Quasi-wavelet formulations of turbulence with intermittency and correlated field properties

Quasi-wavelets (QWs) are similar to customary wavelets in that they are based on translations and dilations of a parent function; however, their positions and orientations are random. In previous research [G. H. Goedecke, V. E. Ostashev, D. K. Wilson, and H. J. Auvermann, Boundary-Layer Meteorology 112, 33–56, 2004], it was shown that a random field of QWs, with size distribution and rotation rates chosen in a manner consistent with Kolmogorov's hypothesis, lead to velocity fields with realistic spectral properties including all three characteristic subranges. In this paper, the QW approach is extended in two main ways that are particularly difficult to achieve with synthesis methods based on Fourier modes: (1) intermittency is incorporated through a multifractal formulation similar to U. Frisch et al [J. Fluid Mech. 87, 719-736, 1978] and (2) multiple QW fields with correlated properties are described. These extensions make possible the synthesis of wind and temperature fields in the surface layer that have very realistic cross spectral and intermittent properties. We also discuss how the number density (packing) of the QWs is related to higher-order statistics of the turbulence fields, such as the kurtosis. Packing fractions must be approximately one or greater to obtain kurtosis close to the Gaussian value of 3.