In this paper,the Cauchy problem for the two layer viscous shallow water equations is investigated with third-order surface-tension terms and a low regularity assumption on the initial data.The global existence and un...In this paper,the Cauchy problem for the two layer viscous shallow water equations is investigated with third-order surface-tension terms and a low regularity assumption on the initial data.The global existence and uniqueness of the strong solution in a hybrid Besov space are proved by using the Littlewood-Paley decomposition and Friedrichs'regularization method.展开更多
This paper is devoted to the analysis of the two-layer shallow-water equations representing gravity currents. A similarity technique which is the characteristic function method is applied for this study. The applicati...This paper is devoted to the analysis of the two-layer shallow-water equations representing gravity currents. A similarity technique which is the characteristic function method is applied for this study. The application of the characteristic function method makes it possible to obtain the similarity forms depending on a group of infinitesimal transformations. Thus, the number of independent variables is reduced by one and the governing partial differential equations with the auxiliary conditions reduce to a system of ordinary differential equations with the appropriate auxiliary conditions. Numeric solutions are presented and discussed.展开更多
A series of experiments is conducted to study shallow-water flow in the wake of a sine shaped island. Digital particle imaging velocimetry (DPIV) is used to measure velocities in the turbulent wake behind a sine shap...A series of experiments is conducted to study shallow-water flow in the wake of a sine shaped island. Digital particle imaging velocimetry (DPIV) is used to measure velocities in the turbulent wake behind a sine shaped island for different characteristic coefficients S. Flow streamlines are given for the wake flows. The measured results show that the characteristic coefficient S is uniquely related to the flow pattern around a sine shaped island in a shallow water layer. An S value of approximately 0.20 is the critical value for transition from a vortex street to unsteady flow and a value of approximately 0.40 is the critical value for transition from unsteady flow to steady flow.展开更多
基金the NSFC(11571046,11671225)the ISF-NSFC joint research program NSFC(11761141008)the BJNSF(1182004)。
文摘In this paper,the Cauchy problem for the two layer viscous shallow water equations is investigated with third-order surface-tension terms and a low regularity assumption on the initial data.The global existence and uniqueness of the strong solution in a hybrid Besov space are proved by using the Littlewood-Paley decomposition and Friedrichs'regularization method.
文摘This paper is devoted to the analysis of the two-layer shallow-water equations representing gravity currents. A similarity technique which is the characteristic function method is applied for this study. The application of the characteristic function method makes it possible to obtain the similarity forms depending on a group of infinitesimal transformations. Thus, the number of independent variables is reduced by one and the governing partial differential equations with the auxiliary conditions reduce to a system of ordinary differential equations with the appropriate auxiliary conditions. Numeric solutions are presented and discussed.
基金Supported by the National Natural Science Foundationof China (No. 5 96 790 2 3) and the Post- DoctoralFoundation of China
文摘A series of experiments is conducted to study shallow-water flow in the wake of a sine shaped island. Digital particle imaging velocimetry (DPIV) is used to measure velocities in the turbulent wake behind a sine shaped island for different characteristic coefficients S. Flow streamlines are given for the wake flows. The measured results show that the characteristic coefficient S is uniquely related to the flow pattern around a sine shaped island in a shallow water layer. An S value of approximately 0.20 is the critical value for transition from a vortex street to unsteady flow and a value of approximately 0.40 is the critical value for transition from unsteady flow to steady flow.
