A five-mode truncation of the Navier-Stokes equations on a three- dimensional torus
type: Item
instance of: scholarly article
title: A five-mode truncation of the Navier-Stokes equations on a three- dimensional torus
zbMATH Open document ID: 0631.76023
DOI: 10.1007/BF00280749
author: Valter Franceschini
author: C. Tebaldi
author: Gabriele Inglese
published in: Computational Mechanics
publication date: 1988-01-01T00:00:00Z
review text: After defining a general N-mode truncation of the three-dimensional Navier-Stokes equations for an incompressible fluid with periodic boundary conditions, a particular 5-mode truncation is considered, with an external force independent of time and acting on one mode only. The truncated system, which originally consists of twenty first order nonlinear differential equations depending on four external parameters, thanks to its peculiar features, can be reduced to only five equations with two parameters, \(\rho\) and \(R_ 2\). The study of this reduced model is performed in deep detail in the case \(\rho =1\), and only roughly for \(\rho\) varying. In the former case a behavior is found which is quite similar to the ones of the Lorenz model and of a 5-mode truncation of the two-dimensional Navier-Stokes equations previously studied.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4027013
zbMATH Keywords: N-mode truncation of the three-dimensional Navier-Stokes equations
zbMATH Keywords: fluid with periodic boundary conditions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4027013