Moving velocities of precursor soliton generation in two-layer flow

Abstract

Based on the AfKdV equation of Xu et al.^[1], a theory on the velocities of the precursor soliton generation in two-layer flow over topography is presented in the present paper. Moving velocities of precursor solitons, of the first zero-crossing of the tailing wavetrain and of the flow behind the topography are found theoretically. It is shown that for a given topography, when its moving velocities are at the resonant points, we have the following rules: the ratio of the moving velocity of the precursor solitons to that of the first zero-crossing of the tailing wavetrain equals −4/3. At the same time, the ratio of the width of generating region of the precursor solitons to that of the depressed water region equals also −4/3. The theoretical results are examined by means of numerical calculation. The comparison between the theoretical and numerical results are found in good agreement. For different stratified parameters of two-layer flow, the velocities of the precursor soliton generation are also predicted in terms of the present theoretical results.