HEAT SOURCE-INFLUENCED FINITE AMPLITUDE ULTRALONG WAVE

Discussed in this paper is finite amplitude ultralong wave under the influence of heat sources.The conditions are first investigated for the existence of periodic and solitary ultralong waves of finite amplitude in the Burger model with the aid of Hamilton function and variation of total energy and then the wave analytical expression is formulated by means of the functional approximation and the Hamilton function as the motion invariant in nature.Results show that the finite amplitude ultralong wave influenced by heat sources is unlikely to generate a solitary wave solution and im- poses no constraints on horizontal divergence as opposed to the case with the effect of heat sources available.

Three－dimensional Global Scale Permanent－wave Solutions of the Nonlinear Quasigeostrophic Potential Vorticity Equation and Energy Dispersion

The three-dimensional nonlinear quasi-geostrophic potential vorticity equation is reduced to a linear form in the stream function in spherical coordinates for the permanent wave solutions consisting of zonal wavenumbers from 0 to n and rn vertical components with a given degree n.This equation is solved by treating the coefficient of the Coriolis parameter square in the equation as the eigenvalue both for sinusoidal and hyperbolic variations in vertical direction. It is found that these solutions can represent the observed long term flow patterns at the surface and aloft over the globe closely. In addition, the sinusoidal vertical solutions with large eigenvalue G are trapped in low latitude,and the scales of these trapped modes are longer than 10 deg. lat. even for the top layer of the ocean and hence they are much larger than that given by the equatorial β-plane solutions.Therefore such baroclinic disturbances in the ocean can easily interact with those in the atmosphere.Solutions of the shallow water potential vorticity equation are treated in a similar manner but with the effective depth H=RT/g taken as limited within a small range for the atmosphere.The propagation of the flow energy of the wave packet consisting of more than one degree is found to be along the great circle around the globe both for barotropic and for baroclinic flows in the atmosphere.

Some studies on mechanics of continuous mediums viewed as differential manifolds

The continuous mediums are divided into two kinds according to their geometrical configurations,the first one is related to Euclidian manifolds and the other one to Riemannian manifolds/surfaces in the point of view of the modern geometry.Two kinds of finite deformation theories with respect to Euclidian and Riemannian manifolds have been developed in the present paper.Both kinds of theories include the definitions of initial and current physical and parametric configurations,deformation gradient tensors with properties,deformation descriptions,transport theories and governing equations of nature conservation laws.The essential property of the theory with respect to Euclidian manifolds is that the curvilinear coordinates corresponding to the current physical configurations include time explicitly through which the geometrically irregular and time varying physical configurations can be mapped in the diffeomorphism manner to the regular and fixed domains in the parametric space.It is quite essential to the study of the relationships between geometries and mechanics.The theory with respect to Riemannian manifolds provides the systemic ideas and methods to study the deformations of continuous mediums whose geometrical configurations can be considered as general surfaces.The essential property of the theory with respect to Riemannian manifolds is that the thickness variation of a patch of continuous medium is represented by the surface density and its governing equation is rigorously deduced.As some applications,wakes of cylinders with deformable boundaries on the plane,incompressible wakes of a circular cylinder on fixed surfaces and axisymmetric finite deformations of an elastic membrane are numerically studied.