### 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 - Jun 25 2007 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics