## Abstract

Using a novel numerical method at unprecedented resolution, we demonstrate that structures of small to intermediate scale in rotating, stratified flows are intrinsically three-dimensional. Such flows are characterized by vortices (spinning volumes of fluid), regions of large vorticity gradients, and filamentary structures at all scales. It is found that such structures have predominantly three-dimensional dynamics below a horizontal scale L approximate to 1/2 L-R, where L-R is the so-called Rossby radius of deformation, equal to the characteristic vertical scale of the fluid H divided by the ratio of the rotational and buoyancy frequencies f/N. The breakdown of two-dimensional dynamics at these scales is attributed to the so-called "tall-column instability" [D. G. Dritschel and M. de la Torre Juarez, J. Fluid, Mech. 328, 129 (1996)], which is active on columnar vortices that are tall after scaling by f/N, or, equivalently, that are narrow compared with L-R. Moreover, this instability eventually leads to a simple relationship between typical vertical and horizontal scales: for each vertical wave number (apart from the vertically averaged, barotropic component of the flow) the average horizontal wave number is equal to f/N times the vertical wave number. The practical implication is that three-dimensional modeling is essential to capture the behavior of rotating, stratified fluids, Two-dimensional models are not valid fur scales below L-R. (C) 1999 American Institute of Physics. [S1070-6631(99)02405-8].

Original language | English |
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Pages (from-to) | 1512-1520 |

Number of pages | 9 |

Journal | Physics of Fluids |

Volume | 11 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 1999 |

## Keywords

- 2-DIMENSIONAL VORTEX INTERACTIONS
- QUASI-GEOSTROPHIC TURBULENCE
- CONTOUR DYNAMICS
- FLUID
- STRATOSPHERE
- INSTABILITY
- EQUATIONS
- MOTION