Transparent boundary conditions as dissipative subgrid closures for the spectral representation of scalar advection by shear flows

Marcel Oliver, Oliver Buhler

Research output: Contribution to journalArticle

Abstract

We consider the evolution of a passive scalar in a shear flow in its representation as a system of lattice differential equations in wave number space. When the velocity field has small support, the interaction in wave number space is local and can be studied in terms of dispersive linear lattice waves. We close the restriction of the system to a finite set of wave numbers by implementing transparent boundary conditions for lattice waves. This closure is studied numerically in terms of energy dissipation rate and energy spectrum, both for a time-independent velocity field and for a time-dependent synthetic velocity field whose Fourier coefficients follow independent Ornstein-Uhlenbeck stochastic processes.

Original languageEnglish (US)
Article number065502
JournalJournal of Mathematical Physics
Volume48
Issue number6
DOIs
StatePublished - 2007

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Transparent Boundary Conditions
Spectral Representation
Shear Flow
Advection
advection
shear flow
closures
Closure
Scalar
boundary conditions
scalars
Velocity Field
velocity distribution
Lattice Differential Equations
Passive Scalar
Ornstein-Uhlenbeck Process
stochastic processes
Energy Dissipation
Fourier coefficients
Energy Spectrum

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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