SEMISPECTRAL MODELS OF HURRICANE MOTION AND
INTENSIFICATION.
Principal Investigator:
H. E. Willoughby
Collaborating scientist(s):
R. W. Jones
Objectives: To evaluate the roles of spectral truncation, domain size and baroclinicity in
hurricane motion using a semispectral model and, more generally, to evaluate the power of the
semispectral vortex tracking (SSVT) formulation to improve physical understanding and
modeling of tropical cyclones.
Rationale: Hurricanes have an essentially cylindrical geometry. Conventional Lagrangian
grid-point.numerical models, cast in fixed Cartesian coordinates, spend a great deal of
computational effort on an advective representation of the terms in the gradient balance equation
and on the essentially linear, though formally nolinear, process of translating the vortex through
a rectangular mesh. True nonlinearity enters the problem only through wave-wave and
wave-mean flow interactions. In SSVT models, the fully nonlinear equations are reduced to a set
of linear equations coupled by nonlinear interactions. The primary circulation is a gradient
balance vortex. It evolves slowly in response to the secondary circulation forced by diabatic
heating, friction, and wave-mean flow interactions. SSVT models thus isolate the genuinely
nonlinear aspects of the problem from the apparent nonlinearities that arise from the awkward
choice of fixed Cartesian coordinates. Nevertheless, the transformation to moving,
vortex-centered coordinates is conceptually and numerically demanding, and is not clear how
domain size, spectral truncation, and baroclinicity affect the solutions.
Method: Testing of a nonlinear SVT model with various domain sizes, spectral truncations,
direct forcing of higher wavenumbers, and various environmental flows. Development of a two
layer, shallow water baroclinic SVT model.
Accomplishment: Testing of a barotropic SSVT model for different domain sizes (Fig. 1)
and spectral truncations (Fig. 2) in a still environment and in uniform and shearing
environmental flows on a beta plane shows that it is generally insensitive to domain size or
spectral truncation. The only exception occurs in a cyclonically sheared environment where
wave energy transferred to wavenumber two cascades to higher and lower wavenumbers causing
substantial scatter in the endpoints of the simulated track after 240h. Generally, truncation at
azimuthal wavenumber six on a 4000 km domain produces convergence of the 10-day track
endpoints to within a few kilometers. Even more severe spectral truncation, say at wavenumber
4, would probably not limit forecast accuracy for 72--84 h durations. The results of Montgomery
et al. (1998), which appear to contradict the present calculations, may stem from improper
treatment of moving coordinates. Direct forcing of higher wavenumbers can lead to a nonlinear
cascade of wave energy to wavenumber one resulting in chaotic cycloidal oscillation of the
vortex track.
Key references:
Montgomery, M. T., J. D. Moller, and C. T. Nicklas, 1998: Linear and Nonlinear Vortex Motion
in an Asymmetric Balance Shallow Water Model. J. Atmos. Sci., 55, (in press).
Willoughby, H. E. and R. W. Jones, 1998: Nonlinear motion of a barotropic vortex in an
environmental zonal flow. J. Atmos. Sci., 55, (in press).
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