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

Abstract

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.

On helical behavior of turbulence in the ship wake

“…Experimental data on turbulent characteristics of surface ship wakes are limited. Only in few laboratory experiments (Patel, Sarda, 1990, Hoekstra, Ligtelijn, 1991, Benilov et al, 2000, Shen, 2002 certain turbulent parameters of the wake, including spectral characteristics, were measured. The ship-wake turbulence is still well detectable even in the far wake, where the Kolmogorov inertial range can be identified (Benilov et al, 2000).…”

“…Main vorticity fluctuations produced with fluctuations of lateral velocity are located at a certain distance from the surface (Shen et al, 2002) and amount to . On the other hand, under experimental conditions (Peltzer et al, 1992) with the wind speed not exceeding 5 m/s, the value of for background turbulence should have amounted to 3 2 6 / 10 3 2 ~s m (Soloviev and Lukas, 2006).…”

“…1. Measurements of short waves suppression in ship wakes were conducted and compared with SAR images of similar wakes in sevaral studies (Munk et al, 1987;Milgram et al, 1993a, b;Reed et al, 2002;Shen et al, 2002 ). They have shown that the phenomenon can be explained by the suppression of short sea waves in the wake, said waves being responsible for radar backscattering associated with a brighter background.…”

“…Main vorticity fluctuations produced with fluctuations of lateral velocity are located at a certain distance from the surface(Shen et al, 2002) and amount to…”

Wake behind a three-dimensional dry transom stern. Part 2. Analysis and modelling of incompressible highly variable density turbulence

“…Until recently, relatively little was understood about the turbulent nature of this flow. Many experiments and simulations provide insight into the mean flow and turbulent nature of real ship wakes in the absence of entrainment (Sotiropoulos & Patel 1995;Gui, Longo & Stern 2001;Kim, Van & Kim 2001;Olivieri et al 2001;Shen, Zhang & Yue 2002;Larsson, Stern & Betram 2003). Part 1 provides a detailed review of the known air entrainment characteristics and surface features of transom wake flows.…”