Quasi-wavelet formulations of turbulence and wave scattering

Quasi-wavelets (QWs) are eddy-like entities similar to customary wavelets in the sense that they are based on translations and dilations of a spatially localized parent function. The positions and orientations are, however, normally taken to be random. Random fields such as turbulence may be represented as ensembles of QWs with appropriately selected size distributions, number densities, and amplitudes. This paper overviews previous results concerning QWs and provides a new, QW-based model of anisotropic turbulence in a shear-dominated surface layer. The following points are emphasized. (1) Many types of QWs and couplings, suitable for various applicatons, can be constructed through differentiation of spherically symmetric parent functions. For velocity fluctuations, QWs with toroidal and poloidal circulations can be derived. (2) Self-similar ensembles of QWs with rotation rates scaling according to Kolmogorov’s hypotheses naturally produce classical inertialsubrange spectra. (3) Momentum and heat fluxes in surface-layer turbulence can be described by introducing preferred orientations and correlations among QWs representing temperature and velocity perturbations. (4) In contrast to Fourier modes, QWs can be naturally arranged in a spatially intermittent manner. Models for both local (intrinsic) and global intermittency are discussed. (5) The spatially localized nature of QWs can be advantageous in wave-scattering calculations and other applications.