Significant Surface Heat Transfer Rate Enhancement and Scalar Transport under Secondary Instabilities of Steady Longitudinal Vorticity Elements in Boundary Layers.

Nonlinear wavy secondary instability of steady longitudinal vortices in boundary layer flow, characterized by the sinuous mode, give rise to skin friction well above the local turbulent boundary layer values$^{1}$ because the Reynolds stress contributes to fluctuation momentum flux towards the wall$^{1}$. Measurements of time-averaged surface heat transfer rates in air show a similar behavior$^{2}$. Similarity between dimensionless total streamwise velocity and dimensionless temperature is valid for the steady problem$^{3}$ for Prandtl number unity, but is hampered here by the presence of fluctuation streamwise-pressure gradient which has no counterpart in the scalar transport equation. Estimates for not-so-long waves relative to the local conductivity scale length show that the fluctuation streamwise pressure gradient is small, thus making similarity approximately possible. We conclude that the normal-to-wall fluctuation heat flux contributes to transport towards the wall, squashing the iso-temperature lines and increasing the temperature gradient thus make plausible a mechanism for the overshoot of surface heat transfer rate. $^{1}$ J.T.C. Liu and I.G Girgis, Abstract in ICTAM'04 Proceedings, Warsaw (2004). $^{2}$ L. Momayez, P. Dupont and H. Peerhossaini, Int. J. Heat Mass Transfer \textbf{47}, 3783 (2004). $^{3 }$J.T.C. Liu and A.S. Sabry, Proc. Royal Soc. \textbf{A432}, 1 (1991).