# Physical Forcings

ERF includes the following forcing terms as options:

## Buoyancy

If

use_gravity == true


then buoyancy is included in the momentum equations in the form

$(0, 0, -\rho^\prime g)$

## Coriolis Forcing

If

use_coriolis == true


then Coriolis forcing is included in the momentum equations, i.e. :

$\mathbf{F} = (C_f \; (\rho v \sin{\phi} - \rho w \cos{\phi}), -C_f \; \rho u \sin{\phi}, C_f \; \rho u \cos{\phi})$

where $$C_f = 4 \pi / P_{rot}$$ is the Coriolis factor with $$P_{rot}$$ the rotational period (measured in seconds), and $$\phi$$ the latitude.

There is no dependence on the radial distance from the center of the earth, thus the curvature of the earth is neglected.

## Rayleigh Damping

If

use_rayleigh_damping == true


then explicit Rayleigh damping is included in the energy and momentum equations as described in Section 4.4.3 of the WRF Model Version 4 documentation (p40), i.e. :

$\mathbf{F} = - \tau(z) \rho \; (u - \overline{u}, v - \overline{v}, 0)$

and

$F_{\rho \theta} = - \tau(z) \rho (\theta - \overline{\theta})$

where $$(\overline{u}, \overline{v}, 0)$$ is the reference state velocity, typically defined as the initial horizontally homogeneous fields in idealized simulations, and $$\overline{\theta}$$ is the reference state potential temperature. As in the WRF model, the reference state vertical velocity is assumed to be zero.

# Problem-Specific Forcing

There are two ways to specify background conditions to drive the simulation:

If

abl_driver_type == "PressureGradient"


then

$\mathbf{F} = (\nabla p_{x,ext}, \nabla p_{y,ext}, \nabla p_{z,ext})$

where $$(\nabla p_{x,ext}, \nabla p_{y,ext}, \nabla p_{z,ext})$$ are user-specified through erf.abl_pressure_grad.

## Geostrophic Forcing

If

abl_driver_type == "GeostrophicWind"


then geostrophic forcing is included in the forcing terms, i.e.

$\mathbf{F} = (-C_f \; v_{geo}, C_f \; u_{geo}, 0)$

where $$C_f = 4 \pi / P_{rot}$$ is the Coriolis factor with $$P_{rot}$$ the rotational period (measured in seconds), and the geostrophic wind $$(u_{geo}, v_{geo}, 0)$$ is user-specified through erf.abl_geo_wind. Note that if geostrophic forcing is enabled, Coriolis forcing must also be included.