3.14.2 Forcing

The model is forced by relaxation to a radiative equilibrium temperature from Held and Suarez [1994]. A linear frictional drag (Rayleigh damping) is applied in the lower part of the atmosphere and account from surface friction and momentum dissipation in the boundary layer. Altogether, this yields the following forcing [from Held and Suarez, 1994] that is applied to the fluid:

$\displaystyle \vec{{\cal F}_\mathbf{v}}$	$\displaystyle =$	$\displaystyle -k_\mathbf{v}(p)\vec{\mathbf{v}}_h$	(3.61)
$\displaystyle {\cal F}_{\theta}$	$\displaystyle =$	$\displaystyle -k_{\theta}(\varphi,p)[\theta-\theta_{eq}(\varphi,p)]$	(3.62)

where $\vec{\cal F}_\mathbf{v}$ , ${\cal F}_{\theta}$ , are the forcing terms in the zonal and meridional momentum and in the potential temperature equations respectively. The term $k_\mathbf{v}$ in equation (3.61) applies a Rayleigh damping that is active within the planetary boundary layer. It is defined so as to decay as pressure decreases according to

$\displaystyle k_\mathbf{v}$	$\displaystyle =$	$\displaystyle k_{f}~\max[0,~(p^*/P^{0}_{s}-\sigma_{b})/(1-\sigma_{b})]$
$\displaystyle \sigma_{b}$	$\displaystyle =$	$\displaystyle 0.7 ~~{\rm and}~~ k_{f} = 1/86400 ~{\rm s}^{-1}$

where

is the pressure level of the cell center and $P^{0}_{s}$ is the pressure at the base of the atmospheric column, which is constant and uniform here ( $= 10^5 {\rm Pa}$ ), in the absence of topography.

The Equilibrium temperature $\theta_{eq}$ and relaxation time scale $k_{\theta}$ are set to:

$\displaystyle \theta_{eq}(\varphi,p^*)$	$\displaystyle =$	$\displaystyle \max \{ 200.K (P^{0}_{s}/p^*)^\kappa,$	(3.63)
		$\displaystyle \hspace{8mm} 315.K - \Delta T_y~\sin^2(\varphi) - \Delta \theta_z \cos^2(\varphi) \log(p^*/P^{0}_s) \}$
$\displaystyle k_{\theta}(\varphi,p^*)$	$\displaystyle =$	$\displaystyle k_a + (k_s -k_a)~\cos^4(\varphi)~\max[0,(p^*/P^{0}_{s}-\sigma_{b})/(1-\sigma_{b})]$	(3.64)

$\displaystyle \Delta T_y = 60.K$		$\displaystyle k_a = 1/(40 \cdot 86400) ~{\rm s}^{-1}$
$\displaystyle \Delta \theta_z = 10.K$		$\displaystyle k_s = 1/(4 \cdot 86400) ~{\rm s}^{-1}$

Initial conditions correspond to a resting state with horizontally uniform stratified fluid. The initial temperature profile is simply the horizontally average of the radiative equilibrium temperature.

Last update 2018-01-23