Abstract
AbstractWe 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.
Highlights
The surface boundary layer of a tropical cyclone is known to have a strong control on the evolution of the vortex (e.g., Braun and Tao, 2000; Nolan et al, 2009a; 2009b; Smith and Thomsen, 2010; Kilroy et al, 2016 and the review by Montgomery and Smith, 2017)
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
Summary
The surface boundary layer of a tropical cyclone is known to have a strong control on the evolution of the vortex (e.g., Braun and Tao, 2000; Nolan et al, 2009a; 2009b; Smith and Thomsen, 2010; Kilroy et al, 2016 and the review by Montgomery and Smith, 2017). According to the foregoing view, the evaporation of water from the underlying ocean supports a nonlinear spin-up mechanism wherein the development of supergradient winds in the boundary layer of the vortex, in combination with the upward transport of absolute angular momentum from the boundary layer, plays an essential role in the intensification of the storm’s eyewall cloud. The scale analysis developed in that study was extended to the more general linear case by Vogl and Smith (2009) and the self-consistency of the linear approximation was investigated in the tropical cyclone context These authors examined the extent to which the accuracy of the linear approximation depends on the profile of the imposed tangential wind field at the top of the boundary layer. The concept of inertial stability has been called upon by numerous authors, including three early landmark studies of the boundary layer itself, by Shapiro (1983), Kepert (2001), Kepert and Wang (2001), in the more recent study by Kepert (2017), as well as explanations for convergence in the boundary layer as part of an explanation for the physics of tropical cyclone intensification by Emanuel (2018)
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