On the structure of bow waves on a ship model

Abstract

Particle image velocitmetry (PIV) measurements and free-surface visualizations around a ship model focus on the flow within the attached liquid sheet, upstream of the point at which the bow wave separates from the model, the origin and structure of the bow wave and the flow downstream of the wave crest. The measurements are performed at Reynolds numbers ranging between 2.8×10⁶ and 7.4×10⁶ and Froude numbers between 0.17 and 0.45 (both are based on ship length L). Representative velocity and vorticity distributions at Fr_L=0.28 and Fr_L=0.45 demonstrate the characteristic structure of mild and steep waves, respectively. Very close to the bow the attached sheet is thin and quite unsteady. With increasing distance from the nose the sheet becomes thicker and its development involves considerable vorticity production. In the mild case this vorticity is originated at the free surface, whereas in the steep wave case, boundary layer separation occurs on the model, which also transports vorticity into the sheet. This vorticity and its associated induced lateral flow remain near the model downstream of the bow wave. By calculating the acceleration component tangent to the free surface of the sheet it is shown that the peaks in the near-surface vorticity appear in regions with high viscous flux of vorticity from the surface. Formation of a bow wave also involves considerable production of vorticity. Similar to two-dimensional breakers, the primary origin of this vorticity is at the toe of the breaker. However, unlike the two-dimensional cases, the region containing vorticity in the ship wave does not appear as an extended shear layer. Instead, this vorticity is convected out of the plane of the laser sheet in a series of distinct vortex filaments. The ship wave also has powerful counter-rotating vorticity concentrated near the wave crest that has been observed in two-dimensional waves, but not of the same strength. Breaking becomes weaker, i.e. there is less vorticity production, with increasing distance from the model, but it persists even at the ‘tail’ of the bow wave. The sites of vorticity entrainment of both signs are consistent with the computed near-surface acceleration. Estimates of the three-dimensional velocity distribution and head losses within the wave are also provided.