Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-23T19:14:30.072Z Has data issue: false hasContentIssue false
  • English
  • Français

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: cgarrett@uvic.ca
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arbic, B. K. & Garrett, C. 2009 A coupled oscillator model of shelf and ocean tides. Cont. Shelf Res. 30, 564–574.Google Scholar
Arbic, B. K., Shriver, J. F., Hogan, P. J., Hurlburt, H. E., McClean, J. L., Metzger, E. J., Scott, R. B., Sen, A., Smedstad, O. M. & Wallcraft, A. J. 2009 Estimates of bottom flows and bottom boundary layer dissipation of the oceanic general circulation from global high-resolution models. J. Geophys. Res. 114, C02024.Google Scholar
Atwater, J. F. & Lawrence, G. A. 2010 Power potential of a split tidal channel. Renewable Energy 35, 329–332.Google Scholar
Blanchfield, J., Garrett, C., Wild, P. & Rowe, A. 2008 The extractable power from a channel linking a bay to the open ocean. J. Power Energy 222, 289–297.CrossRefGoogle Scholar
Cummins, P. F. 2013 The extractable power from a split tidal channel: An equivalent circuit analysis. Renewable Energy 50, 395–401.Google Scholar
Cummins, P. F. & Holloway, G. 2010 Reynolds stress and eddy viscosity in direct numerical simulations of sheared two-dimensional turbulence. J. Fluid Mech. 657, 394–412.Google Scholar
Garrett, C. & Cummins, P. 2004 Generating power from tidal currents. J. Waterways Port Coast. Ocean Engng 130, 114–118.Google Scholar
Garrett, C. & Cummins, P. 2005 The power potential of tidal currents in channels. Proc. R. Soc. Lond. A 461, 2563–2572.Google Scholar
Garrett, C. & Cummins, P. 2007 The efficiency of a turbine in a tidal channel. J. Fluid Mech. 588, 243–251.Google Scholar
Garrett, C. & Cummins, P. 2008 Limits to tidal current power. Renewable Energy 33, 2485–2490.Google Scholar
Inoue, R. & Garrett, C. 2007 Fourier representation of quadratic friction. J. Phys. Oceanogr. 37, 593–610.Google Scholar
International Energy Agency, 2011 Key World Energy Statistics. OECD/IEA, Paris.Google Scholar
Miller, L. M., Gans, F. & Kleidon, A. 2011 Estimating maximum global land surface wind power extractability and associated climatic consequences. Earth Syst. Dyn. 2, 1–12.Google Scholar
Müller, M., Haak, A., Jungclaus, J. H., Sündermann, J. & Thomas, M. 2010 The effect of ocean tides on a climate model simulation. Ocean Model. 35, 304–313.Google Scholar
Munk, W. & Wunsch, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. 45, 1977–2010.CrossRefGoogle Scholar
Roquet, F., Wunsch, C. & Madec, G. 2011 On the patterns of wind-power input to the ocean circulation. J. Phys. Oceanogr. 31, 2328–2342.CrossRefGoogle Scholar
Shapiro, G. I. 2011 Effect of tidal stream power generation on the region-wide circulation in a shallow sea. Ocean Sci. 7, 165–174.Google Scholar
Vennell, R. 2010 Tuning turbines in a tidal channel. J. Fluid Mech. 663, 253–267.Google Scholar
Wunsch, C. 1998 The work done by the wind on the oceanic general circulation. J. Phys. Oceanogr. 28, 2332–2340.Google Scholar
Yang, Z., Wang, T. & Copping, A. 2012 Modelling tidal stream energy extraction and its effects on transport processes in a tidal channel and bay system using a three-dimensional coastal ocean model. Renewable Energy 50, 605–613.Google Scholar
Supplementary material: PDF

Garrett and Cummins supplementary material

Appendix

Download Garrett and Cummins supplementary material(PDF)
PDF 35.7 KB