Abstract
Abstract. 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 R-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 S-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 (FTLE-field), the Eulerian Q-field, and the angular velocity field. Because of the high shearing, the FTLE-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 FTLE-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 R-field, and their propagation speed indicates that transport across shear-lines is caused by Rossby waves. A radial mixing rate derived from the R-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 R-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 R-field ridges elucidates the role of radial mixing for the interaction and breakdown of the mesovortices shown by the model.
Highlights
Several recent studies (Frank and Ritchie, 1999, 2001; Montgomery et al, 2006; Hendricks and Schubert, 2009) are devoted to the mixing of fluid from different regions of a hurricane, which is considered as a fundamental mechanism that is intimately related to hurricane intensity
Much progress has been made in recent years in the study of Lagrangian mixing in twodimensional incompressible flows (Haller and Poje, 1997; Haller and Yuan, 2000; Haller, 2000, 2001, 2002; Shadden et al, 2005), resulting in a number of different, though related diagnostics, most of which are based on concepts from dynamical systems theory
In order to diagnose hyperbolicity, we exploit the Lagrangian field introduced in Haller and Iacono (2003), in which hyperbolic trajectory splitting is separated from particle separation due to shearing
Summary
Several recent studies (Frank and Ritchie, 1999, 2001; Montgomery et al, 2006; Hendricks and Schubert, 2009) are devoted to the mixing of fluid from different regions of a hurricane, which is considered as a fundamental mechanism that is intimately related to hurricane intensity. While Eulerian measures of mixing can only diagnose instantaneous particle separation, Lagrangian techniques utilize a moving frame approach along trajectories and compute measures for the average separation over a finite integration time This approach is useful in timedependent velocity fields, where trajectories may cross Eulerian streamlines (Dunkerton et al, 2009). The structures are distinct after polygonal eyewall formation, and they persist until the vortex breaks down, in regions where the Okubo-Weiss criterion predicts pools of high separation associated with the formation of pools of high vorticity We note that another approach to diagnosing mixing in the presence of shear is based on subtracting a mean shear from the flow.
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