摘要:

This paper is concerned with the propagation of wavelike disturbances in shear flows. The analysis shows that three dimensionality may dominate the evolution process.

ISSN:0022-2526    

DOI:10.1002/sapm19847011

年代:1984

数据来源: WILEY

摘要:

The weakly nonlinear theory of baroclinic wave trains and wave packets is examined by the use of systematic expansion procedures in appropriate powers of a small parameter measuring the supercriticality according to linear theory; well‐known multiple scaling techniques are employed. Crucial importance is ascribed to the magnitude of parameters measuring dissipation and dispersion relative to each other and to the supercriticality, and equations describing the slow evolution in space and time of the wave amplitude are established for a range of parameter values. For vanishingly small dissipation the wave train equations have straightforward oscillatory solutions, dependent on initial conditions, and for large dissipation steady equilibration, independent of initial conditions, is predicted. For moderately small dissipation, however, a wide variety of behaviors is possible—including steady equilibration, single and multiple periodicity, and aperiodicity—in the solutions of the equations, which are recognizable as generalisations of the well‐known Lorenz attractor equations. Equations describing the evolution of wave packets take a variety of forms; for vanishingly small dissipation or for large dissipation, they are essentially parabolic and of nonlinear Schrödinger type, whilst for moderate dissipation they are of Lorenz type, modified by spatial variations. Solutions of a number of these equations are discussed and compared, where appropriate, with experimental

ISSN:0022-2526    

DOI:10.1002/sapm198470121

年代:1984

数据来源: WILEY

摘要:

This work concerns the dynamics of a two‐dimensional (surface) fluid membrane which resists bending in a manner reminiscent of elastic shells. Such bending stiffness can arise from the molecular structure of the membrane, the molecules being treated as “directors” oriented normal to the surface. In this paper we unify the hydrodynamics of a two‐dimensional viscoelastic fluid with the mechanics of an elastic shell in the spirit of a Cosserat continuum. The kinematics of the evolving surface geometry is developed, along with the dynamics of this surface phase, in the time‐dependent, non‐Euclidean metric space of the surface itself. Considerations of linear‐ and angular‐momentum balance lead to an asymmetric surface stress tensor as well as a moment (or couple‐stress) tensor for which a variety of constitutive relations are considered. The antisymmetric component of stress, along with a transverse shear force, couples the membrane bending motion to the surface flow vorticity. The relevance of this theory to the dynamics of coated droplets in general, and to biological cell membranes in particular, is

ISSN:0022-2526    

DOI:10.1002/sapm198470163

年代:1984

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm198470187

年代:1984

数据来源: WILEY