Characteristics of Turbulence Induced by Mechanical Waves in a Tank

Three components of current velocity u i ( i = x , y , z ) induced by mechanical waves generated by a wave maker are measured in a wind-wave tank for three variants of dominant frequencies f 0 and a set of significant wave heights H s for each frequency. To study the degree of anisotropy of wave-induced turbulence and estimate its dissipation rate ε, standard deviations (SDs) σ i and frequency spectra S i ( f ) are calculated for the components of the measured currents. By the proposed filtering procedure, the characteristics σ iF and S iF ( f ) are calculated for the turbulent components of currents in which wave motions are filtered. It is shown that the SDs σ i exhibit a strong anisotropy the degree of which varies with the variation of the wave parameters. For the turbulent components of the currents, the relation σ xF ≈ σ yF ≥ (1.5–3)σ zF holds, which suggests a significant anisotropy of turbulence in the cases of horizontal and vertical motions. A semiphenomenological approach provides an analytical representation for σ iF in terms of wave parameters. The spectra of the turbulent components for the horizontal velocity components S xF ( f ) and S yF ( f ) in the frequency range f > 2 f 0 are similar in shape and intensity and, as a rule, are characterized by a power-law decay in intensity with exponent –1.6 ± 0.1. In the same frequency range, the intensity of the spectra of the vertical velocity component S zF ( f ) is an order of magnitude lower and decreases according to the power law with exponent –2.0 ± 0.1. The power-law regions are interpreted as analogs of the Kolmogorov spectra due to the up-frequency energy transfer from orbital motions of mechanical waves. A phenomenological model of the spectrum with the decay law –2 is proposed, which makes it possible to determine the dissipation rate ε of the kinetic energy of turbulence from the intensity of the power-law region of S z ( f ). Estimates of ε are obtained and its parameterization is constructed. Discussion and possible interpretation of the results are presented.