Dissipation scaling in constant-pressure turbulent boundary layers

We use previous direct numerical simulations and experimental data to investigate the streamwise and wall-normal evolution of the dissipation parameter $C_{\varepsilon}$ (namely the dissipation rate scaled by appropriate powers of the local turbulent kinetic energy and integral length scale) in the outer region of spatially evolving turbulent boundary layers. For $Re_{\theta}\geq 10,000$, $C_{\varepsilon}$ is essentially constant in the streamwise direction, but varies measurably in the wall-normal direction. For lower $Re_{\theta}$, however, $C_{\varepsilon}$ changes in both directions. The constancy of $C_{\varepsilon}$ is a central assumption of turbulence models based on the eddy viscosity concept and so they would inadequately represent wall bounded flows as they evolve spatially, a scenario that is common in engineering and atmospheric science applications. Accounting for the dependence of $C_{\varepsilon}$ on the local $Re_{\lambda}$ provides a means for possibly improving such models.