Texture and fractal methods for analyzing the characteristics of unsteady gas flows in pipelines

Turbulent structures in two-dimensional model gas flows are analyzed by estimating the fractal dimension and the texture characteristics of the gas flows. The fractal dimension is estimated using the self-similarity indices of the power spectra for the following characteristics of the gas flows: the Coriolis and Boussinesq coefficients, average pressure, hydraulic resistance coefficient, velocity loss in a pipeline element, and curvature of the gas flow. The texture characteristics are calculated using the following texture indices: energy, entropy, inertia coefficient, uniformity coefficient, cluster excess coefficient, cluster asymmetry coefficient, and also information measure of cluster correlation. Computer experiments show that, in propagation of a shock wave, the wavelet spectra of the indices of the model gas flows contain a large number of self-similar figures, which is indicative of a hierarchical structure and a fractal character of the model gas flows.