framework in which the disturbances and perturbation are now measured in respective selected space–time semi-norms ; the semi-norm theory permits rigorous and sharp quantification of, for example, the growth of initial disturbances or functional outputs. We then develop a (Brezzi–Rappaz–Raviart) nonlinear theory which provides, for disturbances which satisfy a certain (rather stringent) amplitude condition, rigorous finite-amplitude bounds for the velocity and output perturbations. Finally, we demonstrate the application of our linear and nonlinear hydrodynamic stability theory to unsteady moderate Reynolds number flow in an eddy-promoter channel.

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