No abstract

This paper is concerned with the theoretical description of long, finite-amplitude waves in the stably stratified lower atmosphere. The time evolution of these waves is governed to first order by the Benjamin-Davis-Ono (BDO) equation when fnctional processes are negligible or by the BDO-Burgers equation when turbulent dissipation is significant. Numerical solutions of both of these model equations are presented for a wide variety of initial conditions ranging from long waves of finite volume to internal deep-fluid bore waves of infinite spatial extent. It is shown that initially smooth long wave disturbances evolve rapidly under ideal homogeneous waveguide conditions into solitary waves of exceptionally large amplitude/The BDO-Burgers equation is found to have highly stable, time-independent, deep-fluid internal bore wave solutions which may be either oscillatory or monotonic depending upon the degree of fnctional dissipation. A number of specific models for the time evolution of long nonlinear atmospheric waves are proposed and discussed in detail. Explicit formulae are given for the wave propagation parameters, surface perturbation pressure, and wind components and these are illustrated for a simple, but realistic, boundary-layer waveguide model. A study has also been made of the influence on nonlinear wave propagation of either spatial or temporal variations in the degree of turbulent dissipation. It is Shown that an increase or decrease in the fnctional damping coefficient, such as might be encountered at a land-sea boundary, can induce a significant variation in the speed of propagation arid a substantial change in the morphology of finite-amplitude boundary layer wave disturbances. Finally, it is shown that wave induced turbulence plays an important role in the evolution of long nonlinear atmospheric waves.

This study is concerned with a fully nonlinear theoretical treatment of internal solitary waves in continuously stratified, incompressible, inviscid, shear-free Boussinesq fluids. Results are presented for wave propagation in both deep and shallow fluids with four different ambient stability profiles. Only the dominant mode with the greatest wave speed is considered. The morphology of finite-amplitude internal solitary waves in Boussinesq fluids is shown to be very sensitive to the precise form of the stability profile. The calculations indicate that a wave of maximum amplitude, which is less than the total fluid depth, exists for all internal solitary waves in continuously stratified Boussinesq fluids of finite depth. There is apparently no upper limit on the amplitude of internal solitary waves in many physically realistic unbounded fluids. Large amplitude waves of this type are mutually similar in form and the morphology of these waves appears to be independent of the ambient stability profile in the waveguide layer. It is shown that the properties of highly nonlinear waves with recirculating flow depend on the density distribution and vorticity of the trapped fluid inside the closed circulation cell. Fluid velocity components associated with the wave motion are evaluated and used to calculate the surface perturbation pressure. The surface perturbation pressure signature for internal solitary waves is found to change with the onset of recirculation from a single-crested profile at small wave amplitudes to a bimodal profile at large wave amplitudes. Results for solitary waves in finite-depth fluids differ from those found for deep fluids in that the surface perturbation pressure at the center of the wave eventually changes sign as wave amplitude increases.

No abstract

No abstract