摘要:

Galerkin (spectral) methods are explored for the numerical simulation of incompressible flows within simple boundaries. A major part of the paper is devoted to the development of transform methods for efficient simulation of flows in box geometries with periodic and free‐slip boundary conditions. Techniques for incorporating known symmetries and invariances into transform methods are illustrated for the Taylor‐Green vortex. Galerkin methods for accurate and efficient representation of rigid no‐slip boundary conditions are also explained. A class of pseudospectral approximations is introduced in order to handle more complicated dynamical interactions in more complicated geometries. Later papers in this series will demonstrate the important advantages of spectral methods over finite‐difference methods for simulation of many of the flows of current interest and will present specific numerical results for various transition and turbulen

ISSN:0022-2526    

DOI:10.1002/sapm1971504293

年代:1971

数据来源: WILEY

摘要:

Previous theories for the slow dispersion of singly periodic and multiply periodic nonlinear wavetrains are applied to various examples. Stability of the solution with respect to large scale variations and possible shocks in the wave properties (frequency, wavenumber, and amplitude) are discussed. The general approach is also used to analyze certain aperiodic waves.

ISSN:0022-2526    

DOI:10.1002/sapm1971504329

年代:1971

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1971504345

年代:1971

数据来源: WILEY

摘要:

The hypothesis is made that the vorticity distribution in a field of random two‐dimensional vorticity (two‐dimensional turbulence) develops discontinuities. The energy spectrum is then calculated and shown to behave likek−4for large values of the wave‐numberk. The rates of decay of mean square vorticity and velocity are estimated. An expression for the growth of length scale is obtained and it is noted that the size of turbulent trailing vortices is apparently well fitted by the

ISSN:0022-2526    

DOI:10.1002/sapm1971504377

年代:1971

数据来源: WILEY

摘要:

It is proved that there exist lattices in any dimension such that the grand partition function of the corresponding repulsive lattice gas has all the zeros in the fugacity on the negative real axis. The argument also furnishes a new proof of the Lee‐Yang circle theore

ISSN:0022-2526    

DOI:10.1002/sapm1971504385

年代:1971

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1971504391

年代:1971

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1971504395

年代:1971

数据来源: WILEY