Three-dimensional waves on the surface of a viscous fluid |
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Authors: | A. A. Abrashkin |
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Affiliation: | (1) Centre for Numerical Modelling and Process Analysis, University of Greenwich, Park Row, London, SE10 9LS, United Kingdom;(2) National Physical Laboratory, Teddington, Middlesex, TW11 0LW, United Kingdom |
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Abstract: | The study of the effect of viscosity on the propagation of surface waves has traditionally been confined to the consideration of plane (two-dimensional) waves [1, 2]. So far the effect associated with taking the transverse modulation of the wave profile into account have not been studied. In what follows, a solution is constructed and analyzed for linear three-dimensional periodic waves in an infinitely deep fluid. Their distinguishing property is the presence of a vorticity in the direction of propagation. An expression for the average (over the wavelength) velocity of horizontal particle drift is found in the quadratic approximation in the small wave steepness. |
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Keywords: | water waves viscosity Lagrangian coordinates |
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