A Convection Reaction Diffusion (CRD) Equation Model for 2-d Transition Pressure Fluctuation Behavior

Abstract

[Abstract] The focus of this research is the derivation of a model for turbulent spot generation in a laminar-turbulent transitioning boundary layer. This analysis utilizes a phenomenological differential equation (convection-reaction-diffusion; CRD) model, extended from Fowler and Howell’s [1] transitional pipe flow model to be valid for flat plate boundary layer flow. The major quantities of interest are the period/frequency and amplitude associated with the turbulent spots which then yield estimates of the associated turbulent intermittency and fluctuating velocity field. Solving the pressure Poisson equation ultimately gives the pressure fluctuation behavior. Pressure results are presented in terms of the power-spectral-density. Comparison of these quantities with available experimental data suggests that the model is both viable and practically useful. Finally we note that the analyses described here are marked by a rather high level of physical and mathematical approximation. Though perhaps inherently unsatisfying, we believe without significant freedom for approximation, there is very little potential for obtaining useable/engineering results to this problem