2-D "Poor Man's Navier-Stokes Equation" Model of Turbulent Flows

This research is part of an ongoing effort to construct "synthetic velocity" subgrid-scale (SGS) models using discrete dynamical systems (DDSs) for use in large-eddy simulations of turbulent flows. Here we will outline the derivation of the two-dimensional (2-D) "Poor Man's Navier–Stokes" (PMNS) equation from the 2-D, incompressible Navier–Stokes equation to be used in such models and report results from subsequent numerical investigations. In our results emphasis is placed on the effects of initial conditions on the dynamics of the 2-D PMNS equation, using such modes of investigation as regime maps, basins of attraction diagrams, phase portraits, time series and power spectra. The most important findings of this investigation concern applicable ranges of bifurcation parameters, causes and effects of symmetries seen in solutions of the PMNS equation, and the suitability of the methods of investigation used here.

Download Full-text

Navier-Stokes equation

Physics Subject Headings (PhySH) ◽

10.29172/a3ff37a7-c0a4-48a9-a32f-0dbc060c2746 ◽

2018 ◽

Keyword(s):

Stokes Equation ◽

Navier Stokes ◽

Navier Stokes Equation

Download Full-text

6 Navier–Stokes equation in 2D and 3D

Critical Parabolic-Type Problems ◽

10.1515/9783110599831-006 ◽

2020 ◽

pp. 141-158

Keyword(s):

Stokes Equation ◽

Navier Stokes ◽

Navier Stokes Equation ◽

2D And 3D

Download Full-text

Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

Computer Physics Communications ◽

10.1016/s0010-4655(98)00113-1 ◽

1998 ◽

Vol 115 (1) ◽

pp. 18-24 ◽

Cited By ~ 22

Author(s):

G.W. Wei ◽

D.S. Zhang ◽

S.C. Althorpe ◽

D.J. Kouri ◽

D.K. Hoffman

Keyword(s):

Stokes Equation ◽

Functional Method ◽

Navier Stokes ◽

Navier Stokes Equation

Download Full-text

Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽

10.3390/sym13020288 ◽

2021 ◽

Vol 13 (2) ◽

pp. 288

Author(s):

Alexei Kushner ◽

Valentin Lychagin

Keyword(s):

Carbon Dioxide ◽

Internal Structure ◽

Stokes Equation ◽

Hydrogen Cyanide ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equation ◽

Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

Download Full-text