New third-order moments for the convective boundary layer

Turbulent convection is inherently a nonlocal phenomenon and a primary condition for a successful treatment of the convective boundary layer is a reliable model of nonlocality. In the dynamic equations governing the convective flux, the turbulent kinetic energy, etc., nonlocality is represented by the third-order moments (TOMs). Since the simplest form, the so-called down gradient approximation (DGA), severely underestimates the TOMs (up to an order of magnitude), a more physical model is needed. In 1994, an analytical model was presented that was derived directly from the dynamical equations for the TOMs. It considerably improved the DGA but was a bit cumbersome to use and, more importantly, it was based on the quasi-normal (QN) approximation for the fourth-order moments. Here, we present a new analytic expression for the TOMs that is structurally simpler than the 1994 expression and avoids the QN approximation. The resulting fit to the LES data is superior to that of the 1994 model.