The generalized Ekman model for the tropical cyclone boundary layer revisited: The myth of inertial stability as a restoring force

We revisit the linear boundary-layer approximation that expresses a generalized Ekman balance and use it to clarify a range of interpretations in the previous literature on the tropical cyclone boundary layer. Some of these interpretations relate to the reasons for inflow in the boundary layer and others relate to the presumed effects of inertial stability on boundary-layer dynamics. Inertial stability has been invoked, for example, to explain aspects of boundary-layer behaviour, including the frontogenetic nature of the boundary layer and its relationship to vortex spin-up. Our analysis exposes the fallacy of invoking inertial stability as a resistance to radial inflow in the boundary layer. The analysis shows also that the nonlinear acceleration terms become comparable to the linear Coriolis acceleration terms in relatively narrow vortices that are inertially stable above the boundary layer. Estimates of the nonlinear accelerations using the linear solutions are expected to underestimate the actual contribution in a nonlinear boundary-layer model, cautioning against neglecting the nonlinear terms in diagnostic or prognostic models