Coastal and Estuarine Hydrodynamics, Waves, Tides and Sediment Transport
This domain supplies the loads - water levels, currents, wave forces - that marine structures and channels must survive, and the sediment transport that decides whether a dredged depth stays dredged.
Waves
- Linear theory: ω² = gk tanh(kd). Deep water (d/L > 0.5) gives L0 = 1.56T²; shallow water (d/L < 0.05) gives c = √(gd); between those limits iterate the dispersion relation.
- Shoaling conserves energy flux; refraction obeys Snell's law, so crests turn toward parallelism with the bottom contours and energy converges on shoals and headlands.
- Breaking is depth-limited at roughly H/h = 0.78 for regular waves (McCowan), with Goda's criterion used for irregular seas; breaking caps the load on walls and armour.
- Design uses a spectrum (JONSWAP) giving Hs and Tp; the largest individual wave is about Hmax ≈ 1.8–2.0 Hs.
Tides and estuaries
- Principal constituents: M2 and S2 semidiurnal, K1 and O1 diurnal. The form factor F = (K1+O1)/(M2+S2) classifies the regime: below 0.25 semidiurnal, 0.25–1.5 mixed, above 3 diurnal.
- Estuary mixing ranges from salt wedge through partially mixed to well mixed, controlled by freshwater flow against tidal energy; stratification suppresses turbulence and traps sediment.
- Alluvial estuaries tend toward a stable relation between tidal prism and cross-sectional area; widening or narrowing a channel shifts that equilibrium and triggers shoaling or erosion.
Sediment transport
- Shields parameter θ = τ/((ρs − ρ)gD) defines initiation of motion; the Hjulström curve relates velocity to erosion, transport and deposition for cohesive and non-cohesive beds.
- Longshore drift is driven by oblique wave approach; the CERC formula makes transport proportional to wave energy flux times sin(2α).
Worked example
Tidal constituents M2 = 1.10 m, S2 = 0.38 m, K1 = 0.32 m, O1 = 0.24 m. F = (0.32 + 0.24)/(1.10 + 0.38) = 0.56/1.48 = 0.38, so the tide is semidiurnal and an M2 harmonic is adequate for first-order current estimates. The spring–neap range still runs from 0.72 m to 1.48 m, which controls dredging and berthing windows.
Traps
- Applying c = √(gd) at 20 m depth for a 10 s wave: L0 = 156 m, so d/L0 = 0.13 - intermediate water, the shallow formula is invalid.
- Using Hs directly as the maximum wave in armour or wall stability checks.