摘要:

A self‐consistent theoretical investigation is described for the nonlinear stability, and spatial development, of disturbances in a plane boundary layer subject to a number of three‐dimensional modes, their nonlinear interactions, and the effects of nonparallelism of the basic flow. For the largest weakly nonlinear disturbances considered, nonparallel‐flow effects appear to be negligible at first sight, and primary, secondary, and/or tertiary bifurcations, usually supercritical but not always so, can occur when two fundamental modes are present. As a result the flow downstream then always has three ultimate possibilities: a unique stable disturbed state, two or more possible stable states, or no stable state possible. It is here that the nonparallel‐flow effects exert their crucial influence. For nonparallelism comes into play significantly during the initial growth or decay of a disturbance, and that initial spatial development, from given initial conditions upstream, controls what happens subsequently as the disturbance increases. Thus in the first possibility above, the stable state is achieved through a smooth bifurcation, due to nonparallelism; in the second possibility the nonparallelism decides which stable state is attained (smoothly) from the initial conditions; and in the third possibility the nonparallel flow effects force the disturbance to terminate in a singular fashion. This singularity then leads to a fully nonlinear effect, locally on the boundary‐layer flow. More complicated interactions can arise if more than two three‐dimensional modes are present. The novel effect of the nonparallelism has a connection with related Navier‐Stokes calculations even at near‐critical R

ISSN:0022-2526    

DOI:10.1002/sapm198470291

年代:1984

数据来源: WILEY

摘要:

A general theorem is obtained for the enumeration of permutations equivalent under cyclic rotation. This result gives the generating function as the logarithm of a determinant which arises in the enumeration of a related linear permutation enumeration. Applications of this theorem are given to a number of classical enumerative problems.

ISSN:0022-2526    

DOI:10.1002/sapm1984702121

年代:1984

数据来源: WILEY

摘要:

The effects of the viscous Ekman layers on a rotating compressible gas in a container of arbitrary shape are described by a set of equivalent boundary conditions on the inviscid flow.

ISSN:0022-2526    

DOI:10.1002/sapm1984702141

年代:1984

数据来源: WILEY

摘要:

An explicit result on the quantum Lax pair for the eight‐vertex free‐fermion model with external fields in both directions is exhibited. Its relation to the quantum spectral transform and its corresponding Hamiltonian—theXYmodel with a transverse field—is discussed. The Yang‐Baxter relation is computed, and the equations of motion a

ISSN:0022-2526    

DOI:10.1002/sapm1984702151

年代:1984

数据来源: WILEY

摘要:

The radially symmetric Burgers vortex is an example of a solution to the Navier‐Stokes equations in which the intensification of vorticity due to vortex stretching is balanced by the diffusion of vorticity through viscosity. The linear stability of the symmetric Burgers vortex to a class of two‐dimensional perturbations is demonstrated. Analytical solutions obtained from a perturbation analysis and numerical computations are presented of nonsymmetric Burgers vortices in which the radial flow field in a plane perpendicular to the vorticity is nonsymmet

ISSN:0022-2526    

DOI:10.1002/sapm1984702163

年代:1984

数据来源: WILEY