Abstract
The effects of finite-amplitude disturbances and nonlinear lower boundary in the leewave problem are discussed as an initial value problem by separating both governing equation system and lower boundary condition into linear and nonlinear forms.
Physical relations among the four cases, i.e. combinations of two equation systems (linear and nonlinear forms) and two boundary conditions (linear and nonlinear forms), are discussed. The nonlinear interactions between the disturbances and the mountain are found to cause the following effects on the flow: (1) weakening of the approaching flow in the lowest layer ahead of the mountain, (2) generation of the strong wind zone near the level of the mountain crest, (3) intensification of the downslope winds and (4) extension of the strong winds far downstream in the lowest layer. These strong winds are associated with weak wind zone, where an S-shaped or closed circulation pattern develops. Such features are obtained also when the waves are not so strongly resonant (when the amplitudes of the resonance leewaves are relatively small). These nonlinear effects become enhanced when the mountain height is increased beyond the critical value for the overturning instability. It is stressed that how to include a finiteness of the mountain is essentially important to simulate such nonlinear phenomena. Our experiments are compared with the analytical solutions by Long (1955). This paper is a supplement to the paper by Furukawa (1973).
