Abstracto

Abstract

Extremely large seiche oscillations are regularly observed in some specific areas around the world even in the absence of any seismic forcing. These seiches have been successfully associated with strong atmospheric pressure perturbations inducing sea level oscillations at the open ocean, before entering the inlet, which are in turn resonantly amplified by the geometric characteristics of the inlet. The coastal behaviour of such waves, although of different origin, is similar to tsunami waves behaviour and is sometimes referred to as meteotsunamis. In some specific places, such as Ciutadella inlet, Balearic Islands, western Mediterranean, these seiche oscillations are stronger than expected, even taking into account the large amplification factor by resonance of the inlet. For these cases, some external amplification, before entering the inlet, is necessary to explain the phenomenon. In this paper, it is numerically shown how the phase speed of the atmospheric pressure disturbance generating the surface waves is a critical factor in the energy transfer between the atmosphere and the ocean.

1. Introduction

Large amplitude seiche oscillations with periods in the tsunami frequency range (several minutes) are periodically observed in some specific areas around the world even in absence of seismic forcing. These waves have been successfully related to atmospheric forcings (mainly atmospheric pressure oscillations) and therefore referred to as meteotsunamis. Strong seiche oscillations associated with atmospheric forcing have been reported in Japan [1, 2], China [3], the Adriatic Sea [4], the Aegean Sea [5], etc.

Waves of this kind are periodically observed in Ciutadella harbour, located at the end of an elongated inlet in Menorca Island, western Mediterranean (Fig. 1), where are locally known as rissaga. It has been demonstrated that rissagas are due to the resonant amplification of the inlet normal mode (10 min period) when this is externally forced by open ocean long waves generated by rapid atmospheric pressure fluctuations [6, 7]. The characteristics of these atmospheric waves are well established [8]. They are non-dispersive waves, travelling from the SW to the NE and with a phase speed always ranging between

Figure 1. Situation of Ciutadella inlet in the western Mediterranean

20 and 30 m/s. The elongated dimensions of Ciutadella inlet (1 km long, 50 m wide) is a key point conferring to this inlet a particularly high amplification factor by resonance. However, the large sea level oscillations recorded at this site (up to 3 m wave height) can only be explained if some amplification of the ocean long wave occurs prior to its arrival to the inlet mouth. A finite difference 2D numerical model, able to simulate ocean long waves generated by atmospheric pressure fluctuations, is used to show how the platform characteristics allow this amplification and how the phase speed of the atmospheric pressure waves is critical in this amplification.

2. Numerical model

The numerical model is a finite difference, 2D long wave model developed by the Ocean and Coastal Research Group at the University of Cantabria. It has been modified to include an atmospheric pressure term in the momentum equation. The model integrates the depth-averaged equations of continuity, momentum and diffusion over a finite difference grid. The equations, in Cartesian coordinates have the form:

• Mass conservation:

• Momentum conservation:

• Diffusion equations for temperature, T and salinity, S (here both are denoted as C):

where, x, y, z form the right-handed Cartesian coordinate system, U and V are the depth-averaged velocity and H=h+η, where η is the free surface and h is the depth. The term f is the Coriolis parameter, Pa is the atmospheric pressure, εh, and εz are, respectively, the horizontal [9] and vertical [10] eddy viscosity coefficients, Dx and Dy are the horizontal diffusivity coefficients and ρ = ρ0+ρ’ is the water density, with ρ0 being the reference density. Density is obtained from the values of T and S using the UNESCO equation of state, as adapted by Mellor [11].

Model equations are written on a staggered grid (Arakawa C) and are solved by means of an implicit finite difference method, except for non-linear terms, which are treated explicitly. The finite difference algorithm is a centered, two time levels scheme, resulting in a second order approximation in space and time.

3. Model inputs

The actual bathymetry between Mallorca and Menorca islands (Fig 2a) may be schematically modelled as shown in Fig. 2b, taking a platform depth of 60m bounded by a 1000m ocean. Both actual and simplified bathymetries are used in separate simulations. A set of atmospheric perturbation propagating upwards with phase speeds ranging between 15 and 50 m/s has been used as the boundary condition along the lower boundary of the computational domain. The atmospheric perturbation employed in simulations

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