Quasi-wavelet Models of Turbulent Temperature Fluctuations

Here, we contribute to the continuing development of the quasi-wavelet (QW) model of turbulence that is currently being used in simulations of sound propagation and scattering in the turbulent atmosphere. We show that a QW model of temperature fluctuations exists for any physically reasonable temperature spectrum of isotropic homogeneous turbulence, including the widely used von Kármán spectrum. We derive a simple formula for the QW shape that reproduces a given spectrum exactly in the energy, transition, and inertial subranges. We also show that simple QW shapes can be normalized to yield an analytic expression for a temperature spectrum that is fairly close to any given spectrum. As an example, we match the Gaussian QW model to the von Kármán spectrum as closely as possible, and find remarkably good agreement in all subranges including the dissipation subrange. We also derive formulae for the variance and kurtosis associated with the QW model, and show how the latter depends on the QW packing fraction and size distribution. We also illustrate how the visual appearance of several QW-simulated temperature fluctuation fields depends on the QW packing fraction, size distribution, and kurtosis.