Wave Resistance for Capillary Gravity Waves: Finite Size Effects

Abstract

We study theoretically the capillary-gravity waves created at the water-air interface by an external surface pressure distribution symmetrical about a point and moving at constant velocity along a linear trajectory. Within the framework of linear wave theory and assuming the fluid to be inviscid, we calculate the wave resistance experienced by the perturbation as a function of its size (compared to the capillary length). In particular, we analyze how the amplitude of the jump occurring at the minimum phase speed $c_{\min }=(4g\gamma /\rho {)}^{1/4}$ depends on the size of the pressure distribution ($\rho$ is the liquid density, $\gamma$ is the water-air surface tension, and $g$ is the acceleration due to gravity). We also show how for pressure distributions broader than a few capillary lengths, the result obtained by Havelock for the wave resistance in the particular case of pure gravity waves (i.e., $\gamma =0$) is progressively recovered.

References in corpus (2)

• On capillary-gravity waves generated by a slow moving object
• Capillary-Gravity Waves Generated by a Sudden Object Motion

Cited by in corpus (9)

• Ship wakes: Kelvin or Mach angle?
• Kelvin wake pattern at large Froude numbers
• Mach-like capillary-gravity wakes
• Drag on a partially immersed sphere at the capillary scale
• Wake and wave resistance on viscous thin films
• Capillary-Gravity Waves on Depth-Dependent Currents: Consequences for the Wave Resistance
• Wave drag on asymmetric bodies
• Hysteretic wave drag in shallow water
• Unsteady Wave Drag on a Disturbance Moving Along an Arbitrary Trajectory