中文摘要：

Wavelet analysis is applied to the results obtained by the direct nu-merical simulation of a three-dimensional (3D) mixing layer in order to investigatecoherent structures in dimension of scale. First, 3D orthonormal wavelet bases areconstructed, and the corresponding decomposition algorithm is developed. Then theNavier-Stokes equations are transformed into the wavelet space and the architecturefor multi-scale analysis is established. From this architecture, the coarse field imagesin different scales are obtained and some local statistical quantities are calculated.The results show that, with the development of a mixing layer, the energy spectrumdensities for different wavenumbers increase and the energy is transferred from theaverage flow to vortex structures in different scales. Due to the non-linear interactionsbetween different scales, cascade processes of energy are very complex. Because vor-tices always roll and pair at special areas, for a definite scale, the energy is obtainedfrom other scales at some areas while it is transferred to other scales at other areas.In addition, energy dissipation and transfer always occur where an intense interactionbetween vortices exists.

英文摘要：

Wavelet analysis is applied to the results obtained by the direct numerical simulation of a three-dimensional (3D) mixing layer in order to investigate coherent structures in dimension of scale. First, 3D orthonormal wavelet bases are constructed, and the corresponding decomposition algorithm is developed. Then the Navier-Stokes equations are transformed into the wavelet space and the architecture for multi-scale analysis is established. From this architecture, the coarse field images in different scales are obtained and some local statistical quantities are calculated. The results show that, with the development of a mixing layer, the energy spectrum densities for different wavenumbers increase and the energy is transferred from the average flow to vortex structures in different scales. Due to the non-linear interactions between different scales, cascade processes of energy are very complex. Because vortices always roll and pair at special areas, for a definite scale, the energy is obtained from other scales at some areas while it is transferred to other scales at other areas. In addition, energy dissipation and transfer always occur where an intense interaction between vortices exists.