📐 Tidal Equations
Sea Level Elevation:
η(t) = Σ[Aᵢ × cos(ωᵢt + φᵢ)] + A₀
Horizontal Velocity (Barotropic):
u_bt = (g/f) × (∂η/∂y) = Σ[Aᵢ × (g×ωᵢ/f) × sin(ωᵢt + φᵢ)]
Horizontal Velocity (Baroclinic):
u_bc = (g'/f) × (∂η'/∂y) × sin(πz/H)
Coriolis Parameter:
f = 2Ω sin(φ) = 1.458 × 10⁻⁴ × sin(φ) [s⁻¹]