- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Statistical Properties of the Navier-Stokes-Voigt Model
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Statistical Properties of the Navier-Stokes-Voigt Model Titi, Edriss
Description
The Navier-Stokes-Voigt model of viscoelastic incompressible fluid has been proposed as a regularization of the three-dimensional Navier-Stokes equations for the purpose of direct numerical simulations. Besides the kinematic viscosity parameter, $\nu>0$, this model possesses a regularizing parameter, $\alpha> 0$, a given length scale parameter, so that $\frac{\alpha^2}{\nu}$ is the relaxation time of the viscoelastic fluid. In this talk I will derive several statistical properties of the invariant measures associated with the solutions of the three-dimensional Navier-Stokes-Voigt equations. Moreover, I will show that, for fixed viscosity, $\nu>0$, as the regularizing parameter $\alpha$ tends to zero, there exists a subsequence of probability invariant measures converging, in a suitable sense, to a strong stationary statistical solution of the three-dimensional Navier-Stokes equations, which is a regularized version of the notion of stationary statistical solutions - a generalization of the concept of invariant measure introduced and investigated by Foias. This fact is also supported by numerical observations, which provides an additional evidence that, for small values of the regularization parameter $\alpha$, the Navier-Stokes-Voigt model can indeed be considered as a model to study the statistical properties of the three-dimensional Navier-Stokes equations and turbulent flows via direct numerical simulations.
Item Metadata
Title |
Statistical Properties of the Navier-Stokes-Voigt Model
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2020-11-27T10:00
|
Description |
The Navier-Stokes-Voigt model of
viscoelastic incompressible fluid has been proposed as a
regularization of the three-dimensional Navier-Stokes equations for
the purpose of direct numerical simulations. Besides the kinematic
viscosity parameter, $\nu>0$, this model possesses a regularizing
parameter, $\alpha> 0$, a given length scale parameter, so that
$\frac{\alpha^2}{\nu}$ is the relaxation time of the viscoelastic
fluid. In this talk I will derive several statistical properties of
the invariant measures associated with the solutions of the
three-dimensional Navier-Stokes-Voigt equations. Moreover, I will show
that, for fixed viscosity, $\nu>0$, as the regularizing parameter
$\alpha$ tends to zero, there exists a subsequence of probability
invariant measures converging, in a suitable sense, to a strong
stationary statistical solution of the three-dimensional
Navier-Stokes equations, which is a regularized version of the
notion of stationary statistical solutions - a generalization of the
concept of invariant measure introduced and investigated by Foias.
This fact is also supported by numerical observations, which provides an
additional evidence that, for small values of the regularization
parameter $\alpha$, the Navier-Stokes-Voigt model can indeed be
considered as a model to study the statistical properties of the
three-dimensional Navier-Stokes equations and turbulent flows via
direct numerical simulations.
|
Extent |
25.0 minutes
|
Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: Texas A&M University
|
Series | |
Date Available |
2021-06-18
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0398463
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Faculty
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International