对同心球间旋转流动的N av ier-S tokes方程谱展开后进行三模态截断,讨论了所得到的类Lorenz型方程组的分歧问题.给出了静态奇异点的条件,并计算出解分支.首先,简要介绍了Lorenz方程组以及用Lorenz截断法讨论非线性问题的意义,其次,推...对同心球间旋转流动的N av ier-S tokes方程谱展开后进行三模态截断,讨论了所得到的类Lorenz型方程组的分歧问题.给出了静态奇异点的条件,并计算出解分支.首先,简要介绍了Lorenz方程组以及用Lorenz截断法讨论非线性问题的意义,其次,推导同心球间旋转流动N av ier-S tokes方程的流函数-涡度形式,最后,讨论同心球间旋转流动的类Lorenz型方程组的分歧问题.展开更多
No error estimate of the spectral Galerkin approximation for the steady-state Navier-Stokes equations was given without assuming that the data of the external force field and the boundary conditions are small enough. ...No error estimate of the spectral Galerkin approximation for the steady-state Navier-Stokes equations was given without assuming that the data of the external force field and the boundary conditions are small enough. In this paper, under the condition that the solutions of the Navier-Stokes equations are nonsingular, we proved the existence and convergence of the spectral Galerkin approkimation solutions and gave the error estimate. At last, this approximation method was applied to simulate the spherical Couette flow.展开更多
The supercritical flow states of the spherical Couette flow between two concentric spheres with the inner sphere rotating are investigated via direct numerical simulation using a three-dimensional finite difference me...The supercritical flow states of the spherical Couette flow between two concentric spheres with the inner sphere rotating are investigated via direct numerical simulation using a three-dimensional finite difference method. For comparison with experiments of Nakabayashi et al. And Wimmer, a narrow gap and a medium gap with clearance ratio β=0.06 and 0.18 respectively areconsidered for the Reynolds number range covering the first Hopfbifurcation point. With adequate initial conditions and temporaryimposition of small wave-type perturbation, multiple periodicflow states with three different pair numbers of spiralTaylor-G{ortler (TG) vortices have been simulated successfullyfor β=0.06, of which the 1-pair and 2-pair of spiral Tgvortices are newly obtained. Three different periodic flow stateswith shear waves, Stuart vortices or wavy outflow boundary, have been obtained for β=0.18. Analysis of the numerical resultsreveals these higher flow modes in terms of fundamental frequency,wave number and spatial structure.展开更多
The steady bifurcation flows in a spherical gap (gap ratio =0.18) with rotating inner and stationary outer spheres are simulated numerically for Reci<Re<1500 1500 by solving steady axisymmetric incompressible Na...The steady bifurcation flows in a spherical gap (gap ratio =0.18) with rotating inner and stationary outer spheres are simulated numerically for Reci<Re<1500 1500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775<Re<1220 and three steady stable flows with 0, 1, or 2 vortices for 1 220<Re<l500. The formation of different flows at the same Reynolds number is related with different initial conditions which can be generated by different accelerations of the inner sphere. Generation of asro-or two-vortex flow depends mainly on the acceleration, but that of one-vortex flow also depends on the perturbation breaking the equatorial symmetry. The mechanism of development of a saddle point in the meridional plane at higher Re number and its role in the formation of two-vortex flow are analy2Ed.展开更多
文摘对同心球间旋转流动的N av ier-S tokes方程谱展开后进行三模态截断,讨论了所得到的类Lorenz型方程组的分歧问题.给出了静态奇异点的条件,并计算出解分支.首先,简要介绍了Lorenz方程组以及用Lorenz截断法讨论非线性问题的意义,其次,推导同心球间旋转流动N av ier-S tokes方程的流函数-涡度形式,最后,讨论同心球间旋转流动的类Lorenz型方程组的分歧问题.
文摘No error estimate of the spectral Galerkin approximation for the steady-state Navier-Stokes equations was given without assuming that the data of the external force field and the boundary conditions are small enough. In this paper, under the condition that the solutions of the Navier-Stokes equations are nonsingular, we proved the existence and convergence of the spectral Galerkin approkimation solutions and gave the error estimate. At last, this approximation method was applied to simulate the spherical Couette flow.
基金This work was supported by the State Key Basic Research Program(Grant No.G1999032801)the National Natural Science Foundation of China(Grant No.10172089).
文摘The supercritical flow states of the spherical Couette flow between two concentric spheres with the inner sphere rotating are investigated via direct numerical simulation using a three-dimensional finite difference method. For comparison with experiments of Nakabayashi et al. And Wimmer, a narrow gap and a medium gap with clearance ratio β=0.06 and 0.18 respectively areconsidered for the Reynolds number range covering the first Hopfbifurcation point. With adequate initial conditions and temporaryimposition of small wave-type perturbation, multiple periodicflow states with three different pair numbers of spiralTaylor-G{ortler (TG) vortices have been simulated successfullyfor β=0.06, of which the 1-pair and 2-pair of spiral Tgvortices are newly obtained. Three different periodic flow stateswith shear waves, Stuart vortices or wavy outflow boundary, have been obtained for β=0.18. Analysis of the numerical resultsreveals these higher flow modes in terms of fundamental frequency,wave number and spatial structure.
基金Project supported by the National Natural Science Foundation of China.
文摘The steady bifurcation flows in a spherical gap (gap ratio =0.18) with rotating inner and stationary outer spheres are simulated numerically for Reci<Re<1500 1500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775<Re<1220 and three steady stable flows with 0, 1, or 2 vortices for 1 220<Re<l500. The formation of different flows at the same Reynolds number is related with different initial conditions which can be generated by different accelerations of the inner sphere. Generation of asro-or two-vortex flow depends mainly on the acceleration, but that of one-vortex flow also depends on the perturbation breaking the equatorial symmetry. The mechanism of development of a saddle point in the meridional plane at higher Re number and its role in the formation of two-vortex flow are analy2Ed.
