Long Ocean Waves Generated by Moving Atmospheric Pressure Disturbances Crossing Topography

Low air pressure within a storm elevates the ocean's surface up to 0.5m, creating an atmospherically forced pressure wave beneath the storm. These works shows that when this pressure wave passes over ridges, seamounts or crosses the continental slope it radiates waves. Also that at crical angles of incidence the generated waves can resonate or be trapped These waves due to air pressure disturbances with these periods are known as ``meteorological tsunamis'' or Rissaga can be up to 5m high.

The plots shows the results from a 1D analytical model. As the forced pressure wave under a storm crosses the ridge it produces transient waves which radiate infront of and behind the storm. These waves in the linear model are stretched squashed copies of the forced pressure wave's shape. In this sub-critical case the transients are faster than the storm. These transient waves bounce back and forth on the ridge, radiating energy out into deep water long after the storm has left the ridge.

Abstracts

Resonance of long waves generated by storms obliquely crossing shelf topography in a rotating ocean

Thiebaut, S., and R. Vennell, Journal of Fluid Mechanics, 682, 261–288, doi:10.1017/jfm.2011.221 (2011) pre print

The oceanic forced wave beneath a moving atmospheric disturbance is amplified by Proudman resonance. When modified by the Earth's rotation this classical resonance only occurs if the disturbance time scale is smaller than the inertial period. With or without Coriolis effects, free transients generated by storm forced waves obliquely crossing step changes in water depth at particular angles are shown to resonate by exciting a range of long barotropic free waves. Rotationally influenced slow atmospherically forced waves crossing a vertical coast at a critical angle lead to a form of subcritical resonance, which occurs only when the component of the disturbances' phase velocities along the coast matches that of a free Kelvin wave (KW). In a rotating ocean, transients generated by disturbances crossing a step at a particular angle are shown to excite a free double Kelvin wave (DKW). This new type of resonance only occurs for sufficiently large steps and disturbances with time scale greater than the inertial period. A storm crossing a step shelf can result in the excitation of an infinite set of edge waves, a single KW, a unique DKW and a first-mode continental shelf wave, depending on the topography and the disturbance time scale, translation speed and incident angle. The study of resonances and wave mode excitations generated by storms crossing a coast or a continental shelf may contribute to understanding how a particular combination of the storm characteristics can result in destructive coastal events with time scales encompassing the typical meteotsunami period band (tens of minutes) and storm surges with periods of several hours or days.

Resonance and Trapping of Topographic Transient Ocean Waves Generated by a Moving Atmospheric Disturbance
R. Vennell,Journal of Fluid Mechanics, 650, 427-442 (2010) pre print

Proudman resonance amplifies the oceanic forced wave beneath moving atmospheric pressure disturbances. The amplification varies with water depth, consequently the forced wave beneath a disturbance crossing topography radiates transient free waves. Transients are shown to magnify the effects of Proudman Resonance for disturbances crossing the coast or shelf at particular angles. A Snell like reflection law gives rise to a type of resonance for relatively slow moving disturbances crossing a coast in an otherwise flat bottomed ocean. This occurs for translation speeds less than the shallow water wave speed for disturbances approaching the coast at a critical angle given by the inverse sine of the disturbance's Froude number. A disturbance crossing the shelf at particular angles can also excite seiche modes of the shelf via generation of a transient at the continental slope. Beyond a typically small angle of incidence transients generated by a disturbance crossing the continental slope and coast will be trapped on the shelf by internal reflection. The refraction law for a fast moving forced wave crossing an ocean ridge at greater than a small angle of incidence also results in trapped free wave transients with tsunami like periods propagating along the ridge. Sub-critical resonance, the excitation of shelf modes and trapping of the transients may have implications for storm surge and the generation of destructive meteotsunami.

Observation of a fast continental shelf wave generated by a storm impacting Newfoundland using Wavelet and Cross Wavelet Analysis
Thiebaut, S., and R. Vennell, Journal of Physical Oceanography , 40, 2 Pages: 417-428 (2010)

Wavelet and cross wavelet power spectra of sea level records from tide gauges along the Atlantic coast of Canada showed a low-frequency barotropic response after Hurricane Florence crossed the Newfoundland shelf in September 2006. In comparison with two other storms, the results showed that Florence was the only one that excited a propagating sea level disturbance with period range similar to the passage time of the storm over the shelf (26-30 hours) and phase shifts consistent with a barotropic continental shelf wave (CSW). The high amplitude of the oscillations generated by Florence along the shore diminished from approximately 45 cm to 12 cm as the CSW propagated from the south coast of Newfoundland to the southern Nova Scotia seaboard. This paper presents the first direct measurement of a remarkably high alongshore group speed (11.4-5.9 m/s) in the manner of free barotropic CSW by examination of sea level wavelet power spectra at different
locations. Furthermore, using cross wavelet analysis of pairs of stations, an exceptional phase speed of 16.0-5.1 m/s has been found, greater than had been previously observed for a free CSW. Results were consistent with dispersion curves for the frist-mode barotropic CSW.

Long Barotropic Waves Generated by a Storm Crossing Topography
R. Vennell, Journal of Physical Oceanography, doi:10.1175/2007JPO3687.1, December (2007).Preprint PDF

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 minutes 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, i.e. 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.