WHEN DO WAVES BECOME TURBULENT?

Abstract

Babanin and Haus (2009) recently presented evidence of high levels of turbulence induced by steep non-breaking waves. They proposed a Reynolds-like threshold wave parameter (a2ω/ν=3000, a wave amplitude, ω wave angular frequency, ν water viscosity) for the spontaneous occurrence of turbulence beneath surface waves. This contradicts the common assumed basis of existing irrotational wave theories and their classical experimental validation. Many laboratory wave experiments were carried out in the early 1960's (e.g. Wiegel, 1964). In those experiments no evidence of turbulence was reported and steep waves behaved as predicted by the high order irrotational wave theories within the accuracy of the theories and experimental techniques at the time. The spontaneous generation of turbulence under waves can have serious consequences for wave modelling, where the irrotational flow assumption has secured its place in engineering design. This contribution describes unique flow visualisation experiments for large scale steep non-breaking waves using conventional dye techniques in the wave boundary layer extending above the wave trough level. The measurements showed no evidence of turbulent mixing for waves up to a2ω/ν=7000. There is presently no evidence that water waves become spontaneously turbulent (up a2ω/ν=7000) except within the bed boundary layers, under wind forcing or at breaking. Excellent agreement was found with higher order irrotational theories. Orbital velocities, Stokes drift and Stokes coefficients were measured and compared with theoretical values, suggesting that conventional theories underestimate unforced monochromatic wave non-linearity, although the corrections remain small.