On prediction of the turbulent flow over a wavy boundary

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Abstract
The importance of fluctuating turbulent stresses in the flow over a wave is examined. It is shown that anisotropic stresses, which are most likely to be turbulent Reynolds stresses, are essential to the process of energy flow to the wave. Two fundamentally different methods of predicting fluctuating turbulent Reynolds stresses are examined. One method makes use of a phenomenological closure of the conservation equation for the turbulent Reynolds stresses and is similar to the turbulent boundary-layer calculation scheme of Bradshaw, Ferriss & Atwell (1967). The second method is based on the assumption that the turbulent stresses are determined by the recent history of velocity shear experienced by a fluid parcel and results in a viscoelastic constitutive relation for the turbulence; in the limit of shortest’ memory’ this relation becomes the eddy viscosity model proposed by Hussain & Reynolds (1970). Comparison of predicted and measured values of surface pressure indicates that the eddy viscoelasticity model can explain measured pressure distributions but the comparison is not conclusive. Suggestions for further measurements are made.