BEACH PROFILES × BREAKING WAVES

Shape the coast.
Change the break.

A gentler slope. A longer swell. A rising tide.
Explore how the seabed shapes a breaking wave.

Live model · editable profile · SI units

START WITH
A PROFILE

01

The cross-shore view

Height envelope

PLUNGING CONDITIONS

Drag the handles to reshape the seabed

THE ESTIMATED FIRST BREAKER

Plunging↷

The crest pitches forward and curls into the water below.

Surf similarity ξ₀0.80

Spilling < 0.5Plunging 0.5–3.3Surging* > 3.3

Approximate transitions. *Includes collapsing.

A closer look

PLUNGING

Illustrative crest motion · not a fluid simulation

Height at first break _Hᵦ1.36 mCrest to trough

Depth at first break _dᵦ1.74 mBelow still-water level

Break from shoreline20 mFirst depth-limited point

Deepwater wavelength _L₀99.9 mgT² / 2π

One variable at a time.

Hold wave height and period steady, then increase beach slope. Watch the crest change from spilling to plunging to surging.

01

Shorten and shoal

At each depth, solve the linear dispersion relation. Before breaking, conserve wave energy flux along a shore-normal ray.

ω² = gk tanh(kd)
H² Cg = constant

H₀ is the equivalent deepwater regular-wave height. The left edge need not be deep water: the wave is transformed from deep water to that finite depth.

02

Find depth-limited breaking

Step shoreward and cap wave height at γd, with γ = 0.78 by default. Carry the reduced energy flux forward. Over a bar, waves can break, reform in the trough, and break again. The cap is a simple saturated-surf-zone approximation, not a calibrated dissipation law.

H = min(√(Q / Cg), γd)
Qnext = min(Q, H² Cg)

03

Estimate the type of breaker

The Iribarren or surf similarity number compares bed slope m with deepwater wave steepness. The CEM deepwater thresholds are approximately 0.5 and 3.3. Surging and collapsing share one range; this model does not independently distinguish them.

L₀ = gT² / (2π)
ξ₀ = m / √(H₀ / L₀)

On edited profiles, m is the positive bed rise/run over a 10 m window centered at the first depth-limited point. Applying uniform-beach thresholds to bars or abrupt slopes is a heuristic. The vertical exaggeration on screen does not enter this calculation.

Plane presets flatten below −12 m and connect to a fixed +4 m upland boundary. On very gentle profiles, a high water level can move the shoreline onto that steeper upland transition.

What the animation means

The cross-shore model calculates wavelength, height, and depth-limited breaking zones. Wave asymmetry, whitewater, the curling lip, and the close-up are explanatory artwork driven by that result. They are not solutions of nonlinear free-surface flow. For surging conditions, γd marks a nominal depth-limit location, not a resolved overturning crest or runup limit.

No spectrum, wind, currents, refraction, reflection, setup, real runup, sediment transport, or bed evolution is modeled. The profile stays fixed until you edit it. These simplifications matter especially for very steep beaches and strong surging.

Basis: USACE Coastal Engineering Manual, Part II-4, equations II-4-1 through II-4-3; breaker regimes and depth index. Thresholds vary with the definitions of wave height and wavelength; this app consistently uses H₀ and L₀ for classification.

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Change each point's horizontal position and elevation in meters. x increases toward shore; z is positive upward. The end points stay at −240 m and +30 m. Coordinates must increase by at least 1 m.

Point	x (m)	z (m)