摘要:

The Ginzburg‐Landau equation may be used to describe the weakly nonlinear 2‐dimensional evolution of a disturbance in plane Poiseuille flow at Reynolds number near critical. We consider a class of quasisteady solutions of this equation whose spatial variation may be periodic, quasiperiodic, or solitarywave‐ like. Of particular interest are solutions describing a transition from the laminar solution to finite amplitude states. The existence of these solutions suggests the existence of a similar class of solutions in the Navier‐Stokes equations, describing pulses and fronts of instability in t

ISSN:0022-2526    

DOI:10.1002/sapm1987763187

年代:1987

数据来源: WILEY

摘要:

A generalized WKB method is used to construct formal asymptotic approximations of solutions of certain forced nonlinear Sturm‐Liouville systems. By means of three connected expansions it is possible to obtain a fairly complete picture of the global behavior of the small‐norm solution branches. Results are presented for both slowly varying and rapidly varying forcing functi

ISSN:0022-2526    

DOI:10.1002/sapm1987763239

年代:1987

数据来源: WILEY

摘要:

A model equation somewhat more general than Burger's equation has been employed by Herron [1] to gain insight into the stability characteristics of parallel shear flows. This equation, namely,ut+ uuy= uxx+ uyy, has an exact solutionU(y) = −2tanhy. It was shown in [1] that this solution is linearly stable, and more recently, Galdi and Herron [3]have proved conditional stability to finite perturbations of sufficiently small initial amplitude using energy methods. The present study utilizes multiple‐scaling methods to derive a nonlinear evolution equation for a long‐wave perturbation whose amplitude varies slowly in space and time. A transformation to the heat‐conduction equation has been found which enables this amplitude equation to be solved exactly. Although all disturbances ultimately decay due to diffusion, it is found that subcritical instability is possible in that realistic disturbances of finite initial amplitude can amplify substantially before finally decaying. This behavior is probably typical of perturbations to shear flows of practical interest, and the results illustrate deficiencies of the energy

ISSN:0022-2526    

DOI:10.1002/sapm1987763265

年代:1987

数据来源: WILEY