Numerical study of the effect of surface waves on turbulence underneath. Part 1. Mean flow and turbulence vorticity

• Published in: Journal of fluid mechanics Vol. 733; pp. 558 - 587
• Main Authors: Guo, Xin, Shen, Lian
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.10.2013
• Subjects: Boundary conditions; Computational fluid dynamics; Exact sciences and technology; Flow velocity; Fluid dynamics; Fluid flow; Fluid mechanics; Free surfaces; Fundamental areas of phenomenology (including applications); Gravity waves; Hydrodynamic waves; Mathematical analysis; Navier-Stokes equations; Numerical analysis; Physics; Propagation; Surface waves; Turbulence; Turbulence simulation and modeling; Turbulent flow; Turbulent flows, convection, and heat transfer; Vorticity; Wave propagation; turbulent flows; wave–turbulence interactions; waves/free-surface flows; Turbulent flow; Surface waves; Digital simulation; Vorticity; Free surface flow; Modelling; Interactions; Turbulence structure
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2013.451

Direct numerical simulation is performed to study the effect of progressive gravity waves on turbulence underneath. The Navier–Stokes equations subject to fully nonlinear kinematic and dynamic free-surface boundary conditions are simulated on a surface-following mapped grid using a fractional-step scheme with a pseudo-spectral method in the horizontal directions and a finite-difference method in the vertical direction. To facilitate a mechanistic study that focuses on the fundamental physics of wave–turbulence interaction, the wave and turbulence fields are set up precisely in the simulation: a pressure-forcing method is used to generate and maintain the progressive wave being investigated and to suppress other wave components, and a random forcing method is used to produce statistically steady, homogeneous turbulence in the bulk flow beneath the surface wave. Cases with various moderate-to-large turbulence-to-wave time ratios and wave steepnesses are considered. Study of the turbulence velocity spectrum shows that the turbulence is dynamically forced by the surface wave. Mean flow and turbulence vorticity are studied in both the Eulerian and Lagrangian frames of the wave. In the Eulerian frame, statistics of the underlying turbulence field indicates that the magnitude of turbulence vorticity and the inclination angle of vortices are dependent on the wave phase. In the Lagrangian frame, wave properties and the accumulative effect on turbulence vorticity are studied. It is shown that vertical vortices are tilted in the wave propagation direction due to the cumulative effects of both the Stokes drift velocity and the correlation between turbulence fluctuations and wave strain rate, whereas for streamwise vortices, these two factors offset each other and result in a negligible tilting effect.