The variance of convection velocity in the turbulent boundary layer and its effect on coherence length

Abstract

The Efimtsov model of coherence length and the Corcos cross spectrum model are commonly used to define the power spectra of the turbulent boundary layer near the wall. The models are useful for defining the pressure fields acting on structures such as aircraft fuselage and ship hulls as they move through fluid. In an effort to establish the validity of the models, the spectral definitions were used to synthesize time series data whose properties could then be compared to the actual data from which the model parameters were derived. Analysis of the synthesized time data indicated that the data contained coherence lengths longer than those specified in the models. The longer coherence lengths are shown to be related to the assumption of constant convection velocity that is fundamental to the Corcos model. A time domain technique is introduced by which the instantaneous convection velocity can be measured. Using this technique, statistics on the convection velocity for wall pressure data acquired during flight tests are shown to be normally distributed. Time data produced using a normally distributed convection velocity contains the specified coherence length, confirming that the assumption of constant convection velocity in the Corcos model was the source of the error. The coherence decay caused by convection velocity variance is shown to be Gaussian. A model is derived which divides the coherence decay into an exponential structural decay term and a Gaussian phase decay term. This is shown to be a good model for the coherence decay, except for frequencies around the peak in the power spectrum. The structural decay term is further divided into exponential and rectangular terms to represent inner layer and outer layer processes, respectively. The partitioned model is shown to correctly describe the coherence decay for the entire frequency band and provides a measure of the allocation of power between the inner and outer layer processes. It is concluded that the variance in the convection velocity has a significant effect on the decay of coherent power in the wall pressure of the turbulent boundary layer.