Tropical Cyclogenesis

Tropical cyclogenesis is the transition from a cloud cluster to a tropical cyclone (TC). Prior to the transition, the cloud cluster can last for days with little change in its characteristics. Thus, one can claim that the cloud cluster is in a quasi-equilibrium state. After the transition, the tropical cyclone can also last for days without changing its basic characteristics. Hence, one can identify the tropical cyclone as a quasi-equilibrium state as well.

Tropical cyclogenesis typically takes only about two or three days. Relative to the duration of either the cloud cluster or the TC, this transition period is very short. Tropical cyclogenesis occurs when the cloud cluster (quasi-equilibrium) state can no longer be sustained (a spontaneous catastrophe) or when a trigger acts on a cloud cluster (a triggered catastrophe). A spontaneous tropical cycloge-nesis must be associated with a certain condition being met; in a triggered tropical cycloge-nesis this condition is very nearly being met. Although the precise details of this condition are still unknown, it is generally associated with what is already known: SST higher than 26.5°C, low background vertical wind shear, and a sufficiently high Coriolis parameter (Chap. 15 of Palmen and Newton, 1969). When the condition is met, all cloud clusters can turn into TC's. It is well known that a series of TC's often occur concurrently. Through these identified characteristics — two quasi-equilibrium states and the rapid transition between the two, etc., — tropical cyclogenesis clearly can be identified as a catastrophe.

It is heuristic to construct a schematic diagram similar to Fig. 3 for understanding the catastrophic nature of tropical cyclogenesis. One can use the 3D mass-weighted average temperature in the core region (e.g. within a 30 km radius) of a disturbance minus that of the environment — i.e. the degree of warming of the core region — as the gross state variable S. Curve A represents the diabatic heating — which is mostly cumulus heating — in the core region. Curve B is the adiabatic cooling due to upward motion in the same region. Assuming that the thermal balance is mainly between A and B, A-B is zero at both quasi-equilibria: the cloud cluster and the TC. Figure 4(a) shows A-B at the moment the cloud cluster loses its equilibrium status. A-B is zero at both the cloud cluster quasi-equilibrium and the TC quasi-equilibria. As shown in Fig. 4(a) at the moment the cloud cluster loses it equilibrium status, A-B does not cross the abscissa at the cloud cluster quasi-equilibrium Si but only touches it tangentially. A-B crosses zero at the TC quasi-equilibrium S3, which is a stable quasi-equilibrium, since a perturbation away from this quasi-equilibrium will be reduced by A-B to zero. The positive value of A-B on the left side of the TC quasi-equilibrium S3 ensures that the state starting from the cloud cluster status will move to the TC status.

Curve B can be roughly represented by a straight line through the origin. This is because a disturbance with a higher core temperature has a stronger meridional circulation, which implies stronger adiabatic cooling in the core region. As a result of these considerations, A and B at the moment of the cloud cluster's losing its quasi-equilibrium status can be represented as in Fig. 4(b). Before that moment, the picture is as depicted in Fig. 4(c). In this figure, the cloud cluster corresponds to S1 and the TC S3. S2 is an unstable quasi-equilibrium. As the boundary conditions change (e.g. the

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