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- W2024677683 abstract "The optical effects of gently deformed water surfaces are studied analytically for three examples: a straight floating edge, a small floating sphere and a dissipating free vortex. The surface deformation is obtained in the first two cases by solving Laplace's surface tension equation, and in the third case from the Bernoulli and Coriolis effects of a velocity field obtained from the Navier-Stokes equation. At small depths, a straight floating edge gives a normal shadow decorated by Fresnel fringes, but at greater depths the illuminated region is bounded by a caustic, giving a bright-edged shadow decorated with Airy-function fringes. A small floating sphere gives an approximately paraboloidal caustic decorated with bright Airy-function fringes (produced by the curved water surface), within which are faint Bessel-function fringes (produced by the ring of water bounding the sphere). A free vortex gives a caustic consisting of two roughly cylindrical sheets joined at a cusp-edged ring, whose section at a given depth consists of two concentric caustics bounding a bright annulus. The sphere and vortex theories are illustrated by experiments. All analytical results are expressed as universal functions whose dimensionless variables are related to the physical variables by scaling laws." @default.
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- W2024677683 date "1983-01-01" @default.
- W2024677683 modified "2023-10-17" @default.
- W2024677683 title "The Shadows of Floating Objects and Dissipating Vortices" @default.
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- W2024677683 doi "https://doi.org/10.1080/713821046" @default.
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