Long Barotropic Waves Generated by a Storm Crossing Topography

Abstract

Storms crossing topography are shown to radiate long surface gravity waves. The waves are transients generated by changes in the depth-dependent amplitude of the atmospherically forced pressure wave beneath a storm. This generation mechanism for long waves, known as "meteorological tsunamis" or rissaga, does not appear to have been previously discussed. The transients have periods equal to the passage time of the storm, of order 30 min for small fast-moving storms. A 1D model is used to give the amplitudes of the transient waves generated by a small fast-moving storm crossing a topographic step on to a continental shelf and across a ridge. Large transients are generated by storms whose translation speed is subcritical in deep water and supercritical in shallow water, that is, faster than the shallow-water wave speed. Surprisingly, when the depth difference between the deep water and the continental shelf is large, a gentle transition from deep to shallow water over 10 storm widths only slightly reduces the amplitudes of the transients. The influence of a finite-width shelf on the enhancement of coastal storm surge is also discussed. A 2D numerical model illustrates the topographic transients generated by sub-and supercritical storms moving across a ridge. Topographic transients are suggested as a source of energy for seiches on shelves and within embayments. The energy may come from a storm crossing the adjacent continental slope and possibly from distant open-ocean storms crossing multiple ridges and seamounts.

Fresh evidence relating the great Adriatic surge of 21 June 1978 to mesoscale atmospheric forcing

“…The Proudman resonance occurs when the speed of an air pressure disturbance c is close to the speed of shallow water waves v = ( gh ) 1/2 [ Proudman , 1929, 1953]. (Let it be mentioned that the term “Proudman resonance” has been questioned recently, on the grounds that Horace Lamb preceded Joseph Proudman in theoretically exploring the mechanism [ Vennell , 2007]. The fact, however, is that Proudman published a detailed theoretical study [ Proudman , 1929] before a part of it appeared in the 6th edition of Lamb's Hydrodynamics [ Lamb , 1932], whereas the mechanism was not mentioned in the 5th edition of the book [ Lamb , 1924].…”

A framework for the probabilistic analysis of meteotsunamis

“…Forcing of the ocean waves is given by a moving pressure change oriented in a straightline trajectory with the functional form g a ðx À UtÞ, where U is the horizontal speed of the pressure disturbance (Hibiya and Kajiura 1982;Vennell 2007). The finite-difference (2005) for landslide tsunamis.…”

“…In the above equations, 1 hPa of atmospheric pressure change translates to -1 cm of wave height. Other one-sided forcing functions for meteotsunamis were used in previous studies (Martinsen et al 1979;Hibiya and Kajiura 1982;Mercer et al 2002;Vennell 2007), whereas a one-cycle sine function (two-sided forcing) was investigated by Vilibić et al (2005). Vilibić (2005) indicates the sensitivity of wave evolution to the shape of the forcing function.…”

“…Vennell (2007) demonstrates that as the coupled disturbance passes over bathymetric discontinuities (e.g., shelf edge, ridges, canyons, etc.) or coastlines, fully or partially reflected phases are generated.…”

Meteorological tsunamis on the US East Coast and in other regions of the World Ocean

“…In the following years, comprehensive studies of meteorological tsunamis were done in various countries of the world oceans, in particular in Spain Liu et al 2003;Jansà et al 2007), Mexico (González et al 2001), New Zealand (Goring 2005;Vennell, 2007), Netherlands (de Jong et al 2003;de Jong and Battjes 2004) and especially in Croatia (Vilibić et al 2004;Vilibić 2005;Belušić et al 2007). …”