Large-eddy dynamics, the energy cascade, and large-eddy simulation - Turbulence in the Atmosphere - page 136

California ( Horst et al . , 2004 ). It produced the first substantial exposition of
measured statistics of the subfilter-scale motion ( Sullivan et al . , 2003 ).
Hatlee and Wyngaard ( 2007 ) have discussed the rate-equation SFS models

τ ik

∂τ ij u j τ ij

T

˜

u i

∂

∂ ˜ δ ij

2 e

3 s ij −

τ jk

3 τ k s k ∂t = ∂x k + ∂x k −

− , (6.81)

u i

c r
∂x j −

∂ ˜

∂f i

R ij ∂

˜ f i

∂t =−

f j

∂x j − T .

(6.82)

Each of these retains the pair of production terms on the rhs of the SFS flux
conservation equations (6.71) and (6.73) and models the pressure destruction term.
Their tests of these models with the HATS data are summarized in Figures 6.4
and 6.5 . In each case the simple rate-equation model is a clear improvement over

Figure 6.4 Modeled (ordinate) and observed (abscissa) SFS deviatoric kine-
matic normal stresses (units m 2 s − 2 ) in the HATS experiment. The left panel
uses the Smagorinsky model, Eqs. (6.75) - (6.77) ; the right panel uses the simple
rate-equation model (6.81) .From Hatlee and Wyngaard ( 2007 ).

Figure 6.5 Modeled (ordinate) and observed (abscissa) temperature fluxes (units
Kms − 1 ) in HATS. The left panel uses the eddy-diffusivity SFS model (6.78) and
(6.79) ; the right panel uses the simple rate-equation model (6.82) .From Hatlee
and Wyngaard ( 2007 ).