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Maximum power from a turbine farm in shallow water

Published online by Cambridge University Press:  02 January 2013

Chris Garrett  and
Patrick Cummins
Chris Garrett*
Affiliation:
Department of Physics and Astronomy, University of Victoria, Victoria, BC V8W 3P6, Canada
Patrick Cummins
Affiliation:
Institute of Ocean Sciences, Fisheries and Oceans Canada, Sidney, BC V8L 4B2, Canada
*
†Email address for correspondence: [email protected]
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Abstract

The maximum power that can be obtained from a confined array of turbines in steady or tidal flows is considered using the two-dimensional shallow-water equations and representing the turbine farm by a uniform local increase in friction within a circle. Analytical results supported by dimensional reasoning and numerical solutions show that the maximum power depends on the dominant term in the momentum equation for flows perturbed on the scale of the farm. If friction dominates in the basic flow, the maximum power is a fraction (half for linear friction and 0.75 for quadratic friction) of the dissipation within the circle in the undisturbed state; if the advective terms dominate, the maximum power is a fraction of the undisturbed kinetic energy flux into the front of the turbine farm; if the acceleration dominates, the maximum power is similar to that for the linear frictional case, but with the friction coefficient replaced by twice the tidal frequency.

JFM classification

Geophysical and Geological Flows: Coastal engineering Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Shallow water flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 714 , 10 January 2013 , pp. 634 - 643
Copyright
©2013 Cambridge University Press

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