Lin, S-J., and R. T. Pierrehumbert, 1988: Does Ekman friction suppress
baroclinic instability? Journal of the Atmospheric Sciences,
45(20), 2920-2933.
Abstract: The effect of Ekman friction on baroclinic instability
is reexamined in order to address questions raised by Farrell concerning
the existence of normal mode instability in the atmosphere. As the degree
of meridional confinement is central to the result, a linearized two-dimensional
(latitude-height) quasi- geostrophic model is used to obviate the arbitrariness
inherent in choosing a channel width in one-dimensional (vertical shear
only) models. The two-dimensional eigenvalue problem was solved by pseudospectral
method using rational Chebyshev expansions in both vertical and meridional
directions. It is concluded that the instability can be eliminated only
by the combination of strong Ekman friction with weak large-scale wind
shear. Estimates of Ekman friction based on a realistic boundary-layer
model indicate that such conditions can prevail over land when the boundary
layer is neutrally stratified. For values of Ekman friction appropriate
to the open ocean, friction can reduce the growth rate of the most unstable
mode by at most a factor of two but cannot eliminate the instability.
By reducing the growth rate and shifting the most unstable mode to lower
zonal wavenumbers, viscous effects make the heat and momentum fluxes of
the most unstable mode deeper and less meridionally confined than in the
inviscid case. Nevertheless, linear theory still underestimates the penetration
depth of the momentum fluxes, as compared to observations and nonlinear
numerical models.