Abstract

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 f₀ 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 > 2f₀ 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.

中文翻译：

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坦克中机械波引起的湍流特性

摘要

由风波发生器产生的机械波感应的当前速度u _i（i = x，y，z）的三个分量在风波罐中测量了三个主频率f ₀和一组重要波高H _{s的变化。}每个频率。为了研究波引起的湍流各向异性程度和估计它的耗散率ε，标准偏差（SDS）σ_我和频谱š_我（˚F）是所测量的电流的分量来计算。通过提出的滤波程序，特征_σiF对于滤波了波动的电流的湍流分量，计算S _iF（f）和S _iF（f）。结果表明，在SDSσ_我表现出强的各向异性，其与波参数的变化而变化的程度。对于电流的湍流部件，该关系σ _xF的≈σ _YF ≥（1.5-3）σ _ZF成立，这表明湍流的在水平和垂直运动的情况下一个显著各向异性。甲semiphenomenological方法提供了σ的分析表示_的iF中的波参数方面。水平速度分量S _xF（f）和S _yF（f）在f > 2 f ₀的频率范围_内在形状和强度上相似，通常以强度的幂律衰减为特征，指数为–1.6±0.1。在相同频率范围内，垂直速度分量S _zF（f）是一个较低的数量级，并且根据幂定律以–2.0±0.1的指数减小。由于来自机械波轨道运动的高频能量转移，幂律区域被解释为Kolmogorov谱的类似物。提出了具有衰减定律–2的频谱现象学模型，这使得可以根据S _z（f）的幂律区域的强度确定湍流动能的耗散率ε 。获得ε的估计值并构建其参数化。提出了对结果的讨论和可能的解释。