摘要:

There are many fluid flows where the onset of transition can be caused by different instability mechanisms which compete in the nonlinear regime. Here the interaction of a centrifugal instability mechanism with the viscous mechanism which causes Tollmien‐Schlichting waves is discussed. The interaction between these modes can be strong enough to drive the mean state; here the interaction is investigated in the context of curved channel flows so as to avoid difficulties associated with boundary layer growth. Essentially it is found that the mean state adjusts itself so that any modes present are neutrally stable even at finite amplitude. In the first instance the mean state driven by a vortex of short wavelength in the absence of a Tollmien‐Schlichting wave is considered. It is shown that for a given channel curvature and vortex wavelength there is an upper limit to the mass flow rate which the channel can support as the pressure gradient is increased. When Tollmien‐Schlichting waves are present then the nonlinear differential equation to determine the mean state is modified. At sufficiently high Tollmien‐Schlichting amplitudes it is found that the vortex flows are destroyed, but there is a range of amplitudes where a fully nonlinear mixed vortex‐wave state exists and indeed drives a mean state having little similarity with the flow which occurs without the instability modes. The vortex and Tollmien‐Schlichting wave structure in the nonlinear regime has viscous wall layers and internal shear layers; the thickness of the internal layers is found to be a function of the Tollmien‐Schlichting w

ISSN:0022-2526    

DOI:10.1002/sapm1989813185

年代:1989

数据来源: WILEY

摘要:

Using the notion of a differential equation which describes anη‐pseudospherical surface (η‐p.s.s.), we give a characterization of the equations of typeuxt=F(u,ux,…,∂ku/∂xk),k≥ 2, with this property. We obtain a systematic procedure to determine a linear problem for which a given equation is the integrability condition. The equations of typeuxt=F(u,ux) were characterized by Rabelo and Tenenblat in another paper. The theory is applied to several equations, some of which were not known to de

ISSN:0022-2526    

DOI:10.1002/sapm1989813221

年代:1989

数据来源: WILEY

摘要:

Traveling wave solutions are sought for a model of combustion in a porous medium. The problem is formulated as a nonlinear eigenvalue problem for a system of ordinary differential equations of order four, defined over an infinite interval. A shooting method is used to prove existence, anda prioribounds for the solution and parameters are obtained.

ISSN:0022-2526    

DOI:10.1002/sapm1989813249

年代:1989

数据来源: WILEY

摘要:

The generalized method of Burniston and Siewert for the derivation of closed‐form formulae for the zeros (and/or poles) of analytic functions inside a closed contour in the complex plane is further extended to the case of generalized analytic functions with real and imaginary parts satisfying homogeneous generalized Cauchy‐Riemann equations. Two special cases and one generalization of this approach are also considered in br

ISSN:0022-2526    

DOI:10.1002/sapm1989813265

年代:1989

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1989813271

年代:1989

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1989813273

年代:1989

数据来源: WILEY