摘要:

This study is concerned with long internal gravity waves in a stratified fluid contained between rigid horizontal boundaries. For a general stratification, long waves of finite amplitude will tend to distort, and no permanent wave shape will result. In certain important cases, however, steady waveforms are found to be possible. The properties of such waves are investigated, and their relationship to the solutions provided by the weakly nonlinear theory is studied.

ISSN:0022-2526    

DOI:10.1002/sapm1978593187

年代:1978

数据来源: WILEY

摘要:

We give a complete analysis of the long‐wave–short‐wave resonance equations which appear in fluid mechanics as well as plasma physics. Using the inverse‐scattering technique, these equations can be reduced to a pair of linear integral equations (Marchenko equations), with theN‐soliton solutions intimately related to the asymptotic state of the evolution equations. The interaction of solitons and the conserved quantities are

ISSN:0022-2526    

DOI:10.1002/sapm1978593201

年代:1978

数据来源: WILEY

摘要:

A closed three layer fluid with small density differences between the layers has two closely related modes of gravity wave propagation. The nonlinear interactions between the wave modes are investigated, particularly the nearly resonant or significant interactions. Permanent wave solutions are calculated, and it is shown that a permanent wave of the slower mode can generate resonantly a wave harmonic of the faster mode. The equations governing resonant triads of the two modes are derived, and solutions having a permanent structure are calculated from them. It is found that some resonant triad solutions vanish when the triad is embedded in the set of all harmonics with wavenumbers in its neighborhood

ISSN:0022-2526    

DOI:10.1002/sapm1978593223

年代:1978

数据来源: WILEY

摘要:

Consider the question: When can the edges in a pair of Hamiltonian circuits be redistributed to form another pair of circuits with the same union and intersection? A class of pairs is exhibited which intersect in two edges and cannot be rearranged in this way. A connection to algorithms for the traveling salesman problem is explained using the convex polytope of Hamiltonian circuits in . The exhibited pair is shown to be an edge of that polytope.

ISSN:0022-2526    

DOI:10.1002/sapm1978593245

年代:1978

数据来源: WILEY

摘要:

A method of quadratic forms for eigenvalue bounds described in an earlier paper is developed and extended. In particular it is shown how restrictions upon eigenvalues may be found for a class of linear partial differential equations whose coefficients depend on one space variable and which are also periodic in time. An application is made to the problem of linear stability of periodic helical flows in a pipe. It is shown that the motion is stable if a criterion of the formis satisfied. Ωn(r) is the Fourier coefficient of thenth harmonic of the periodic angular velocity Ω(r), andWn(r) is the corresponding coefficient of the axial velocity.bis the radius of the pipe, andR0is about 4.4. Stronger but less simple results are possible. Bounds for steady inviscid flows are also give

ISSN:0022-2526    

DOI:10.1002/sapm1978593249

年代:1978

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1978593283

年代:1978

数据来源: WILEY