An infinity of conservation laws of fKdV equation is derived in terms of the Miura and Gardner's transform. The pseudo-mass and energy theorems are studied by the first two conservation laws. As a typical example,...An infinity of conservation laws of fKdV equation is derived in terms of the Miura and Gardner's transform. The pseudo-mass and energy theorems are studied by the first two conservation laws. As a typical example, the theoretical mean wave resistance and the regional distribution of energy of the precursor soliton generation are determined by means of the first and the second conservation laws.展开更多
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
In this study, the moving velocitiy of precursor solitons, of the flow in depressed region, and of the zero-crossing of the trailing wavetrain relative to the moving disturbance for single-layer flow over topography w...In this study, the moving velocitiy of precursor solitons, of the flow in depressed region, and of the zero-crossing of the trailing wavetrain relative to the moving disturbance for single-layer flow over topography were theorecticaly determined in terms of the mass and energy conservation theorems, and were examined with numerical calculations showing good agreement with theoretical results.展开更多
Theoretical mean wave resistance and regional division of the energy of single-layer flow over topogra-phy is studied at the near-resonant region in the weakly nonlinear, long wave limit. The theoretical meanwave resi...Theoretical mean wave resistance and regional division of the energy of single-layer flow over topogra-phy is studied at the near-resonant region in the weakly nonlinear, long wave limit. The theoretical meanwave resistance is determined in terms of the 1st and 2nd conservation laws of the fKdV equation. It isproved by the asymptotic mean method that the theoretical mean wave resistance depends only on the intensityand moving velocity of the topography. The theoretical results of this paper are in good agreement withnumerical calculations. Comparisons between the theoretical and numerical results showed that the theoryof the present paper holds for any small compact topography.展开更多
The resonant flow of an incompressible, inviscid fluid with surface tension on varying bottoms was researched. The effects of different bottoms on the nonlinear surface waves were analyzed. The waterfall plots of the ...The resonant flow of an incompressible, inviscid fluid with surface tension on varying bottoms was researched. The effects of different bottoms on the nonlinear surface waves were analyzed. The waterfall plots of the wave were drawn with Matlab according to the numerical simulation of the fKdV equation with the pseudo-spectral method. From the waterfall plots, the results are obtained as follows： for the convex bottom, the waves system can be viewed as a combination of the effects of forward-step forcing and backwardstep forcing, and these two wave systems respectively radiate upstream and downstream without mutual interaction. Nevertheless, the result for the concave bottom is contrary to the convex one. For some combined bottoms, the wave systems can be considered as the combination of positive forcing and negative forcing.展开更多
In this paper, the resonant generation of nonlinear capillary-gravity waves in a fluid system with the effect of surface tension and the concave topography is examined by using a perturbation method and numerical method.
Hydraulic falls of single-layer now are determined theoretically in terms of a time-dependent averaged fKdV equation(AfKdV equation)in phase coordinate. From the theory of the present paper it was known that differenc...Hydraulic falls of single-layer now are determined theoretically in terms of a time-dependent averaged fKdV equation(AfKdV equation)in phase coordinate. From the theory of the present paper it was known that difference of the asymptotic mean levels upstream and downsream at the subcritical cutoff points is just equal to a subcritical value of the AfKdV equation An experiment is carried out to examine the theoretical results. From comparison between theoreticaland experimental results, it was shown that they are in good agreement.At the same time, it should be pointed out that the theory of the present paper is agreement with the experimental and numerical results of Forbes and can be employed to find the generating properties of the precursor solitons at near-resonance.展开更多
Hydraulic falls and asymptotic mean levels of two-layer flow are determined by means of AfKdV equation in phase coordinate theoretically. By present theory, the hydraulic falls Hf depend on a characteristic value of t...Hydraulic falls and asymptotic mean levels of two-layer flow are determined by means of AfKdV equation in phase coordinate theoretically. By present theory, the hydraulic falls Hf depend on a characteristic value of the MfKdV equation at the subcritical cutoff points It is proved that the differences of the asymptotic mean levels upstream and downstream at the subcritical cutoff points are equal to 2 A relation between and the asymptotic mean levels at the subcritical cutoff points is also found in terms of the solution of the hydraulic falls. Because the AfKdV equation is derived based on the small topography assumption, for semicircular topography the valid region of this theory is α< 0. 35, in which α is radius of the semicircular topography. An experiment is carried out to examine the theory of the present paper. From comparisons between the theoretical and experimental results. it is shown that they are in better agreement. Under conditions of different stratified parameters, the hydraulic falls of two-layer flow are predicted theoretically. This work was supered by the Foundation of the State Education COmmission 'The dynamics of upper ocean'.展开更多
In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries （fKdV） equation, which possesses a great number of excellent properties and is of current importance in physical and engineering ...In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries （fKdV） equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.展开更多
Six physical universals and two general relations in the problem of locally forced precursor soliton generation are found theoretically in terms of the AfKdV equation derived by authors. These six universals and two g...Six physical universals and two general relations in the problem of locally forced precursor soliton generation are found theoretically in terms of the AfKdV equation derived by authors. These six universals and two general relations are examined by experiment and numerical calculation of two-layer flow based on the canonical character of the coefficients of the fKdV equations. From comparisons among the theoretical, numerical and experimental results, it is shown that they are in good agreement. There is not any free parameter in this theory, so the theory of the present paper can be used to predict the wave properties of locally forced precursor soliton generation.展开更多
A universal in tailing wave-train generation of forced soliton generationover topography is found theoretically as the flows are at the resonant points and it is examinedwith the numerical calculation of the correspon...A universal in tailing wave-train generation of forced soliton generationover topography is found theoretically as the flows are at the resonant points and it is examinedwith the numerical calculation of the corresponding fKdV e-quatioa From the comparisons, it is shownthat theoretical and numerical results on the invariance is in good agreement and the theory givenin this paper does not include the modulus truncation, any free constant and unknown function.展开更多
基金This project is supported by the foundation of the State Education Commission "The Dynamics of Upper Ocean" and the open grants of Physical Oceanography Laboratory.
