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Giménez Curto 1985
Giménez Curto, L.A. (1985). On the motion of very small bodies in water waves. Journal of Geophysical Research 90: doi: 10.1029/JC090iC01p01127. issn: 0148-0227.

The equation of motion of a small isolated body that moves in translational motion through a fluid which is itself in unsteady and nonuniform motion is established on the assumption that actual forces acting on the body can be split up in gravity; a drag component, which accounts for viscosity and vorticity effects; and an inertial force with the same formal expression as the force that would act on the body if the flow were irrotational (this force is obtained for an unrestricted flow in the appendix). By assuming that flow acceleration is small compared with that due to gravity and that &egr;=wfω/g≪1, which defines what here is called ''very small body'' (wf being still water terminal fall velocity, ω angular frequency, and g acceleration due to gravity), some approximate equations are obtained using a perturbation scheme. Subsequently, a simple expression is derived for the leading order approximation of the velocity of very small bodies in water waves. This solution shows that, at least under certain conditions, the hypothesis of some delay time (Kennedy and Locher, 1982) is sound, although this time is not the same, in general, for the vertical component as for the horizontal one. From a practical point of view, owing to the assumptions involved in this derivation, the appliability of the solution must be restricted to suspended sediment particles in low concentrations and to reasonably well-behaved wave conditions, including superposition of linear waves (particularly standing waves and irregular wave fields), slightly nonlinear waves, and weak currents superimposed on waves. The direct application of the results of this investigation to flows with a high degree of turbulence intensity must be precluded because of the existence of large flow accelerations.

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Journal of Geophysical Research
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