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M2 Baroclinic Tides in Johnstone Strait, British Columbia

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  • 1 Institute of Ocean Sciences, Patricia Day, Sidney, B.C., Canada V8L 4B2
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Abstract

Tide, current and water property data collected in the western basin of Johnstone Strait, British Columbia, are compared with analytical models for M2 semidiurnal motions in a stratified, rotating channel of uniform depth. We show that, for a rectangular basin in which there is a depth-independent mean flow, the tidal fluctuations are readily expressible in terms of a landward (eastward) propagating Kelvin wave and exponentially damped, seaward (westward) propagating baroclinic Kelvin waves. The internal M2 tide appears to be generated through interaction of the surface tide with the shallow sill at the eastern end of the basin and is dominated by a first-mode baroclinic wave whose amplitude undergoes attenuation over an e-folding distance of one wavelength (∼26 km). Near the sill the baroclinic current speed may exceed 50% of the barotropic flow speed. The along-channel energy flux (power) of the barotropic tide is comparatively uniform at ∼1.4×109 W throughout the western portion of the Strait but decreases by a factor of 2 across the sill. Less than 0.3% of this power loss is needed to account for the baroclinic energy flux of ∼2×106 W near the sill; dissipation due to bottom friction is the main sink for the barotropic tidal energy. Attenuation of the baroclinic waves appears to result from a combination of turbulent horizontal friction and bottom boundary layer friction. Based on the first mode amplitudes, we find a horizontal eddy viscosity of ∼4×106 cm2 s−1 and a vertical eddy viscosity of ∼103 cm2 s−1. Our analysis further indicates that higher modes may be subject to attenuation by critical-layer absorption in the presence of the mean estuarine circulation in the basin. The M2 tides and currents are shown to possess considerable variability over periods of weeks and to have seasonal trends that, qualitatively at least, are related to changes in the mean density structure.

Abstract

Tide, current and water property data collected in the western basin of Johnstone Strait, British Columbia, are compared with analytical models for M2 semidiurnal motions in a stratified, rotating channel of uniform depth. We show that, for a rectangular basin in which there is a depth-independent mean flow, the tidal fluctuations are readily expressible in terms of a landward (eastward) propagating Kelvin wave and exponentially damped, seaward (westward) propagating baroclinic Kelvin waves. The internal M2 tide appears to be generated through interaction of the surface tide with the shallow sill at the eastern end of the basin and is dominated by a first-mode baroclinic wave whose amplitude undergoes attenuation over an e-folding distance of one wavelength (∼26 km). Near the sill the baroclinic current speed may exceed 50% of the barotropic flow speed. The along-channel energy flux (power) of the barotropic tide is comparatively uniform at ∼1.4×109 W throughout the western portion of the Strait but decreases by a factor of 2 across the sill. Less than 0.3% of this power loss is needed to account for the baroclinic energy flux of ∼2×106 W near the sill; dissipation due to bottom friction is the main sink for the barotropic tidal energy. Attenuation of the baroclinic waves appears to result from a combination of turbulent horizontal friction and bottom boundary layer friction. Based on the first mode amplitudes, we find a horizontal eddy viscosity of ∼4×106 cm2 s−1 and a vertical eddy viscosity of ∼103 cm2 s−1. Our analysis further indicates that higher modes may be subject to attenuation by critical-layer absorption in the presence of the mean estuarine circulation in the basin. The M2 tides and currents are shown to possess considerable variability over periods of weeks and to have seasonal trends that, qualitatively at least, are related to changes in the mean density structure.

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