Towards understanding the dynamics of spin up in Emanuel's tropical cyclone model

Abstract

We seek to understand the mechanisms of vortex spin up in Emanuel’s 2012 axisymmetric theory for tropical-cyclone intensification in physical coordinates, starting from first principles. It is noted that, while spin up must occur in the friction layer, this spin up is unconstrained by a radial momentum equation in this layer. Rather, the spin up in this layer is constrained by a parameterization of turbulent mixing in the upper troposphere. It is shown that the inclusion of a nonlinear radial momentum equation into the theory using the assumed geometry of the Emanuel model (i.e. the assumption of a well-mixed boundary layer in terms of specific entropy and absolute angular momentum to leading order, together with the assumption that the absolute angular momentum is continuous at the top of this layer) strongly constrains the vortex evolution. If, for example, the initial radial inflow and its radial derivative are not too large in magnitude, then the boundary layer dynamics would damp this inflow and would lead to outflow just above it so that the vortex would ultimately spin down. The physics of how upper-tropospheric mixing leads to spin up in the boundary layer are unclear and, as discussed, may be irrelevant to spin up in Emanuel’s model.