Measurements of the flow structure and turbulence within a ship bow wave

Particle image velocimetry measurements around a 7-m-long ship model focus on the flow within the attached liquid sheet, upstream of the point at which the bow wave separates from the model. Performed in a towing basin at a Reynolds number of $1.6×107$ and a Froude number of 0.30 (both based on ship length L), these measurements expand upon previous work by examining the bow wave flow at a higher Reynolds number than before. Further, the increased scale of the model and the flow allows finer observation of the flow structure. Individual vector maps show a growing region of negative vorticity originating at the toe of the wave. This shear layer, which first appears at $X/L=0.0619,$ penetrates further into the wave as $X/L$ increases but curves upward to remain close to the forward face. Positive vorticity appears on the top of the wave and at the ship boundary. Repeated runs at $X/L=0.0690$ produce mean flow and turbulent stress data for this three-dimensional spilling wave. Normal and shear Reynolds stresses are concentrated at the forward face of the wave in the same region as the negative vorticity. The magnitudes of the Reynolds stresses are consistent with theoretical expectations, with maximum $vrms′$ and $wrms′$ attaining 16% and 11% of the local fluid speed, respectively. The correlation coefficient of $−v′w′$ is between 0.5 and 0.7 in the turbulent region, indicating the presence of coherent structures. Although the Reynolds stresses penetrate deeply into the bow wave, turbulent production is concentrated in a small region at the toe. Changing from a fixed coordinate system to a system that shifts with the free surface causes the Reynolds stresses and turbulent production to form thinner regions closer to the free surface with no reduction in intensity. Calculations of the three-dimensional velocity on the free surface in the ship frame of reference indicate that it turns sharply at the toe of the bow wave and that the forward face forms a three-dimensional region of separated flow. Energy losses of 30% are experienced at the toe.