Abstract
Piecewise linear flow profiles are commonly used in quasigeostrophic (QG) stability analyses as idealizations of the smooth profiles found in nature. In such studies the QG potential vorticity (PV) equation is generally solved in layers of uniform PV with solutions matched at interfaces. While such a procedure is formally valid, it will he shown that nearby smooth flow profiles, which the piecewise linear profiles are supposed to represent, violate QG scaling assumptions. A scaling analysis suggests that the maximum vertical curvature in the isentropes consistent with quasigeostrophic theory is O(U/ fL2), where U is the tropospheric scale of the zonal wind, f is the Coriolis parameter, and L is the horizontal length scale. Comparisons are made between the stability characteristics of a piecewise linear flow profile and nearby smooth flows that better satisfy this curvature constraint, and significant qualitative differences are found. The authors conclude that extreme caution must be exercised when using piecewise linear flow profiles in QG stability theory.
