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Application of a Frictional Channel Flow Theory to Flow in the Prince of Wales Channel, Torres Strait

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  • 1 CSIRO, Division of Oceanography, Hobart, Tasmania, Australia
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Abstract

Turbulent flow is considered in a narrow, constant-depth channel connecting two basins having a time-dependent sea-level difference. The bosom stress is taken to be linear rather than quadratic in velocity, even when flows are quite strong. This approximation is justified theoretically by comparing appropriate linear and nonlinear solutions. Simple formulae are available for the depth-averaged current speed ū along the channel axis in terms of the sea-level gradient along that axis. Application of suitable mixing length theory shows that the stress should vary linearly with depth even for time-dependent flows. The mixing length theory predicts the current profile to be logarithmic near the bottom and slightly greater than logarithmic near the surface.

The theory was applied to sea level tidal constants and some acoustic Doppler and ship drift measurements recently made in the Prince of Wales Channel, Torres Strait. Sea level gradients and tidal flows in the channel are large because the channel joins two very different tidal regions, one in the Gulf of Carpentaria and the other in the Coral Sea. In accordance with theory, the channel is short enough that tidal constants vary linearly down the channel. The simple formulae for ū model the data reasonably well and clarity and improve previous tide table estimates. Depth averaged currants peak at about 2 m s−1 and have a root mean squared depth averaged velocity of 0.74 m s−1. The bottom r, resistance coefficient r, the drag coefficient CD and roughness length zo take the large values 4.8 × 10&minus:1 m s−1, 5.3 × 10-3 and 0.029 m.

Abstract

Turbulent flow is considered in a narrow, constant-depth channel connecting two basins having a time-dependent sea-level difference. The bosom stress is taken to be linear rather than quadratic in velocity, even when flows are quite strong. This approximation is justified theoretically by comparing appropriate linear and nonlinear solutions. Simple formulae are available for the depth-averaged current speed ū along the channel axis in terms of the sea-level gradient along that axis. Application of suitable mixing length theory shows that the stress should vary linearly with depth even for time-dependent flows. The mixing length theory predicts the current profile to be logarithmic near the bottom and slightly greater than logarithmic near the surface.

The theory was applied to sea level tidal constants and some acoustic Doppler and ship drift measurements recently made in the Prince of Wales Channel, Torres Strait. Sea level gradients and tidal flows in the channel are large because the channel joins two very different tidal regions, one in the Gulf of Carpentaria and the other in the Coral Sea. In accordance with theory, the channel is short enough that tidal constants vary linearly down the channel. The simple formulae for ū model the data reasonably well and clarity and improve previous tide table estimates. Depth averaged currants peak at about 2 m s−1 and have a root mean squared depth averaged velocity of 0.74 m s−1. The bottom r, resistance coefficient r, the drag coefficient CD and roughness length zo take the large values 4.8 × 10&minus:1 m s−1, 5.3 × 10-3 and 0.029 m.

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