The drift velocity U0 at the interface between two homogeneous turbulent fluids of arbitrary relative densities in differential mean motion is considered. It is shown that an analytical expression for U0 follows from the classical scaling for these flows when the scaling is supplemented by standard turbulent universality and symmetry assumptions. This predicted U0 is the weighted mean of the free-stream velocities in each fluid, where the weighting factors are the square roots of the densities of the two fluids, normalized by their sum. For fluids of nearly equal densities, this weighted mean reduces to the simple mean of the free-stream velocities. For fluids of two widely differing densities, such as air overlying water, the result gives U0 ≈ αV∞, where α ≪ 1 is the square root of the ratio of the fluid densities, V∞ is the free-stream velocity of the overlying fluid, and the denser fluid is assumed nearly stationary. Comparisons with two classical laboratory experiments for fluids in these two limits and with previous numerical simulations of flow near a gas–liquid interface provide specific illustrations of the result. Solutions of a classical analytical model formulated to reproduce the air–water laboratory flow reveal compensating departures from the universality prediction, of order 15% in α, including a correction that is logarithmic in the ratio of dimensionless air and water roughness lengths. Solutions reproducing the numerical simulations illustrate that the logarithmic correction can arise from asymmetry in the dimensionless laminar viscous sublayers.

中文翻译：

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两种均质流体界面处的湍流普适性和漂移速度

考虑微分平均运动中任意相对密度的两种均匀湍流流体之间界面处的漂移速度U0。结果表明，当标度由标准湍流普遍性和对称性假设补充时，U0 的解析表达式遵循这些流动的经典标度。这个预测的 U0 是每种流体中自由流速度的加权平均值，其中加权因子是两种流体密度的平方根，通过它们的总和进行归一化。对于密度几乎相等的流体，该加权平均值将简化为自由流速度的简单平均值。对于两种密度差异很大的流体，例如空气覆盖在水面上，结果给出 U0 ≈ αV∞，其中 α ≪ 1 是流体密度比的平方根，V∞ 是上覆流体的自由流速度，假设密度较大的流体几乎是静止的。与这两个限制中流体的两个经典实验室实验以及先前对气液界面附近流动的数值模拟的比较提供了结果的具体说明。为重现空气-水实验室流量而制定的经典分析模型的解决方案揭示了与普遍性预测的补偿偏差，α 为 15%，包括对无量纲空气和水粗糙度长度比值的对数校正。再现数值模拟的解决方案表明，对数校正可能源于无量纲层流粘性子层的不对称性。与这两个限制中流体的两个经典实验室实验以及先前对气液界面附近流动的数值模拟的比较提供了结果的具体说明。为重现空气-水实验室流量而制定的经典分析模型的解决方案揭示了与普遍性预测的补偿偏差，α 为 15%，包括对无量纲空气和水粗糙度长度比值的对数校正。再现数值模拟的解决方案表明，对数校正可能源于无量纲层流粘性子层的不对称性。与这两个限制中流体的两个经典实验室实验以及先前对气液界面附近流动的数值模拟的比较提供了结果的具体说明。为重现空气-水实验室流量而制定的经典分析模型的解决方案揭示了与普遍性预测的补偿偏差，α 为 15%，包括对无量纲空气和水粗糙度长度比值的对数校正。再现数值模拟的解决方案表明，对数校正可能源于无量纲层流粘性子层的不对称性。为重现空气-水实验室流量而制定的经典分析模型的解决方案揭示了与普遍性预测的补偿偏差，α 为 15%，包括对无量纲空气和水粗糙度长度比值的对数校正。再现数值模拟的解决方案表明，对数校正可能源于无量纲层流粘性子层的不对称性。为重现空气-水实验室流量而制定的经典分析模型的解决方案揭示了与普遍性预测的补偿偏差，α 为 15%，包括对无量纲空气和水粗糙度长度比值的对数校正。再现数值模拟的解决方案表明，对数校正可能源于无量纲层流粘性子层的不对称性。