Tidal Turbine Array: Actuator-Disc Power & Wake Model (2D)

Tidal Current

Peak flow speed 2.5 m/s

Clock speed 1.0×

Turbine Array

Turbine count 16

Blade pitch 6°

Live Readout

Cycle time

0.0 h

Flow speed

0.00 m/s

Array power

0.00 MW

Energy (this cycle)

0.00 MWh

Power coefficient Cp

Capacity factor

How it works

Each turbine converts kinetic energy from the current through the actuator-disc power law, exactly the equation used for wind and tidal turbines alike:

P = 0.5 · ρ · A · Cp · v³
ρ = 1025 kg/m³ (seawater), A = π(D/2)², D = 18 m

The tidal current itself reverses direction every half-cycle: v(t) = v_amp·sin(2πt/T) with the real M2 semi-diurnal period T = 12.42 h (the clock-speed slider only changes how fast you watch it, not the physics). Because power scales with the cube of speed, the array barely generates near slack water and peaks sharply near maximum flood/ebb — visible as the two humps per cycle in the power strip below.

Blade pitch sets the power coefficient Cp via a resonance-style curve peaking near 6° (Cp_max = 0.42, safely under the 0.593 Betz limit) and falling off either side — feathering the blades trades efficiency for reduced loading. Each row of the array also removes momentum from the flow it faces, so downstream rows see a reduced "wake" speed: the induction factor a is solved numerically from the actuator-disc relation Cp = 4a(1−a)², giving a far-wake speed of v·(1−2a), with partial turbulent recovery between rows.

Array view — turbine rows on the seabed; blade spin rate follows |v|, flow markers show current direction and the wake-deficit shading between rows.
Power strip — instantaneous array output over the last ~2 tidal cycles.
Cp vs pitch — the efficiency curve with your current pitch marked, showing why feathering trades power for protection.

Turbine row Flow / wake Power output