There are three main problems in the weakly nonlinear theory of hydrodynamic stability:(1)The ra- dius of convergence with respect to the perturbation parameter is too small and there is no concrete estimation for it....There are three main problems in the weakly nonlinear theory of hydrodynamic stability:(1)The ra- dius of convergence with respect to the perturbation parameter is too small and there is no concrete estimation for it.(2)The solution has a special structure, thus in general, it can not satisfy the initial condition posed by many practical problems.(3) When the linear part of its solution does not correspond to a neutral case. there are more than one way in determining the Landau constants, and practically no one knows which is the best way. In this paper, problems(1)and(2)are solved theoretically, and ways for its improvement have been proposed. By comparing the theoretical results with those obtained by numerical simulations, problem(3)has also been clari- fied.展开更多
The weakly nonlinear theory has been widely applied in the problem of hydrodynamic stability and also in other fields. However, although its application has been successful for some problems, yet, for other problems, ...The weakly nonlinear theory has been widely applied in the problem of hydrodynamic stability and also in other fields. However, although its application has been successful for some problems, yet, for other problems, the results obtainedhre not satisfactory, especially for problems like transition or the evolution of the vortex in the free shear flow, for which the goal of the theoretical investigation is not seeking for a steady state, but predicting an evolutional process. In this paper, we shall examine the reason for the unsuccessfulness and suggest ways for its amendment.展开更多
The problems of the weakly nonlinear theory of hydrodynamic stability has been re addressed; namely, (i) why is the radius of convergence of its solution too small? (ii) it is not appropriate to use it to deal with th...The problems of the weakly nonlinear theory of hydrodynamic stability has been re addressed; namely, (i) why is the radius of convergence of its solution too small? (ii) it is not appropriate to use it to deal with the evolution problem of disturbances; the main reason is that the way of calculating the mean flow distortion is inappropriate, (iii) it cannot be used to deal with the initial value problem. Ways of its improvement were proposed. Its correctness was confirmed by its comparison with the results of numerical simulations.展开更多
The weakly nonlinear theory has been widely applied to the problems of hydrodynamic stability and other fields in the last three decades, but only few theoretical results have been proved to be quantitatively consiste...The weakly nonlinear theory has been widely applied to the problems of hydrodynamic stability and other fields in the last three decades, but only few theoretical results have been proved to be quantitatively consistent with the experimental observations. The main reason lies in the fact that the way of calculating the mean flow modification is dubious, making the theoretical predictions, in general, not very satisfactory. A correct way is proposed in this paper, which can yield results comparable with those obtained by numerical simulation.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘There are three main problems in the weakly nonlinear theory of hydrodynamic stability:(1)The ra- dius of convergence with respect to the perturbation parameter is too small and there is no concrete estimation for it.(2)The solution has a special structure, thus in general, it can not satisfy the initial condition posed by many practical problems.(3) When the linear part of its solution does not correspond to a neutral case. there are more than one way in determining the Landau constants, and practically no one knows which is the best way. In this paper, problems(1)and(2)are solved theoretically, and ways for its improvement have been proposed. By comparing the theoretical results with those obtained by numerical simulations, problem(3)has also been clari- fied.
基金Dedicated to the Tenth Anniversary and One Hundred Numbers of AMM(Ⅲ)The Project Supported by the NNSF of China
文摘The weakly nonlinear theory has been widely applied in the problem of hydrodynamic stability and also in other fields. However, although its application has been successful for some problems, yet, for other problems, the results obtainedhre not satisfactory, especially for problems like transition or the evolution of the vortex in the free shear flow, for which the goal of the theoretical investigation is not seeking for a steady state, but predicting an evolutional process. In this paper, we shall examine the reason for the unsuccessfulness and suggest ways for its amendment.
文摘The problems of the weakly nonlinear theory of hydrodynamic stability has been re addressed; namely, (i) why is the radius of convergence of its solution too small? (ii) it is not appropriate to use it to deal with the evolution problem of disturbances; the main reason is that the way of calculating the mean flow distortion is inappropriate, (iii) it cannot be used to deal with the initial value problem. Ways of its improvement were proposed. Its correctness was confirmed by its comparison with the results of numerical simulations.
基金Project supported by the National Natural Science Foundation of China
文摘The weakly nonlinear theory has been widely applied to the problems of hydrodynamic stability and other fields in the last three decades, but only few theoretical results have been proved to be quantitatively consistent with the experimental observations. The main reason lies in the fact that the way of calculating the mean flow modification is dubious, making the theoretical predictions, in general, not very satisfactory. A correct way is proposed in this paper, which can yield results comparable with those obtained by numerical simulation.
