On the solutions of Navier-Stokes equations for turbulent channel flows in a particular function class

TL;DR

This paper investigates specific non-stationary solutions of the Navier-Stokes and Navier-Stokes-alpha models for turbulent channel flows, focusing on solutions with particular functional forms and harmonic pressure-potential sums.

Contribution

It extends previous work by analyzing non-stationary solutions with special function classes and harmonic properties in turbulent channel flows.

Findings

Pressure and potential sum to a harmonic function in space.

Identification of particular solution classes for Navier-Stokes models.

Insights into the structure of turbulent channel flow solutions.

Abstract

In this paper, we continue the discussion as done in \cite{CTZ15} on turbulent channel flow described by the Navier-Stokes model and the Navier-Stokes-alpha model. We study the non-stationary solutions for the Navier-Stokes equations and Navier-Stokes-$\alpha$ model having particular function forms. In particular, the term of sum of pressure and potential can be shown to be harmonic in the space variable.