MY SIMULATOR

Shoreline Evolution Lab

Sand moves along the coast. What happens when you build in its way?

INTERACTIVE 3D

Year 0.0Drift 0 k m³/yrMax gain 0 mMax loss 0 mHouses lost 0FPS 0

Shoreline Evolution Lab: Longshore Drift, Groynes, Seawalls & Nourishment

Waves that hit a beach at an angle push sand along the coast. Build a groyne to trap it, a seawall to stop erosion, nourish the beach with new sand, or let the sea rise — and read what happens to the shoreline and to the houses behind it. Click the beach with the selected tool.

Scenario

Time warp

Live numbers

Shoreline along the coast (m seaward)

Largest gain and loss through time (m)

1 · Waves

Transport follows Hb^5/2 sin 2α: doubling the wave height more than quintuples it; it peaks at 45 degrees and vanishes for waves that arrive straight on.

2 · Structures

A groyne is a wall into the sea. It blocks the part of the surf zone it reaches (bypass = 1 - length / surf width), so sand piles up on the updrift side and the downdrift side starves.

3 · Sea level

Bruun rule: a profile that must stay in equilibrium retreats R = S · W* / (B + h*), about 37 times the sea-level rise S for these numbers.

Experiments (measured vs predicted)

Run an experiment. They use private copies of the model and do not touch your beach.

Independent numerical checks

Also run outside the browser: node src/check.js (Pelnard-Considere erfc solution, Gaussian spreading of a nourishment bump, sand budget, stationarity and time-step convergence, CERC coefficient and Bruun rule).

Educational model. The one-line model keeps only the shoreline position, not the 2-D wave field: no wave diffraction behind the groyne, no cross-shore storm erosion, no rip currents, no sediment sources other than the beach itself, constant profile shape. The CERC coefficient (K = 0.39) and active profile height (8 m) are typical values [assumption]; real drift rates differ by a factor of 2-3 between sites. Houses are drawn at fixed positions and marked lost when the shoreline reaches them.

Controls

Drag / one finger: orbit; wheel / pinch: zoom; Hero, Map, Beach buttons (keys H, T, G).
Click or tap the beach: Place groyne puts the groyne there, Nourish here adds sand centred there (volume from the slider). Storm triples the wave height for about 10 days. Seawall protects the stretch shown by the sliders.
Waves from the left (positive angle) drive sand to the right. Reset beach restores the straight shoreline and the houses.

The science

Longshore transport (CERC). The volume of sand moved along the shore per unit time is Q = K ρ √g / (16 √κ (ρ_s - ρ)(1 - p)) · H_b^5/2 sin 2α_b with breaking-wave height H_b, breaker angle α_b to the shoreline, K = 0.39, breaker index κ = 0.78, sand density ρ_s = 2650 kg/m³ and porosity p = 0.4. For H_b = 1 m and 20 degrees this is 1.8 million m³/yr, the right order of magnitude for an exposed coast.

One-line model. Conservation of sand: D ∂y/∂t = -∂Q/∂x, with D the active profile height (closure depth + berm, 8 m). The breaker angle depends on the local shoreline orientation, α_b = α₀ - atan(∂y/∂x). For small angles this is a diffusion equation ∂y/∂t = ε ∂²y/∂x² with ε = 2 Q₀ cos 2α₀ / D. The code solves the full non-linear form implicitly (backward Euler with a linearised flux), so any wave height is stable.

Groyne (Pelnard-Considere 1956). A groyne that blocks all transport forces Q = 0 at x = 0, i.e. a shoreline angle θ_b = tan(2α₀)/2 there. The exact linear solution on the updrift side is y(s,t) = θ_b [2√(εt/π) e^-s²/4εt - s erfc(s/2√(εt))], so the shoreline advances at the groyne like √t. The check compares the numerical solution with this formula.

Nourishment. A bump of sand spreads as a Gaussian, σ² = σ₀² + 2εt, so the peak falls as σ₀/√(σ₀² + 2εt) and the half-life is 3σ₀²/(2ε). Rougher seas (larger ε) spread the sand sooner.

Seawall. The wall fixes the back of the beach: the shoreline cannot retreat behind it and the sand it would have supplied is not released (tracked as "wall-denied erosion" in the sand budget). In reality the beach in front of a wall often narrows by scour; this model shows only the loss of supply.

Sea-level rise (Bruun rule). R = S W* / (B + h*) with active profile width W* = h*/tanβ (here 6 m / 0.02 = 300 m), berm height B = 2 m and closure depth h* = 6 m. It is applied here as a uniform retreat on top of the drift.

Not modelled: 2-D wave transformation and diffraction, storm surge and cross-shore bar dynamics, tides, sand sources (rivers, cliffs), changing wave climate, groyne outflanking, hard-structure scour, shoreline stability limits for waves at more than 42 degrees. Constants marked [assumption] are typical values, not a calibration to any beach.