The free convection case  SEEING  Full Width Half Maximum

Relationship of the temperature structure coefficient to the mean velocity and temperature fields

The parameterization of  in terms of the temperature and velocity fields in the atmospheric surface layer is obtained using the similarity theory. One expression, derived by Wyngaard[9], is

$$C_T^2 = f(Ri) \left( \frac{dT}{dz} \right)^2 z^{\frac{4}{3}}$$ (10)

 

where Ri is the Richardson number:

$$Ri = \frac{g}{T} \frac{dT}{dz}\left(\frac{dU}{dz}\right)^{-2}$$

The function f(Ri) (tabulated by Wyngaard[9]) is obtained from experimental measurements.

By choosing other scaling variables, namely the friction velocity u_* and the normalized surface heat flux q (in K m s^-1), and as the stability parameter the ratio z/L, where L is the Monin-Obukhov length

$$L = - \frac{u_*^3 T}{k g q}$$

Wyngaard[9] obtains another expression for $C_{\scriptscriptstyle T}^2$ :

$$C_T^2 = g(z/L) \left( \frac{q}{u_*} \right)^2z^{-\frac{2}{3}}$$ (11)

 

where g(z/L) is an empirical function evaluated from experimental data as:

$$4.9 \left( 1 - 7 \frac{z}{L}\right)^{-\frac{2}{3}} \; \; \; \; \; \; \; \; \; \; \;\frac{z}{L} < 0$$ g(z/L) = (12)

$$4.9 \left( 1 + 2.75 \frac{z}{L}\right)^{-\frac{2}{3}} \; \; \; \; \; \; \; \; \; \; \;\frac{z}{L} > 0$$ g(z/L) = (13)

  

We note also that $C_{\scriptscriptstyle T}^2$ can also be put in relation with the outer scale of turbulence L_u:

$$C_{T}^{2} = a^2 \beta L_u^{4/3} \left(\frac{dT}{dz} \right)^2$$ (14)

   

 

Figure 2: Relationship between C_T² (K² m^-2/3), height and surface heat flux in free convection over a horizontal surface 

1998-07-05