Capillary - gravity waves : a “ fixed - depth ” analysis

Europhysics Letters PREPRINT Capillary-gravity waves: a " fixed-depth " analysis. PACS. 68.10.-m – Fluid surfaces and fluid-fluid interfaces. PACS. 47.17.+e – Mechanical properties of fluids. Abstract. – We study the onset of the wave-resistance due to the generation of capillary-gravity waves by a partially immersed moving object in the case where the object is hold at a fixed immersion depth. We show that, in this case, the wave resistance varies continuously with the velocity, in qualitative accordance with recent experiments by Burghelea et al. Introduction. – The dispersive properties of capillary-gravity waves are responsible for the complicated wave pattern generated at the free surface of a still liquid by a disturbance moving with a velocity V greater than the minimum phase speed V c = (4gγ/ρ) 1/4 , where g is the gravity, γ is the surface tension and ρ the density of the fluid [1]. The disturbance may be produced by a small object partially immersed in the liquid or by the application of an external surface pressure distribution [2]. The waves generated by the moving perturbation propagate momentum to infinity and, consequently, the disturbance experiences a drag R called the wave resistance [3]. For V < V c the wave resistance is equal to zero since, in this case, no propagating long-range waves are generated by the disturbance [4]. A few years ago, it was predicted that the wave resistance corresponding to a surface pressure distribution symmetrical about a point should be discontinuous at V = V c [5]. More precisely, if F 0 is the the total vertical force exerted on the fluid surface, the wave resistance is expected to reach a finite value R c > 0 for V → V