Vertical Mixing in Basin Waters of Fjords

Anders Stigebrandt Dept. of Oceanography, University of Gothenburg, Gothenburg, Sweden

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Jan Aure Institute of Marine Research, Bergen, Norway

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Abstract

The rate of work against the buoyancy forces due to vertical mixing (W) has been determined from repeated measurements of vertical density profiles in a large number of fjordic sill basins (basins dammed by sills). It is found that there is a weak “background” rate of work W0, probably driven by the local wind. Superposed upon this is work driven by the tide. Thus W = W0 + RfE, where E is the mean energy flux from the surface tide to turbulence in the sill basin and Rf is an efficiency factor. We distinguish between “wave basins” and “jet basins.” In the former category progressive internal tides are generated in the mouths, while in the latter there are tidal jets at the mouths. For wave basins, about 5.6% of the energy flux E from the surface tide is used for work against the buoyancy forces in the basin water (i.e., Rf ≈ 0.056). The corresponding figure for jet basins appears to be less than 1%.

We have also studied the dependence of the vertical diffusivity κ upon the vertical stratification N. For well-behaved vertical distributions of N, it is found that κ ∼ N−1.5. A formula for κ, which appears to be applicable to many wave sill basins in fjords, is derived. From this, κ may be predicted if the vertical stratification NN(z), the characteristics of the topography and the sea level statistics are known.

Abstract

The rate of work against the buoyancy forces due to vertical mixing (W) has been determined from repeated measurements of vertical density profiles in a large number of fjordic sill basins (basins dammed by sills). It is found that there is a weak “background” rate of work W0, probably driven by the local wind. Superposed upon this is work driven by the tide. Thus W = W0 + RfE, where E is the mean energy flux from the surface tide to turbulence in the sill basin and Rf is an efficiency factor. We distinguish between “wave basins” and “jet basins.” In the former category progressive internal tides are generated in the mouths, while in the latter there are tidal jets at the mouths. For wave basins, about 5.6% of the energy flux E from the surface tide is used for work against the buoyancy forces in the basin water (i.e., Rf ≈ 0.056). The corresponding figure for jet basins appears to be less than 1%.

We have also studied the dependence of the vertical diffusivity κ upon the vertical stratification N. For well-behaved vertical distributions of N, it is found that κ ∼ N−1.5. A formula for κ, which appears to be applicable to many wave sill basins in fjords, is derived. From this, κ may be predicted if the vertical stratification NN(z), the characteristics of the topography and the sea level statistics are known.

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