Advective mixing in a nondivergent barotropic hurricane model B. Rutherford^{1}, G. Dangelmayr^{1}, J. Persing^{1}, W. H. Schubert^{2}, and M. T. Montgomery^{3} ^{1}Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA ^{2}Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371, USA ^{3}Department of Meteorology, Naval Postgraduate School, Monterey, CA 93943-5114, USA

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 clear 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, distinct and 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.

Citation: Rutherford, B., Dangelmayr, G., Persing, J., Schubert, W. H., and Montgomery, M. T.: Advective mixing in a nondivergent barotropic hurricane model, Atmos. Chem. Phys. Discuss., 9, 16085-16129, doi:10.5194/acpd-9-16085-2009, 2009.