| A new turbulence closure scheme, called instability wave modeling, is applied to the two-dimensional, incompressible turbulent wake behind a flat plate. The turbulence at a pont in the wake is assumed to be dominated by fluctuations associated with large-scale coherent structures. It is proposed that these structures may be represented by evolving instability waves.;The streamwise prediction of the mean flow properties is found to agree well with experiments. The centerline velocity and the wake half-width are found to increase and agree with measurements. The mean velocity profiles are also well predicted. The frequency and wavenumber variation of the large-scale structures are also predicted. They both also decrease as expected. Thus the streamwise wavelength and the phase velocity of the large-scale structure or instability wave also increase. A slight deviation in magnitude is found between the predicted Reynolds stress distribution and measurements. Only qualitative agreement is found between the local prediction of the turbulence intensities and measurements. It is proved that the use of all unstable eigenmodes, rather than the use of the single most unstable mode, would improve the local predictions.;Generally this approach has been found to be very useful in extending our understanding of the modelling of large-scale coherent structures in free shear flows. The model uses a minimum of empiricism and does not require excessive computation time. This analysis provides the first full closure scheme based on wave modeling.;The Reynolds stress term in the governing mean flow equation is modeled by a local instability analysis. Since this provides only a local representation, an energy integral method is used. This enables a connection to be made between the local turbulence properties, such as the Reynolds stress distribution, and their streamwise variation. An appropriate normalization of the local eigenfunction enables the amplitude of the instability wave to be defined consistently. An implicit, finite-difference scheme, using a normalized streamfunction coordinate system, is used for the solution of the parabolic turbulent boundary layer equations. |
