Numerical assessments of ocean energy extraction from western boundary currents using a quasi-geostrophic ocean circulation model

A single-layer, quasi-geostrophic (QG), large-scale ocean circulation model is developed in this paper to study available ocean current energy potentials harnessed by using the ocean current turbines. Power extraction is modeled by adding a parameterized Rayleigh friction term in the barotropic vorticity equation. Numerical assessments are performed by simulating a set of mid-latitude ocean basins in the beta plane, which are standard prototypes of more realistic ocean dynamics considering inter-decadal variability in turbulent equilibrium. The third-order Runge-Kutta scheme for the temporal discretization and the second-order conservative Arakawa scheme for the spatial discretization are utilized to perform Munk scale resolving high-resolution computations. A sensitivity analysis with respect to the turbine parameters is performed for various physical conditions. Results show that the proposed model captures the quasi-stationary ocean dynamics and provides the four-gyre circulation patterns in time mean. After an initial spin-up process, the proposed model reaches a statistically steady state at an average maximum speed between 1.5 m/s and 2.5 m/s, which is close to the observed maximum zonal velocities in the western boundary currents. The probability density function of the available power over a long time period is computed for a wide range of parameters. Numerical results shows that 10 GW mean power can be extracted from the turbines distributed over a length scale of 100 km along the western boundaries. However, it is demonstrated that bigger turbine areas would alter the flow patterns and energetics due to excessive dissipation. An increase in the turbine area results in an increase in the available power ranging from 8 to 22 GW depending on the values of turbine modeling parameters. This first step in the numerical assessment of the proposed QG model shows that the present framework could represent a viable tool for evaluating energy potentials in a highly turbulent flow regime.