The Multi-Scale Structure of Roll Vortices in Hurricane BoundaryLayers

Even though the surface enthalpy flux for hurricanes over the ocean
can be enormous, the extreme near-surface wind shear results in
nearly-neutral stratification. These conditions are ideal for the
formation of approximately wind-aligned boundary layer roll
vortices. However, it wasn't until 1998 that the nearly ubiquitous
prevalence of hurricane boundary layer rolls was documented by Wurman
and Winslow using the Doppler on Wheels radar. Their observations were
dominated by rolls with sub-km wavelengths. Later studies documented
frequent hurricane boundary layer rolls with characteristic
wavelengths of 1 to 4 km. However, rolls at these scales were not as
consistently observed as the sub-km rolls. One study suggested that
these intermediate scale rolls interacted with rolls that had sub-km
wavelengths. Hints of O(10 km) roll wavelengths were found in the
upper boundary layer/lower troposphere portion of hurricanes. Most
recently, the signature of such large wavelength rolls have been
documented in synthetic aperture radar (SAR) images of the sea surface
under hurricanes. Furthermore, the signature of the typically 1 to 4 km
rolls are routinely used in the calculation of surface wind vectors
from SAR images of hurricanes.

The clear suggestion from observations is that the hurricane boundary
layer is characterized by roll vortices at small, intermediate and
large wavelengths. Since these rolls make an important non-local
contribution to the fluxes of momentum and enthalpy across the
boundary layer, we must explore the complex nonlinear dynamics of
this organized part of the turbulent hurricane boundary layer.

Standard (single-mode) roll theory is based on the nonlinear
equilibration of mixed shear/convective instabilities of the mean
boundary layer state. The predicted structure induces an additive
non-gradient flux over the local down-gradient fluxes. The selection
optimizes the strength of the nonlinear circulation against
dissipation. These models clearly show that both the O(10 km) and
sub-km rolls would not be expected to play an important nonlinear role
the hurricane PBL dynamics.

Single-mode instability models omit the important process of
inter-scale transfer of energy. The simplest model of this transfer
process is associated with resonant wave-vector triads. We use a
low-order model of this interaction to explore the reasons why sub-km
and O(10 km) rolls are prevalent and often more evident than the
predicted-to-be dominant intermediate scale rolls, which in fact
appear to be somewhat less common. We show that super-exponential
'algebraic' growth allows the sub-km modes to interact with the
intermediate scale modes and transfer energy into the largest scale
modes. Unlike single-mode theory, there is no a priori selection
mechanism. However, we find that realistic results appear to be
associated with maximizing the downward transfer of momentum across
the hurricane boundary layer.