Energy stability analysis of turbulent incompressible flow based on the triple decomposition of the velocity gradient tensor

06/21/2021
by   Johan Hoffman, et al.
0

In the context of flow visualization a triple decomposition of the velocity gradient was proposed by Kolat in 2007 who demonstrated the technique in two dimensions, which was later realized in three dimensions by Nagata et al. in 2020. The triple decomposition opens for a refined energy stability analysis of the Navier-Stokes equations, with implications for the mathematical analysis of the structure, computability and regularity of turbulent flow. We here perform an energy stability analysis of turbulent incompressible flow, which suggests a scenario where any exponentially unstable irrotational flow structures rapidly evolve towards linearly unstable shear flow and stable rigid body rotational flow, which dissipates to heat. In contrast to worst case energy stability estimates, this refined stability analysis reflects the existence of stable flow structures in turbulence over extended time, and the robustness of average quantities.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

12/01/2020

Convergence analysis of a fully discrete energy-stable numerical scheme for the Q-tensor flow of liquid crystals

We present a fully discrete convergent finite difference scheme for the ...
07/02/2019

A mixed discontinuous Galerkin method with symmetric stress for Brinkman problem based on the velocity-pseudostress formulation

The Brinkman equations can be regarded as a combination of the Stokes an...
01/23/2020

Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow

The two-step time discretization proposed by Dahlquist, Liniger and Neva...
10/09/2017

On Variants of Network Flow Stability

We present a variant of the stable flow problem. Instead of the traditio...
09/30/2020

Stability analysis of a singlerate and multirate predictor-corrector scheme for overlapping grids

We use matrix stability analysis for a singlerate and multirate predicto...
01/21/2022

Numerical Analysis of A MODIFIED SMAGORINSKY MODEL

The classical Smagorinsky model's solution is an approximation to a (res...
10/19/2005

First-Order Modeling and Stability Analysis of Illusory Contours

In visual cognition, illusions help elucidate certain intriguing latent ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.