### Abstract

We have examined the transient critical-level effect for internal gravity waves produced by thermal forcing in a stably stratified shear flow. For this, we have solved analytically the equations governing small-amplitude perturbations in a two-dimensional, hydrostatic, nonrotating, inviscid, and Boussinesq flow system. In the case of the point pulse forcing, there is only one transient critical-level line at any time and every internal gravity wave passing through the critical level is attenuated by a factor of e ^{-πμ}[μ = ( Ri - 1/4)^{1/2}, Ri: Richardson number (=N^{2}/α^{2}, where N is the buoyancy frequency and α the vertical shear of the basic-state horizontal velocity)]. In the case of the line-type pulse forcing (bell-shaped in the horizontal), there are an infinite number of transient critical-level lines at any time. The attenuation factor for internal gravity waves is a function of space and time. This is because internal gravity waves passing through any point at any time coasist of internal gravity waves which have already experienced the transient critical-level effect and those which have not experienced the effect yet.

Original language | English |
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Pages (from-to) | 238-240 |

Number of pages | 3 |

Journal | Physics of Fluids |

Volume | 11 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1999 Jan |

### All Science Journal Classification (ASJC) codes

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes

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## Cite this

*Physics of Fluids*,

*11*(1), 238-240. https://doi.org/10.1063/1.869916