An fKdV equation of two-layer how and an averaged fKdV equation (AfKdV equation) with respect to phase are derived to determine the theoretical amplitude and period of the precursor solitons in the present paper. In t...An fKdV equation of two-layer how and an averaged fKdV equation (AfKdV equation) with respect to phase are derived to determine the theoretical amplitude and period of the precursor solitons in the present paper. In terms of the AfKdV equation derived by the authors, a new theory on the precursor soliton generation based on Lee et al.'s concept is presented. Concepts of asymptotic mean hydraulic fall and level are introduced in our analysis, and the theoretical amplitude and period both depend on the asymptotic mi-an levels and stratified parameters. From the present theoretical results, it is obtained that when the moving velocity of the topography is at the resonant points, there exist two general relations: (1) amplitude relation (A) over circle = 2F, (2) period relation <(tau)over circle> = -8m(1)m(3)(-1)root 6m(4)m(3)(-1)F, in which (A) over circle and <(tau)over circle> are the amplitude and period of the precursor solitons at the resonant points respectively, m(1), m(3) and m(4) are coefficients of the fKdV equation, and F is asymptotic mean half-hydraulic fall at subcritical cutoff points. The theoretical results of this paper are compared with experiments and numerical calculations of two-layer flow over a semicircular topography and all these results are in good agreement. Due to the canonical character of the coefficients of fKdV equations, this theory also holds for any two-dimensional system, which can be reduced to fKdV equations.展开更多
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 soliton...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 how, the velocities of the precursor soliton generation are also predicted in terms of the present theoretical results.展开更多
基金The project supported by the foundation of The State Education Commission"The dynamics of upper ocean"the open grants of Physical Oceanography Laboratory
文摘An fKdV equation of two-layer how and an averaged fKdV equation (AfKdV equation) with respect to phase are derived to determine the theoretical amplitude and period of the precursor solitons in the present paper. In terms of the AfKdV equation derived by the authors, a new theory on the precursor soliton generation based on Lee et al.'s concept is presented. Concepts of asymptotic mean hydraulic fall and level are introduced in our analysis, and the theoretical amplitude and period both depend on the asymptotic mi-an levels and stratified parameters. From the present theoretical results, it is obtained that when the moving velocity of the topography is at the resonant points, there exist two general relations: (1) amplitude relation (A) over circle = 2F, (2) period relation <(tau)over circle> = -8m(1)m(3)(-1)root 6m(4)m(3)(-1)F, in which (A) over circle and <(tau)over circle> are the amplitude and period of the precursor solitons at the resonant points respectively, m(1), m(3) and m(4) are coefficients of the fKdV equation, and F is asymptotic mean half-hydraulic fall at subcritical cutoff points. The theoretical results of this paper are compared with experiments and numerical calculations of two-layer flow over a semicircular topography and all these results are in good agreement. Due to the canonical character of the coefficients of fKdV equations, this theory also holds for any two-dimensional system, which can be reduced to fKdV equations.
基金The project supported by the National Natural Science Foundation of China under the Grant No.49776284
文摘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 how, the velocities of the precursor soliton generation are also predicted in terms of the present theoretical results.
