Using Lagrangian boundary concepts to investigate environmental interaction of tropical cyclones in vertical shear

A mature tropical cyclone constitutes a strong atmospheric vortex within an environmental background flow. A dividing streamline, separating the area of rotation-dominated flow from the larger scale environment, is a simple fluid dynamical concept for stationary flows. The assumption of stationarity certainly does not hold true in the near environment of a tropical cyclone. The primary transient flow features associated with the tropical cyclone are vortex Rossby waves (VRWs) propagating azimuthally and radially within the potential vorticity gradient wave guide of the tropical cyclone near core region. VRWs arguably manifest in spiral rain bands. We need to apply Lagrangian concepts to investigate the flow boundaries between the environment and the hurricane circulation that are suggested by the simple stationary picture. The existence of such dividing surfaces would have useful implications for our understanding of the interaction of the tropical cyclone with environmental dry or dusty air at middle levels.

Here we hypothesize that Lagrangian boundaries exist between a hurricane and its environment that show basic similarity with the dividing streamline concept. The VRWs and their highly nonlinear filamentary structure, however, give rise to a strong time dependence and partial breaking of this Lagrangian boundary around the vortex. Mixing of environmental air towards the core of the cyclone is thus predominantly accomplished by VRWs.

To explore the concept of Lagrangian boundaries in the environment of a tropical cyclone we perform idealized numerical experiments on an f-plane using a non-hydrostatic mesoscale model. We employ a simple bulk aerodynamic boundary layer scheme in which the surface exchange coefficients of heat and momentum can be prescribed and also 'warm rain' microphysics. The environmental flow consists of unidirectional vertical shear that is imposed on the tropical cyclone after a spin up period. We perform a suite of experiments with varying shear strength.

To begin with, we construct a quasi-stationary flow field by considering the time and height (3-7 km) averaged flow and investigate the streamlines of the storm relative motion. In this stationary picture we find a strong indication of the separation of the environmental flow and the swirling winds of the tropical cyclone. The putative dividing streamline gradually moves closer to the storm center for stronger vertical shear. Stronger shear should thus promote environmental interaction in two ways: by moving the dividing surface closer to the storm's core and by exciting stronger VRW activity, leading to stronger mixing of environmental air towards the core.

In a time varying flow the interaction of the tropical cyclone and the environment generally takes place along the trajectories of individual air parcels. We conclude the presentation by showing more recent results using Lagrangian coherent structure concepts.