Free-surface turbulent wake behind towed ship models: Experimental measurements, stability analyses and direct numerical simulations

We combine experimental, theoretical and numerical efforts to investigate the turbulent wake far behind a surface ship at model scales. Experimental measurements using digital particle image velocimetry (DPIV) are performed for the wakes of three towed hulls with beam-to-draught ratios b/d = 1, 2, 6. Based on model speed and beam, the Reynolds and Froude numbers are O(10³) and O(10^-2) respectively. Distinct surface features associated with persistent surface-normal vorticity have been identified, which are characterized by large-scale meandering structures. Both lateral and longitudinal scales of the meandering are quantified, with the former found to increase as b/d decreases and the latter independent of b/d. Based on measurements at multiple horizontal and vertical planes, profiles of the mean flow and fluctuation intensity for each velocity component are obtained. To understand the turbulence transition mechanism, an Orr-Sommerfeld stability analysis (OS) is formulated for the wake flow with free-surface boundary conditions, and solved by using a fourth-order finite-difference scheme. Unstable modes antisymmetric to the wake centre-plane are identified. Consistent with the experimental results, the growth rates of unstable modes increase substantially as b/d decreases, while the dependence of meandering wavelengths on b/d is found to be weak. Finally, we perform direct numerical simulation (DNS) of Navier-Stokes equations for the wake flow. The growth rates of unstable modes agree well with the predictions by OS analysis. Compared with experiments, DNS accurately captures the surface-normal vorticity signatures, the meandering features, as well as statistics of turbulence intensity. We also obtain from DNS a detailed description of enstrophy, turbulence length scales, and vortex structures for the wake flow.