Numerical study of the effect of surface wave on turbulence underneath. Part 2. Eulerian and Lagrangian properties of turbulence kinetic energy

The effect of the rapid distortion of a surface wave on the kinetic energy of turbulence underneath is studied based on the simulation data of Part 1 (Guo & Shen, J. Fluid Mech., vol. 733, 2013, pp. 558-587). In the Eulerian frame, Reynolds normal stresses, which contribute to turbulence kinetic energy, are found to vary with the wave phase. An analysis of their budgets shows that their variation is dominated not only by the normal production term representing the wave straining effect on wave-turbulence energy exchange, but also by pressure effects including the pressure-strain correlation and pressure transport terms. In the Lagrangian frame, the net energy transfer from the wave to turbulence is analysed. It is found to be mainly contributed by the mean Lagrangian effect and the correlation between the Lagrangian fluctuations of the wave and turbulence; the former plays a major role in the overall wave energy dissipation, while the latter is associated with the viscous effect of the wave surface and is appreciable in the near-surface region. Models for various terms in wave-turbulence energy flux are discussed. The decay time scale of swells in oceans estimated from our simulations compares well with the results in the literature.