Three-dimensional effects in quasi two-dimensional free surface scalar experiments

Abstract

The disagreement between free surface scalar experiments and the two-dimensional (2D) transport equation is discussed. An effective diffusivity coefficient, $\kappa _{{\rm eff}}$, is introduced and defined as the quotient between variance decay and mean gradient square. In all the experiments performed, $\kappa _{{\rm eff}}$ is significantly larger than the scalar diffusivity, $\kappa$. Three mechanisms are identified as responsible for the differences between the quasi two-dimensional (Q2D) experiments and the 2D behaviour of a diffusive scalar. These are the vertical velocity gradients, the free surface divergence and the gravity currents induced by the scalar. These mechanisms, which affect the diffusive term in the 2D transport equation for large Péclet number ($Pe\gg 1$), are evaluated for steady and time-dependant laminar flows driven by electromagnetic body forces.