## Velocity Profile

The following explains the difference between each of the 3 mooring options investigated, in terms of their position in the vertical velocity profile, and the resulting flow velocity at the turbine in each case. Assuming a 100m depth, for each of the 3 mooring options, the objective is to maintain both the turbine and the buoy within the 35 m high window, in order to avoid the low energy flow in the bottom 50 m and the wave-induced turbulent zone in the top 15 m.

### Mooring Option 1

In Option 1 (Shallow Buoy - Single Line), the depth of the turbine and the buoy vary as a function of the flow velocity, since the drag forces increase as the flow velocity increases. Therefore, the height of the turbine varies over both the diurnal and bi-monthly tidal cycles. However, the flow velocity is a function of depth, due to the variation in the vertical velocity profile. Therefore the turbine height and the flow velocity the turbine experiences are inter-dependent, requiring an iterative calculation, derived as follows:

The height of the turbine above the seabed is calculated as follows:

where L is the length of the mooring line and theta is the angle between the seabed and the mooring line.

The vertical velocity profile is calculated as follows:

where v is the velocity at height z above the seabed and vs is the velocity at the surface.

The angle between the seabed and the mooring line is calculated as follows:

where B is the buoyancy force, FD is a drag force, CD is a drag coefficient, the subscript b refers to the buoyancy, the subscript c refers to the CoRMaT turbine and C is a constant defined as follows:

For any given surface velocity, vs the velocity, v at the turbine, located at height, z above the seabed is calculated by an iterative solution of the following: