A SCALAR 3-DIMENSIONAL SPECTRAL MODEL WITH VARIABLE ANISOTROPY

This paper introduces a simple three-dimensional (3-D) spectral model for scalar fluctuations with variable anisotropy. This heuristic model is useful in the study of statistical properties of stably stratified flows. It goes a step further than existing analogues by explicitly t aking into account variation of anisotropy with the size of the fluctu ations. The spectral model is specified by its isovalue surfaces and b y its generalized energy spectrum. These surfaces are ellipsoids, (var iably) elongated in the vertical direction. The model depends on two a rbitrary functions of the spectral parameter. The possibilities of suc h var table anisotropy models are demonstrated by choosing specific fu nctions. The choice was guided by maximal simplicity requirement and b y the ''tradition'' of turbulent studies which heavily uses ''power la w'' functions. These examples show how quantitative predictions are ob tained using such 3-D spectral models. They were selected in order to display characteristics that depend explicitly on the variable anisotr opy and that could not have been obtained with previous models. The fi rst example is the calculation of the one-dimensional spectrum of temp erature for arbitrary direction of measurement and the natural predict ion of a change in slope for quasi-horizontal spectra, while the obliq ue and vertical spectra retain the same slope. The second example is t o account for radar echo aspect sensitivity, with angular contrast dep ending on the radar wavelength. The main advantages of the present mod el are its great flexibility provided by the use of two arbitrary func tions and also the (relative) simplicity of its mathematical formulati on.