A New Second-Order Turbulence Closure Scheme for the Planetary Boundary Layer

Assessment of heat flux turbulence models for flows dominated by buoyancy effects

“…5b, the counter-gradient term γ θ , Eq. (15), is compared with those reported in Abdella and McFarlane (1997). In a larger portion of the mixed layer, all three γ θ formulations exhibit good agreement.…”

“…(12), as a sum of the gradient and nongradient (buoyant) terms, can be expressed in a frequently used form (14) where eddy diffusivity K H and the nongradient (buoyant) correction γ θ are given by (15) This formulation incorporates models of all existing components in the fluctuating pressure-temperature gradient correlation term, Φ θi , but neglects, as in Deardorff's approach, the contribution of the transport term in the heat-flux equation. None of the existing formulations (e.g., Deardorff, 1972;Holtslag and Moeng, 1991;Abdella and McFarlane, 1997;Zilitinkevich et al, 1999) incorporates so-called wall-induced pressure reflection effects. Both Canuto et al (1994) and Zilitinkevich et al (1999) have emphasized the necessity for more complete modelling of the nonlocal fluctuating pressure effects to improve models' prediction capabilities of both second-and third-order moments.…”

“…Both Canuto et al (1994) and Zilitinkevich et al (1999) have emphasized the necessity for more complete modelling of the nonlocal fluctuating pressure effects to improve models' prediction capabilities of both second-and third-order moments. In the recent proposals (e.g., Holtslag and Moeng, 1991;Abdella and McFarlane, 1997;Zilitinkevich et al, 1999), turbulent transport of the turbulent heat flux plays a key role. These authors have applied different physical arguments in deriving models which distinguish between the so-called bottom-up and top-down diffusion processes.…”

“…Such a counter-gradient heat transport, which is an essential feature of CBL, cannot be reproduced by the isotropic eddy diffusivity models (Deardorff, 1972;Schumann, 1987). Based on specific approaches, a number of counter-gradient heat flux formulations have been proposed (e.g., Deardorff, 1972;Gibson and Launder, 1978;Troen and Mahrt, 1986;Holtslag and Moeng, 1991;Abdella and McFarlane, 1997;Zilitinkevich et al, 1999) to relax or to eliminate this obvious deficiency of the eddy diffusivity models. Various arguments that authors have used to parametrize the unknown terms and to estimate their importance in the governing equation of the turbulent heat flux, have resulted in considerably different formulations.…”

“…Various arguments that authors have used to parametrize the unknown terms and to estimate their importance in the governing equation of the turbulent heat flux, have resulted in considerably different formulations. Simple formulations (e.g., Deardorff, 1972;Gibson and Launder, 1978;Troen and Mahrt, 1986) entirely neglect the contribution of the turbulent transport in the turbulent heat flux equation, while in the more recent proposals (e.g., Holtslag and Moeng, 1991;Abdella and McFarlane, 1997;Zilitinkevich et al, 1999) turbulent transport plays a key role. Despite the evident progress in developing more reliable turbulent heat flux models for the prediction of CBL, operational atmospheric models, as noted by Holtslag and Moeng (1991), often employ only down-gradient formulations.…”