摘要:

A uniformly valid asymptotic theory of resonantly interacting high‐frequency waves for nonlinear hyperbolic systems in several space dimensions is developed. When applied to the equations of two‐dimensional compressible fluid flow, this theory both predicts the geometric location of the new sound waves produced from the resonant interaction of sound waves and vorticity waves as well as yielding a simplified system which governs the evolution of the amplitudes. In this important special case, this system is two Burgers equations coupled by a linear integral operator with known kernel given by the vortex strength of the shear wave. Several inherently multidimensional assumptions for the phases are needed in this theory, and theoretical examples are given which delineate these assumptions. Furthermore, explicit necessary and sufficient conditions for the validity of the earlier noninteracting wave theory of Hunter and Keller are derived; these explicit conditions indicate that generally waves resonate and interact in several dimensi

ISSN:0022-2526    

DOI:10.1002/sapm1986753187

年代:1986

数据来源: WILEY

摘要:

The direct resonance mechanism between vertical vorticity and vertical velocity is studied for plane Poiseuille flow. The resonance term, obtained from the initialvalue problem, has been determined numerically for various initial disturbances. The amplitude, in wave‐number space, is found to decay with time for all resonances. Because of its appearance in the Laplace‐transform plane as a double pole, it is shown that a resonance term will have an initial amplitude which grows with Reynolds number, thus indicating that resonances will dominate the initial development of a disturbance at large Reynolds num

ISSN:0022-2526    

DOI:10.1002/sapm1986753227

年代:1986

数据来源: WILEY

摘要:

This paper studies the spectral properties of the partial differential operatorover a finite region Ω. This operator, which arises in the analysis of nonaxisymmetric, rapidly rotating compressible flows, is treated as a perturbation of the operatorwhich is generated by the termsUsing the fact that , when defined on a suitable domain, is closed and self‐adjoint, it is shown that[when acting on elements of ]is an operator with compact resolvent whose generalized eigenvectors are complete in ℒ

ISSN:0022-2526    

DOI:10.1002/sapm1986753249

年代:1986

数据来源: WILEY

摘要:

It is shown how a conjecture of G. B. Whitham on the completeness of the functions {ψn} = {e−np(x)cosnx,e−np(x)sinnx} in the interval [0, 2π] is indeed true providedphas a Hölder continuous first derivative, i.e.,p∈C1,α[0, 2π]. Also an elementary proof of Whitham's conjecture is given forp

ISSN:0022-2526    

DOI:10.1002/sapm1986753265

年代:1986

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1986753273

年代:1986

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1986753275

年代:1986

数据来源: WILEY