Use of Ducting Theory in an Observed Case of Gravity Waves

Abstract

This paper attempts to explain the properties of a gravity wave event observed on Mallorca (Balearic islands) using an array of microbarographs. The waves propagated coherently for a relatively long distance with a speed of about 29 m s?1 and were nondispersive. In the absence of a continuous forcing, long-lived atmospheric gravity waves can only exist if some mechanism prevents the vertical leakage of energy through wave propagation, trapping the gravity wave in a duct layer near the surface. Lindzen and Tung showed the necessary conditions for trapping and discussed the properties of neutral modes for constant stability and wind in the duct. The role of shear in the wind profile near the ground is examined here by first finding three distinct neutral mode types using a matrix eigenvalue method. Applying the wave theory given by Booker and Bretherton, those neutral modes in the sheared duct that have critical levels within the stable duct will be mostly absorbed at their critical level. Therefore, they will be negligible in surface pressure measurements. Another mode type has no critical level and propagates energy away from the duct. On the other hand, neutral modes with a critical level above the top of the duct will be reflected and so will constitute the main signal in the surface observations. This appears to explain observations in Mallorca and shows the significant role of wind shear in selecting the phase speed of the ducted waves.