Wave Resistance for Stochastic Motion at Interfaces

Maxence Arutkin; Shlomi Reuveni; Elie Raphael

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arXiv · 2606.08732

Wave Resistance for Stochastic Motion at Interfaces

Maxence Arutkin·Shlomi Reuveni·Elie Raphael

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Abstract

Wave resistance is the drag generated by the wave radiation that a source moving at a fluid interface sustains. Under stochastic trajectories, the mean drag is controlled by the ensemble-averaged surface profile built from the trajectory history. We show that the result is a finite resistance below the deterministic radiation threshold and a regularization of the singular response at the minimum phase velocity of the capillary-gravity waves. We derive explicit scaling laws for drifted Brownian trajectories, including a universal high-diffusivity decay. For drifted L\'evy flight, we find the mean wave resistance in closed-form, extending wave-drag theory to non-Gaussian trajectories.

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Maxence Arutkin, Shlomi Reuveni, Elie Raphael. 2026-06-07. Wave Resistance for Stochastic Motion at Interfaces. https://arxiv.org/abs/2606.08732

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