THE ORIGINS OF WATER WAVE THEORY

By A. Craik. 2004

308 citations recorded by the source corpus.

Subfields: Oceanography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dea1d086e8f3ccd7a9e87952bb13c964b250eb07

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In Oceanography

In Statistical and Nonlinear Physics

Citations in the corpus

Analyticity of periodic traveling free surface water waves with vorticity (2011, background): “The real analyticity of each streamline beneath the free surface holds even if the vorticity is only Hölder continuously differentiable.”
Water wave optimization: A new nature-inspired metaheuristic (2015, background): “Historically, the first to attempt a theory of water waves subjected to gravity force, surface tension, and other forces, traces back the work by Newton in 1687, against hydrostatics by Archimedes in the 3rd century BC [24].”
Pressure beneath a Stokes wave (2009, background): “Within the linear theory, which is suitable as an approximation for waves of small amplitude, such regular waves are considered to be of sinusoidal shape, as pioneered by Airy [1] (see also the discussion in [9]).”
The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations (2007, background): “Until the second half of the 20’th century, the study of water waves was confined almost exclusively to linear theory [12].”
Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity (2005, background): “1 Linear Theory When the standing water-wave problem is linearized about a trivial solution, we find a linear boundary-value problem, first derived satisfactorily by Poisson in 1818, although Laplace in 1776 came very close (see [10]): ∂(2)φ ∂x2 + ∂(2)φ ∂y2 = 0, x, t ∈ R, y < 0, (1.”
The trajectories of particles in Stokes waves (2006, background): “However, the only known explicit solution to the governing equations (1)–(5) for water waves, discovered by Gerstner in 1809 [16] and rediscovered by Rankine in 1863 [28] (see the historical survey [ 12 ]), has the property that all particles move on circles; Gerstner’s wave is in water of infinite ”