A Preferred Scale for Warm-Core Instability in a Nonconvective Moist Basic State

The existence, scale, and growth rates of subsynoptic-scale warm-core circulations are investigated with a simple parameterization for latent heat release in a nonconvective basic state using a linear two-layer shallow-water model. For a range of baroclinic flows from moderate to high Richardson number, conditionally stable lapse rates approaching saturated adiabats consistently yield the most unstable modes with a warm-core structure and a Rossby number O(1), with higher Rossby numbers stabilized. This compares to the corresponding most unstable modes for the dry cases that have cold-core structures and Rossby numbers O(10 ) or in the quasigeostrophic range. The maximum growth rates of 0.45 of the Coriolis parameter are an order of magnitude greater than those for the corresponding most unstable dry modes. Because the Rossby number of the most unstable mode for nearly saturated conditions is virtually independent of Richardson number, the preferred scale of these warm-core modes varies directly with the mean vertical shear for a given static stability. This scale relation suggests that the requirement to maintain nearly saturated conditions on horizontal scales sufficient for development can be met more easily on the preferred subsynoptic horizontal scales associated with weak vertical shear. Conversely, the lack of instability for higher Rossby numbers implies that stronger vertical shears stabilize smaller subsynoptic regions that are destabilized for weaker vertical shears. This has implications for the scale and existence of warm-core circulations in the tropics, such as those assumed a priori in wind-induced surface heat exchange (WISHE).