Theoretical Criteria for the Occurrence of Turbulence in Burger's Equation

TL;DR

This paper investigates the onset of turbulence in fluid flows by analyzing Burger's equation in one and two dimensions, providing mathematical support for existing conjectures on turbulence criteria.

Contribution

It offers a theoretical analysis of Burger's equation to illustrate and support conjectures about turbulence onset criteria in fluid dynamics.

Findings

Supports conjectures on turbulence criteria through mathematical solutions

Demonstrates criteria arise from solutions of Burger's equation

Provides a theoretical foundation for turbulence onset conditions

Abstract

Throughout the history of the study of turbulence in fluid dynamics, there has yet to arise a unique definition or theoretical criterion for this important phenomenon. There have been interesting conjectures made by Ruelle [2], Muriel [3], and Getreuer, Albano and Muriel [6], however, attempting to provide the sufficient criteria for the onset of turbulence. In this paper, a classic equation in fluid dynamics, Burger's equation, is solved in one and two dimensions, and these conjectures are illustrated. This illustration supports these conjectures by showing that the proposed criteria do arise mathematically from the solutions of an equation modelling fluid flows.