On the Angular Momentum Loss of Tropical Cyclones: An f-Plane Approximation

Abstract

The angular momentum for ideal axisymmetric tropical cyclones on the f-plane is investigated with a focus on the total-volume integrated quantity. Budget analysis of the momentum equation at cylindrical coordinates shows that a tropical cyclone loses angular momentum during its development and mature stages due to the dynamical difference between the viscous inward-flow near the surface and the angular momentum conserving outward-flow aloft. The total relative angular momentum of a tropical cyclone, as a result, can be negative (i.e., implying anticyclonic rotation as a whole) despite intense cyclonic wind in the tropospheric layers. This anticyclonic rotation was measured in terms of the super-rotation ratio, the ratio of total relative angular momentum to the planetary angular momentum. Simulations with the numerical model of Weather Research and Forecasting (WRF) version 3.4.1 was found to be in favor of the theoretical angular-momentum budget analysis. It was revealed in the numerical simulations that the super-rotation ratio was negative, indicating a sub-rotation, as was predicted by analysis. The sub-rotation ratio was found to be less than one percent for typical tropical cyclones. To show the angular momentum decrease even in the decaying stage, numerical simulations where the thermal forcing by sea surface temperature switched off in the mature stage were carried out. In support of the angular momentum budget analysis, the results indicated that the angular momentum also decreases for a while soon after the forcing was eliminated.