Advective mixing in a nondivergent barotropic hurricane model

Abstract

Abstract. This paper studies Lagrangian mixing in a twodimensional 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 Rfield gives a time-dependent measure of flux across the shearlines. 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.

Lagrangian coherent structures in tropical cyclone intensification

“…As in previous studies (Rutherford and Dangelmayr, 2010;Rutherford et al, 2010b), the time-variation of fluid velocities along trajectories is small compared to the spatial derivatives, which are included in the terms of A for short integration times. Thus, we use Eq.…”

“…Results from a 2-D barotropic turbulence simulation (Haller and Iacono, 2003) show the role of the hyperbolic component as a transport barrier between vortices. In contrast to the 2-D case of Haller and Iacono (2003) and Rutherford et al (2010b), the matrix A is not upper triangular, and thus Eq. (9) is not solvable unless the flow is integrable.…”

“…While FTLE's are an efficient measure of trajectory separation, they do not differentiate between hyperbolicity and shear (d'Ovidio, 2009). The study of LCSs in sheared flow for a 2-D nondivergent barotropic vortex (Rutherford et al, 2010b) showed that FTLE's were not well suited for rotational flows when the system-scale radial derivative of angular velocity ∂ω/∂r was large. For the experiment used in this study, the shear is small enough so that FTLE-fields show well defined ridges in many cases.…”

“…The method of FTLE's was shown to be robust under approximation errors of the velocity fields (Haller, 2002). Applications to atmospheric flows include Pierrehumbert (1991); Pierrehumbert and Yang (1993); Ngan and Sheperd (1999) Haller and Iacono (2003), and was applied by Rutherford et al (2010b) to detect LCSs in the presence of large-scale shear. The LCSs found move with the dominant vortex Rossby wave structure, a propogating feature that is not simply the result of advection by the flow, but were shown to be robust across time, and were shown to influence the systematic radial transport of fluid particles within the evolving vortex.…”

Lagrangian mixing in an axisymmetric hurricane model

“…In recent work in fluid dynamics, time dependent invariant manifolds, i.e. curves on which particle trajectories remain, have been studied that partition the domain into distinct regions and are visualized as local maxima of Lagrangian stretching fields, Haller (2002), Haller and Poje (1997), Haller and Yuan (2000), Haller (2000), see Rutherford et al (2010) for a recent application to a 2-D hurricane-like vortex model. Most of these studies are for time-varying 2-D velocity fields in closed and bounded domains.…”