Advective mixing in a nondivergent barotropic hurricane model 1Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA
2Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371, USA
3Department of Meteorology, Naval Postgraduate School, Monterey, CA 93943-5114, USA
Received: 18 Jun 2009 – Published in Atmos. Chem. Phys. Discuss.: 28 Jul 2009Abstract. 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.
Revised: 29 Nov 2009 – Accepted: 29 Dec 2009 – Published: 20 Jan 2010
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., 10, 475-497, doi:10.5194/acp-10-475-2010, 2010.