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The weakly nonlinear regime of single mode ablative Rayleigh–Taylor instability is studied, with consideration of preheat effect and the width of the ablation front. The Rayleigh–Taylor linear growth rate agrees well with the direct numerical simulation. For the density perturbation, the amplitude distribution of the fundamental mode has one peak value whereas those of the second and third harmonics have two and three peak values, respectively. Harmonics generation versus wave number is also given and it is close to the result of direct numerical simulation.

The compressible Rayleigh–Taylor instability of accelerated ablation front is analysed in consideration of the preheat effects, and the corresponding eigen-problem is solved numerically using the fourth-order accurate two-point compact difference scheme. Both the growth rate and perturbation profiles are obtained, and the obtained growth rate is close to the results of direct numerical simulation. Our results show that the growth rate is more reduced and the cutoff wave length becomes longer as preheat increases.

Through temporal mode direct numerical simulation, flow field database of a fully developed turbulent boundary layer on a flat plate with Mach number 4.5 and Reynolds number Re θ =1094 has been obtained. Commonly used detection methods in experiments are applied to detecting coherent structures in the flow field, and it is found that coherent structures do exist in the wall region of a supersonic turbulent boundary layer. The detected results show that a low-speed streak is detected by using the Mu-level method, the rising parts of this streak are detected by using the second quadrant method, and the crossing regions from a low-speed streak to the high-speed one are detected by using the VITA method respectively. Notwithstanding that different regions are detected by different methods, they are all accompanied by quasi-stream-wise vortex structures.

Physical argument shows that eddy viscosity is essentially different from molecular viscosity. By direct numerical simulation, it was shown that for periodic turbulent flows, there is phase difference between Reynolds stress and rate of strain. This finding posed great challenge to turbulence modeling, because most turbulence modeling, which use the idea of eddy viscosity, do not take this effect into account.

In this paper, several mathematical models for the large scale structures in some special kinds of mixing layers, which might be practically useful for enhancing the mixing, are proposed. First, the linear growth rate of the large scale structures in the mixing layers was calculated. Then, using the much improved weakly non-linear theory, combined with the energy method, the non-linear evolution of large scale structures in two special mixing layer configurations is calculated. One of the mixing layers has equal magnitudes of the upstream velocity vectors, while the angles between the velocity vectors and the trailing edge were π/2-φ and π/2+φ, respectively. The other mixing layer was generated by a splitter-plate with a 45-degree-sweep trailing edge.

Numerical simulations have been done for a compressible mixing layer, in which the inflow speed on the low speed side was made to have periodic undulations, so as to see if this method could enhance the mixing effect of the layer. Systematic computations for a 2-D compressible mixing layer with Mach number M e = 0.6 have been done, and the results showed that the proposed method was indeed effective in enhancing the mixing.

One of the key problems in the nonlinear theory of the hydrodynamic stability is to determine the law of the evolution of the disturbance velocity amplitude. The methods, which have been obtained, can only be used for quasi-neutral flow and have some artificial factors. In this paper, a method is proposed for this problem.

In this paper, the formation of the coherent structures in the wall region of a turbulent boundary layer was studied, using the nonlinear theory of the hydrodynamic stability. The spanwise and streamwise wavelengths of the most amplified unstable wave obtained by this study were found in good agreement with the experiments, which makes the distinct feature of this study in the present paper, as the basis of the stability analysis, a more rational velocity profile has been used, which is different from that of the turbulent mean flow. And also, the new nonlinear theory was used. The result is useful in understanding of the quasi-periodicity of the coherent structure in the turbulent boundary layer.

A model is proposed for the problem of 'receptivity' of the boundary layer of a flat plate to the free-stream turbulence. The basic idea is that two harmonic components of the turbulent velocity spectrum may generate Tollmien-Schlichting waves in the boundary layer through nonlinear interaction. The numerical calculations based on this model show that Tollmien-Schlichting waves can actually be generated and the amplitudes may have the same order of magnitude as the disturbance amplitude in the free stream, at least for certain ranges of the Reynolds number, wavenumber and frequency.