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Water, air and heat

Strange Water

Four things water does, each on its own solver, drawn in 3D and held to the physics by tests. The rogue wave is linear water-wave theory summed exactly: the tests hold its dispersion law to the deep and shallow limits and see the focused train make a wave more than twice the significant height of the 4 m sea round it, the definition of a rogue wave. The wake is the steady linear wake of a pressure patch on deep water, solved with one two-dimensional Fourier transform: the tests see its highest waves within 1.2 degrees of Kelvin's 19.47 at a Froude number of 0.6, and narrowing close to 1 over the speed past Froude 1, as Rabaud and Moisy found in 2013. The solitons are the Korteweg-de Vries equation solved spectrally: a single wave keeps its height and its exact speed, and two come out of their collision at their own heights, shifted as the exact solution says. The channel is the shallow water equations solved by a shock-capturing method: the tests hold a dam break to Stoker's exact solution and a hydraulic jump to Belanger's depth. Ours: every size and speed, a smooth hull, the wake's small damping, and no friction anywhere.