TL;DR
This paper explores the application of ultrametric analysis and wavelet theory to turbulence, providing explicit solutions for nonlinear ultrametric equations using a hierarchical cascade approach.
Contribution
It introduces a novel ultrametric framework for turbulence modeling and constructs explicit solutions for nonlinear ultrametric integral equations.
Findings
Explicit solutions for nonlinear ultrametric equations derived
Hierarchical procedure analogous to turbulence cascade models developed
Links ultrametric analysis with turbulence theory established
Abstract
Relation of ultrametric analysis, wavelet theory and cascade models of turbulence is discussed. We construct the explicit solutions for the nonlinear ultrametric integral equation with quadratic nonlinearity. These solutions are built by means of the recurrent hierarchical procedure which is analogous to the procedure used for the cascade models of turbulence.
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