Excitation of ship waves by a submerged object: new solution to the classical problem

Abstract

We have proposed a new method for solving the problem of ship waves excited on the surface of a non-viscous liquid by a submerged object that moves at a variable speed. As a first application of this method, we have obtained a new solution to the classic problem of ship waves generated by a submerged ball that moves rectilinearly with constant velocity parallel to the equilibrium surface of the liquid. For this example, we have derived asymptotic expressions describing the vertical displacement of the liquid surface in the limit of small and large values of the Froude number. The exact solution is presented in the form of two terms, each of which is reduced to one-dimensional integrals. One term describes the "Bernoulli hump" and another term the "Kelvin wedge." As a second example, we considered vertical oscillation of the submerged ball. In this case, the solution leads to the calculation of one-dimensional integral and describes surface waves propagating from the epicenter above the ball.

Submitted to Physical Review A

References in corpus (7)

• Ship waves in the presence of uniform vorticity
• What is the apparent angle of a Kelvin ship wave pattern?
• Mach-like capillary-gravity wakes
• Wake pattern and wave resistance for anisotropic moving objects
• Caustic graphene plasmons with Kelvin angle
• Scaling of far-field wake angle of non-axisymmetric pressure disturbance
• Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

Cited by in corpus (4)

• A hydrodynamic model approach to the formation of plasmonic wakes in graphene
• Kelvin wake pattern at small Froude numbers
• Kelvin-Froude wake patterns of a traveling pressure disturbance
• Membrane flutter induced by radiation of surface gravity waves on a uniform flow