BAMOS Sep 2020

Charitha Pattiaratchi Oceans Graduate School and The UWA Oceans Institute , The University of Western Australia Email : chari . pattiaratchi @ uwa . edu . au

Introduction

Resonance is generally described as a phenomenon that results in an increased response that occurs when the frequency of an applied force is equal or close to a natural frequency of the system . Under these resonance conditions , energy transfer from the atmosphere to ocean is at a maximum with the oceanic response higher than what would be expected . Transfer of energy from the atmosphere to the ocean could be considered as a forced oscillator . If an oscillator is forced at a frequency of 0 , this is analogous to simply displacing the oscillator to a fixed position , or an atmospheric forcing that is stationary ( e . g . inverted barometric effect ). In contrast , if an oscillator is forced at the natural frequency , there is a resonant response with increased amplitude . There are many resonance effects through atmosphere‐ocean interaction through surface wave phenomena such as when the speed of tropical cyclone is close to the group velocity of surface gravity waves ( Zhang and Oey , 2019 ) and harbour oscillations ( Thotagamuwage and Pattiaratchi , 2014 ). Three different examples of atmosphere ocean resonance are presented here :

1 . meteorological tsunamis ( Proudman resonance ); results when the propagation speed of the pressure jump ( V ) is equal to the local surface gravity wave speed ( c ). Analysis of equations presented by Proudman ( 1929 ) indicated that a positive higher pressure change will produce a forced wave with positive sea level elevation and vice‐versa ( Williams et al ., 2020 ) and the sea level peak is in advance of the pressure jump ( Figure 1 ).

Meteotsunamis are considered as a multi‐resonant phenomenon where destructive events occur only when a coincidence of several crucial factors takes place at the same time ( Monserrat et al . 2006 ).

These include ( Pattiaratchi and Wijeratne , 2015 ):

1 . local weather systems able to efficiently transfer energy into the ocean ;

2 . the continental shelf and slope topography ; and

3 . the topography and geometry of the coastline ( harbours , bays , river mouths etc .) which could have a natural frequency similar to the incoming meteotsunami waves .

2 . diurnal‐inertial resonance ; and , 3 . generation of continental shelf waves by tropical storms

In this article , the underlying theory is briefly outlined and recent examples from Western Australia are shown , although these conditions also occur globally .

Meteorological tsunamis , or meteotsunamis , are similar to tsunami waves that are generated by seismic activity , except they are forced through the atmosphere . They have periods of the order of minutes and duration < 6 hours and are distinct from storm surges . The main forcing mechanism is an abrupt change in sea surface atmospheric pressure propagating over the ocean ( Figure 1 ). Proudman resonance ( Proudman , 1929 ) is the primary generation mechanism for meteotsunamis that

Figure 1 . Schematic of the generation of a meteotsunami through Proudman resonance . An atmospheric pressure jump is travelling with speed V over the ocean with water depth h . The shallow water wave speed ( celerity ) is c (= √gh ). If V ≈ c , then Proudman resonance occurs .