Asymptotic probability density functions in turbulence

TL;DR

This paper introduces a formalism to derive closed-form evolution equations for the asymptotic probability density functions of turbulence magnitudes, applicable to a wide range of problems in turbulence analysis.

Contribution

The paper presents a general formalism for obtaining evolution equations of asymptotic PDFs in turbulence, adaptable to various problems and validated against known cases.

Findings

Formalism yields correct results in well-known turbulence problems.

Applicable to generic evolution equations in turbulence.

Provides a systematic way to study turbulence magnitude distributions.

Abstract

A formalism is presented to obtain closed evolution equations for asymptotic probability distribution functions of turbulence magnitudes. The formalism is derived for a generic evolution equation, so that the final result can be easily applied to rather general problems. Although the approximation involved cannot be ascertained a priori, we show that application of the formalism to well known problems gives the correct results.