Statistics in a Backscatter Eddy Viscosity Turbulence Model

TL;DR

This paper improves a backscatter eddy viscosity turbulence model by proving solution existence, ensuring energy dissipation matches input, and proposing parameter ranges, addressing key limitations of previous models.

Contribution

It introduces a mathematically rigorous analysis of the Baldwin-Lomax model with backscatter, ensuring realistic energy dissipation and providing parameter guidelines.

Findings

Proved existence and uniqueness of global weak solutions.

Demonstrated energy dissipation aligns with energy input.

Proposed parameter ranges for the model.

Abstract

This paper addresses two significant drawbacks of an eddy viscosity turbulence model: the issue of excessive dissipation relative to energy input and the lack of a universal parameter specification. Considering the Baldwin-Lomax model with backscatter effects, we first prove the existence and uniqueness of global weak solutions under mild conditions. Our next result shows that this model maintains energy dissipation rates consistent with energy input, thereby avoiding over-dissipation and aligning with K41 phenomenology. Additionally, we propose a range for the model's parameters.