# Randomly stirred perfect gas

## TL;DR

This paper develops a stochastic differential equation framework for analyzing energy transfer in randomly stirred perfect gases, proposing a new model for polytropic fluids that improves upon previous isothermal models.

## Contribution

It introduces a renormalizable model for randomly stirred polytropic fluids, providing a more accurate description of perfect gases under stochastic stirring.

## Key findings

- Steady cascade energy transfer is compatible with hydrodynamic equations.
- The stress tensor structure is characterized in arbitrary dimensions.
- A new model for stirred perfect gas is proposed and justified.

## Abstract

Foundations of the analysis of scaling in randomly stirred compressible fluid with the aid of stochastic differential equations are discussed in the example of perfect gas. The structure of the stress tensor with nonnegative shear and bulk viscosities is determined in $d$-dimensional space. It is argued that the steady cascade picture of energy transfer is compatible with generic hydrodynamic equations. A renormalizable model of randomly stirred polytropic fluid is put forward and it is shown that this model should be used for description of randomly stirred perfect gas instead of the model of 'isothermal' fluid.