### 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 language | English (US) |
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Article number | 065502 |

Journal | Journal of Mathematical Physics |

Volume | 48 |

Issue number | 6 |

DOIs | |

State | Published - 2007 |

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### ASJC Scopus subject areas

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

### Cite this

**Transparent boundary conditions as dissipative subgrid closures for the spectral representation of scalar advection by shear flows.** / Oliver, Marcel; Buhler, Oliver.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Transparent boundary conditions as dissipative subgrid closures for the spectral representation of scalar advection by shear flows

AU - Oliver, Marcel

AU - Buhler, Oliver

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

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U2 - 10.1063/1.2668705

DO - 10.1063/1.2668705

M3 - Article

VL - 48

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 6

M1 - 065502

ER -