Based on the indirect Trefftz approach, a wave number method （WNM） is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a s...Based on the indirect Trefftz approach, a wave number method （WNM） is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a set of wave functions, which exactly satisfy the Helmholtz equation. The set of wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions. The unknown coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions. Compared with the boundary element method （BEM）, the WNM have a smaller system matrix, and is applicable to the radiation problems since the wave functions are independent of the domain size. A 3D acoustic cavity is exemplified to show the properties of the method. The results show that the wave number method is more efficient than the BEM, and it is fairly accurate.展开更多
We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on...We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear equations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.展开更多
The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is te...The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is testified clearly. It dominates gradually in nonlinear resonant interactions. As a consequence, the energy cascades to a second plant wave packet which has lower frequencies and higher wavenumbers than that of the primary wave. With the growth of this wave packet, wave breaking occurs and causes strongly nonlinear regime, i.e. stratified turbulence. The strong mixing and intermittent of the turbulence can be learned from the evolution of the total energy and kurtosis of vorticity vs. time. Some statistic properties of the stratified turbulence are also analyzed, including the spectra of KE （kinetic energy） and PE （potential energy）. The results show that the PE spectra display a wavenumber range scaling as 0. 2 N^4ky^-3 （N is the Brunt - Vaisala frequency, k, is the vertical wavenumber）, which is called buoyancy sub-range. However, the KE spectra cannot satisfy the negative cubic law of vertical wavenumber, which have a much larger downtrend than that of the PE spectra, for the potential energy is transferred more efficiently toward small scales than the kinetic energy. The Cox number of diapycnal diffusivity is also calculated, and it shows a good consistency with the observations and deductions in the ocean interior, during the stage of the stratified turbulence maintaining a fairly active level.展开更多
文摘Based on the indirect Trefftz approach, a wave number method （WNM） is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a set of wave functions, which exactly satisfy the Helmholtz equation. The set of wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions. The unknown coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions. Compared with the boundary element method （BEM）, the WNM have a smaller system matrix, and is applicable to the radiation problems since the wave functions are independent of the domain size. A 3D acoustic cavity is exemplified to show the properties of the method. The results show that the wave number method is more efficient than the BEM, and it is fairly accurate.
文摘We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear equations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.
基金The National Nature Science Foundation of China under contract No.40706002the National High Technology Development Project of China under contract No.2007AA09Z122.
文摘The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is testified clearly. It dominates gradually in nonlinear resonant interactions. As a consequence, the energy cascades to a second plant wave packet which has lower frequencies and higher wavenumbers than that of the primary wave. With the growth of this wave packet, wave breaking occurs and causes strongly nonlinear regime, i.e. stratified turbulence. The strong mixing and intermittent of the turbulence can be learned from the evolution of the total energy and kurtosis of vorticity vs. time. Some statistic properties of the stratified turbulence are also analyzed, including the spectra of KE （kinetic energy） and PE （potential energy）. The results show that the PE spectra display a wavenumber range scaling as 0. 2 N^4ky^-3 （N is the Brunt - Vaisala frequency, k, is the vertical wavenumber）, which is called buoyancy sub-range. However, the KE spectra cannot satisfy the negative cubic law of vertical wavenumber, which have a much larger downtrend than that of the PE spectra, for the potential energy is transferred more efficiently toward small scales than the kinetic energy. The Cox number of diapycnal diffusivity is also calculated, and it shows a good consistency with the observations and deductions in the ocean interior, during the stage of the stratified turbulence maintaining a fairly active level.
