# Stochastically generated turbulence with improved kinematic properties

## TL;DR

This paper introduces a stochastic turbulence generator based on vorticity formulation that produces incompressible, divergence-free turbulent fields with enhanced kinematic properties suitable for numerical simulations.

## Contribution

It presents a novel vorticity-based stochastic turbulence generator that ensures incompressibility and allows for additional constraints, improving the realism of generated turbulence fields.

## Key findings

- Generated turbulence fields have improved kinematic properties.
- The method ensures divergence-free vorticity and flow fields.
- Turbulent fields can be integrated into simulations with minimal energy loss.

## Abstract

We present a stochastic turbulence generator based on a vorticity formulation where the generated turbulent field implicitly fulfills the kinematic constraints of an incompressible flow. The generator allows direct access to the turbulent velocity and vorticity field. Enforcing additional constraints such as a divergence-free vorticity field and a specified differentiability of the flow field can also implemented directly within this formulation. The resulting turbulent field contain improved kinematic properties and may be imported into numerical simulations without an excessive loss of energy.