On the balance of forces and radial accelerations in hurricanes

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Abstract
The degree to which the gradient or cyclostrophic wind equation is applicable for hurricane winds above the surface friction layer is tested on 10 levels in four hurricanes (8 different days) in which aircraft of the National Hurricane Research Project of the United States Weather Bureau flew radial leg penetrations during the 1957–58 seasons. All 10 levels flown were between 6,000 and 16,000 ft altitude and each level had six or more radial leg penetrations except one that had five. Application of the cylindrical radial equation of motion is made for the constant‐pressure levels flown. Results show that there is lack of radial balance by a wide margin between pressure gradient, centrifugal and Coriolis forces. Evaluation of the local and advective changes of the substantial derivative only partly makes up for this lack of balance. It is therefore necessary to postulate the existence of internal radial friction, both in an instantaneous fixed‐coordinate system and in one that moves with the storm centre. This residual radial friction averages 25 to 30 per cent of the pressure‐gradient force. As a consequence, the gradient wind equation in both cyclindrical and in natural coordinates is invalid. Also, steady‐state or deepening hurricanes must have stronger pressure gradients than corresponding centrifugal and Coriolis accelerations. Comments on the possible mechanism for this internal friction are given.

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