Relation between pressure defect and maximum wind in the field of a tropical cyclone - theoretical derivation of proportionality constant based on an idealised surface pressure model

Abstract

The surface pressure defect ΔP and the surface maximum wind speed Vm of a tropical cyclone which are two important measures for the intensity of a tropical cyclone are related by the well known relation Vm =K√ ΔP where K is the proportionality constant. Based on composites of observations of Vm and ΔP within the cyclone field, the empirical values of K have been derived in a large number of studies. The value of K thus derived has been found to vary in the range 10.5-16.0 when Vm and ΔP are measured in knots and hPa respectively. In this study the problem of estimating the value of K has been approached and treated from an entirely different angle. A general idealised pressure model derived using the concept of Pearson's Distributions in Statistical Distribution Theory has been initially assumed. Based on a few logical and acceptable assumptions such as - validity of cyclostrophic balance near the centre of the cyclone, existence of radius of maximum pressure gradient, convergence of integral defining cumulative surface pressure drop, relative vorticity to remain positive up to some distance from the centre, absolute vorticity to remain always positive within the cyclone field - the ranges of variables defining the general pressure model, and hence for K, have been derived without in any way relying upon actual observations of Vm or ΔP. After incorporating frictional forces, environmental flow and force due to translation speed of a tropical cyclone, the final value of K has been derived as 11.0. This theoretically estimated K value compared very well with the empirically derived values but was slightly on the lower side. Apparently most of the empirical K values derived in other studies generated overestimated Vm values for given ΔP and this aspect has been discussed.