ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-10-475-2010 Advective mixing in a nondivergent barotropic hurricane model Rutherford B. 1 Dangelmayr G. 1 Persing J. 1 Schubert W. H. 2 Montgomery M. T. 3 Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371, USA Department of Meteorology, Naval Postgraduate School, Monterey, CA 93943-5114, USA 20 01 2010 10 2 475 497 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.atmos-chem-phys.net/10/475/2010/acp-10-475-2010.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/10/475/2010/acp-10-475-2010.pdf

This paper studies Lagrangian mixing in a two-dimensional barotropic model for hurricane-like vortices. Since such flows show high shearing in the radial direction, particle separation across shear-lines is diagnosed through a Lagrangian field, referred to as <i>R</i>-field, that measures trajectory separation orthogonal to the Lagrangian velocity. The shear-lines are identified with the level-contours of another Lagrangian field, referred to as <i>S</i>-field, that measures the average shear-strength along a trajectory. Other fields used for model diagnostics are the Lagrangian field of finite-time Lyapunov exponents (<i>FTLE</i>-field), the Eulerian <i>Q</i>-field, and the angular velocity field. Because of the high shearing, the <i>FTLE</i>-field is not a suitable indicator for advective mixing, and in particular does not exhibit ridges marking the location of finite-time stable and unstable manifolds. The <i>FTLE</i>-field is similar in structure to the radial derivative of the angular velocity. In contrast, persisting ridges and valleys can be clearly recognized in the <i>R</i>-field, and their propagation speed indicates that transport across shear-lines is caused by Rossby waves. A radial mixing rate derived from the <i>R</i>-field gives a time-dependent measure of flux across the shear-lines. On the other hand, a measured mixing rate across the shear-lines, which counts trajectory crossings, confirms the results from the <i>R</i>-field mixing rate, and shows high mixing in the eyewall region after the formation of a polygonal eyewall, which continues until the vortex breaks down. The location of the <i>R</i>-field ridges elucidates the role of radial mixing for the interaction and breakdown of the mesovortices shown by the model.

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