Stokes wave¶
A periodic nonlinear surface wave modeled with amplitude-dependent Stokes expansions of fluid motion.
Core Idea¶
A Stokes wave is a nonlinear model of a periodic water-surface wave. Its strict form is a traveling wave of permanent shape on an idealized fluid layer of constant mean depth. Stokes's perturbation expansion starts from a fundamental wave and adds higher harmonics and amplitude-dependent changes in elevation, velocity, and phase speed.
Those corrections matter when a single sinusoid no longer describes crest–trough asymmetry adequately. The model is useful for intermediate and deep water, but depth and steepness constrain the validity of a truncated order; long shallow waves may call for another theory. The word can be used loosely for related wave contexts, but that does not erase the strict solution's assumptions.
Scope of Application¶
This model applies to periodic surface waves within stated depth and steepness limits, not to arbitrary sea states.
- Wave theory. Analyze amplitude-dependent periodic free-surface shape and phase speed.
- Coastal engineering. Estimate surface elevation and velocity under stated depth and steepness conditions.
- Offshore loading. Supply idealized kinematics to a separate structural load calculation.
- Model comparison. Choose among linear, Stokes, and shallow-water theories by physical regime.
Clarity¶
A Stokes wave is a nonlinear periodic free-surface model, not any ocean wave or a single linear sinusoid. State depth, steepness, propagation, and expansion order before trusting a modeled elevation or velocity.
Manages Complexity¶
The expansion replaces the full nonlinear free-surface problem with successive, interpretable harmonic corrections. A finite order can yield usable kinematics without solving every field detail, but it also moves complexity into validity checks: steepness, depth, omitted currents, and breaking determine whether the approximation serves the intended calculation.
Abstract Reasoning¶
Specify wave and fluid conditions, compare depth with wavelength, and choose an expansion order matched to steepness. Use its kinematic output only after checking shallow-water and idealization limits.
Knowledge Transfer¶
The formal model transfers literally across sites only when the water-depth and wave-regime assumptions are restated and satisfied. The idea of perturbing a simple periodic solution with higher-order corrections travels to other physics, but those are not automatically Stokes surface waves. The broad parent wave pattern is propagation; the specialized child adds a particular nonlinear free-surface solution.
Relationships to Other Abstractions¶
Current abstraction Stokes wave Domain-specific
Parents (1) — more general patterns this builds on
-
Stokes wave is a kind of Wave Prime
A Stokes wave is a propagating surface-wave disturbance with nonlinear fluid-specific corrections.
Hierarchy path (1) — routes to 1 parentless root
- Stokes wave → Wave
Neighborhood in Abstraction Space¶
Stokes wave sits in a sparse region of the domain-specific corpus (60th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Geophysical Wave & Flow Parameters (11 abstractions)
Nearest neighbors
- Surface-wave inversion — 0.87
- Selberg zeta function — 0.85
- P-Laplacian — 0.84
- Volume viscosity — 0.84
- Eshelby's inclusion — 0.84
Computed from structural-signature embeddings · 2026-10-08