Improved Modelling of Vertical Velocity Profiles at a Tidal Energy Site

Abstract

The Minas Passage, one of the Bay of Fundy’s tidal channels, located in Nova Scotia, Canada, presents significant potential for tidal energy development because of its highly energetic flows. As development in the region gains traction, the implementation of floating tidal energy platforms is a topic of growing interest. Tidal energy deployments in Minas Passage have historically been bottom-mounted and stationary, and the transition to arrays of floating turbines requires additional considerations. Particularly, this new application demands characterization of flow over the entire water column, including near the free surface. Complete vertical velocity profiles are essential for the successful deployment of floating tidal turbines, allowing for the estimation of key metrics such as tidal power and shear across turbine blades. Here we explore adaptations to the well-established logarithmic law of the wall with the goal of extending the vertical range over which a fitting regime based in classical turbulence theory can capture the observational records of flow in Minas Passage.
 Observational site characterization efforts in Minas Passage have primarily consisted of stationary, bottom mounted Acoustic Doppler Current Profiler (ADCP) deployments. Using historical ADCP records collected in Minas Passage between 2008 and 2021, we fit the vertical profiles of velocity using three methods: logarithmic law of the wall, power law, and an adapted logarithmic law of the wall which includes a “wake function” to improve fits in the upper water column. We find that although the law of the wall results in well-fitted estimations of the vertical velocity profiles near the seabed, observational profiles consistently deviate from the fitted curves in the middle and upper water column, recording significantly faster flow speeds than predicted by the law of the wall. The adapted model, which is rooted in turbulence theory and includes a wake term, is successful in capturing flow in the outer layer of the water column and allows for reverse shear to be captured in the profile. The resulting fits show a sizeable reduction in error throughout the entirety of the water column compared to the law of the wall profiles, and consistently reduce the error in the vertical profile fits when compared to power law fits. In addition to resulting in low error for both individual and averaged vertical profiles of flow, the physical quantities estimated from the adapted model, including drag coefficient, agree well with those computed from the law of the wall, demonstrating the physical usefulness of the adapted model.