Third-order transport and nonlocal turbulence closures for convective boundary layers

The turbulence closure problem for convective boundary layers is considered with the chief aim to advance the understanding and modeling of nonlocal t ransport due to large-scale semiorganized structures. The key role here is played by third-order moments (fluxes of fluxes). The problem is treated by the example of the vertical turbulent flux of potential temperature. An ov erview is given of various schemes ranging from comparatively simple counte rgradient-transport formulations to sophisticated turbulence closures based on budget equations for the second-order moments. As an alternative to con ventional "turbulent diffusion parameterization" for the flux of flux of po tential temperature, a "turbulent advection plus diffusion parameterization " is developed and diagnostically tested against data from a large eddy sim ulation. Employing this parameterization, the budget equation for the poten tial temperature flux provides a nonlocal turbulence closure formulation fo r the Aux in question. The solution to this equation in terms of the Green function is nothing but an integral turbulence closure. In particular cases it reduces to closure schemes proposed earlier, for example, the Deardorff counter-gradient correction closure, the Wyngaard and well transport-asymm etry closure employing the second derivative of transported scalar, and the Berkowicz and Prahm integral closure for passive scalars. Moreover, the pr oposed Green-function solution provides a mathematically rigorous procedure for the Wyngaard decomposition of turbulence statistics into the bottom-up and top-down components. The Green-function decomposition exhibits nonline ar vertical profiles of the bottom-up and top-down components of the potent ial temperature flux in sharp contrast to universally adopted linear profil es. For modeling applications, the proposed closure should be equipped with recommendations as to how to specify the temperature and vertical velocity Variances and the vertical velocity skewness.