文摘An infinity of conservation laws of fKdV equation is derived in terms of the Miura and Gardner's transform. The pseudo-mass and energy theorems are studied by the first two conservation laws. As a typical example, the theoretical mean wave resistance and the regional distribution of energy of the precursor soliton generation are determined by means of the first and the second conservation laws.
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.
文摘In this study, the moving velocitiy of precursor solitons, of the flow in depressed region, and of the zero-crossing of the trailing wavetrain relative to the moving disturbance for single-layer flow over topography were theorecticaly determined in terms of the mass and energy conservation theorems, and were examined with numerical calculations showing good agreement with theoretical results.
基金This work supported by the Foundation of the State Education Commission" The Dynamics of Upper Ocean" and grants from The Physical Oceanography Laboratory
文摘Theoretical mean wave resistance and regional division of the energy of single-layer flow over topogra-phy is studied at the near-resonant region in the weakly nonlinear, long wave limit. The theoretical meanwave resistance is determined in terms of the 1st and 2nd conservation laws of the fKdV equation. It isproved by the asymptotic mean method that the theoretical mean wave resistance depends only on the intensityand moving velocity of the topography. The theoretical results of this paper are in good agreement withnumerical calculations. Comparisons between the theoretical and numerical results showed that the theoryof the present paper holds for any small compact topography.
基金Project supported by the National Natural Science Foundation of China(No.10272044)the Ph. D. Programs Foundation of Ministry of Education of China(No.20040079004)
文摘The resonant flow of an incompressible, inviscid fluid with surface tension on varying bottoms was researched. The effects of different bottoms on the nonlinear surface waves were analyzed. The waterfall plots of the wave were drawn with Matlab according to the numerical simulation of the fKdV equation with the pseudo-spectral method. From the waterfall plots, the results are obtained as follows： for the convex bottom, the waves system can be viewed as a combination of the effects of forward-step forcing and backwardstep forcing, and these two wave systems respectively radiate upstream and downstream without mutual interaction. Nevertheless, the result for the concave bottom is contrary to the convex one. For some combined bottoms, the wave systems can be considered as the combination of positive forcing and negative forcing.
文摘In this paper, the resonant generation of nonlinear capillary-gravity waves in a fluid system with the effect of surface tension and the concave topography is examined by using a perturbation method and numerical method.
文摘Hydraulic falls of single-layer now are determined theoretically in terms of a time-dependent averaged fKdV equation(AfKdV equation)in phase coordinate. From the theory of the present paper it was known that difference of the asymptotic mean levels upstream and downsream at the subcritical cutoff points is just equal to a subcritical value of the AfKdV equation An experiment is carried out to examine the theoretical results. From comparison between theoreticaland experimental results, it was shown that they are in good agreement.At the same time, it should be pointed out that the theory of the present paper is agreement with the experimental and numerical results of Forbes and can be employed to find the generating properties of the precursor solitons at near-resonance.
文摘Hydraulic falls and asymptotic mean levels of two-layer flow are determined by means of AfKdV equation in phase coordinate theoretically. By present theory, the hydraulic falls Hf depend on a characteristic value of the MfKdV equation at the subcritical cutoff points It is proved that the differences of the asymptotic mean levels upstream and downstream at the subcritical cutoff points are equal to 2 A relation between and the asymptotic mean levels at the subcritical cutoff points is also found in terms of the solution of the hydraulic falls. Because the AfKdV equation is derived based on the small topography assumption, for semicircular topography the valid region of this theory is α< 0. 35, in which α is radius of the semicircular topography. An experiment is carried out to examine the theory of the present paper. From comparisons between the theoretical and experimental results. it is shown that they are in better agreement. Under conditions of different stratified parameters, the hydraulic falls of two-layer flow are predicted theoretically. This work was supered by the Foundation of the State Education COmmission 'The dynamics of upper ocean'.
基金The project supported by the Key Project of the Chinese Ministry of Education under Grant No.106033the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024+2 种基金Chinese Ministry of Education,the National Natural Science Foundation of China under Grant Nos.60772023 and 60372095the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-07-001Beijing University of Aeronautics and Astronautics,and by the National Basic Research Program of China(973 Program)under Grant No.2005CB321901
文摘In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries （fKdV） equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.
基金Project supported by Foundation of the State Education Commission for Teh Dynamics Upper Ocean and grants of Physical Oceanography Laboratory of Ocean University of Qingdao
文摘Six physical universals and two general relations in the problem of locally forced precursor soliton generation are found theoretically in terms of the AfKdV equation derived by authors. These six universals and two general relations are examined by experiment and numerical calculation of two-layer flow based on the canonical character of the coefficients of the fKdV equations. From comparisons among the theoretical, numerical and experimental results, it is shown that they are in good agreement. There is not any free parameter in this theory, so the theory of the present paper can be used to predict the wave properties of locally forced precursor soliton generation.
文摘A universal in tailing wave-train generation of forced soliton generationover topography is found theoretically as the flows are at the resonant points and it is examinedwith the numerical calculation of the corresponding fKdV e-quatioa From the comparisons, it is shownthat theoretical and numerical results on the invariance is in good agreement and the theory givenin this paper does not include the modulus truncation, any free constant and unknown function.
