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Forcing of a Two-Layered Water Column over a Sloping Seafloor

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  • 1 The University Centre in Svalbard (UNIS), Svalbard, Norway
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Abstract

The response of a time-dependent atmospheric function close to a slope region is studied. A forced two-layered model over a sloping topography is examined with focus on the particular solution and interaction between the constructed barotropic and baroclinic mode. The water column responds with long periodic waves along the sloping bottom, and the solution includes a time-dependent Ekman transport in the upper layer. Despite its relative simplicity, the model produces a resonant response in the barotropic mode to a northward-propagating plane-wave wind stress field. The particular solution shows that a state close to resonance in the barotropic mode is given by a 1/λy line for the barotropic coefficient when plotted as a function of the forcing wave period and wavelength λy. From the Norwegian Meteorological Institute (NMI) Hindcast database, the calculated time series of the wind stress curl reveals a high energy level in the forcing period interval between 48 and 185 h. The Vøring Plateau slope has a natural oscillation period around 100 h for topographically trapped waves, and the model shows that an along-slope wavelength of 76 km will produce a resonant response in the water column for this wave period. Hence, when the forcing function is constructed as a sum of (infinitely) many Fourier components, topographic waves will be triggered along the Vøring Plateau slope for a northward-moving atmospheric pressure system.

Corresponding author address: Dr. Frank Nilsen, University Centre in Svalbard, P.O. Box 156, N-9171 Longyearbyen, Norway. Email: frank.nilsen@unis.no

Abstract

The response of a time-dependent atmospheric function close to a slope region is studied. A forced two-layered model over a sloping topography is examined with focus on the particular solution and interaction between the constructed barotropic and baroclinic mode. The water column responds with long periodic waves along the sloping bottom, and the solution includes a time-dependent Ekman transport in the upper layer. Despite its relative simplicity, the model produces a resonant response in the barotropic mode to a northward-propagating plane-wave wind stress field. The particular solution shows that a state close to resonance in the barotropic mode is given by a 1/λy line for the barotropic coefficient when plotted as a function of the forcing wave period and wavelength λy. From the Norwegian Meteorological Institute (NMI) Hindcast database, the calculated time series of the wind stress curl reveals a high energy level in the forcing period interval between 48 and 185 h. The Vøring Plateau slope has a natural oscillation period around 100 h for topographically trapped waves, and the model shows that an along-slope wavelength of 76 km will produce a resonant response in the water column for this wave period. Hence, when the forcing function is constructed as a sum of (infinitely) many Fourier components, topographic waves will be triggered along the Vøring Plateau slope for a northward-moving atmospheric pressure system.

Corresponding author address: Dr. Frank Nilsen, University Centre in Svalbard, P.O. Box 156, N-9171 Longyearbyen, Norway. Email: frank.nilsen@unis.no

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