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
Coriolis Forcing¶
If
use_coriolis == true
then Coriolis forcing is included in the momentum equations, i.e. :
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¶
Rayleigh damping can be imposed on any or all of \(u, v, w, T\) and is controlled by setting
rayleigh_damp_U = true
rayleigh_damp_V = true
rayleigh_damp_W = true
rayleigh_damp_T = true
in the inputs file. When one or more of those is true, explicit Rayleigh damping is included in the energy and/or momentum equations as described in Section 4.4.3 of the WRF Model Version 4 documentation (p40), i.e. :
and
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:
Pressure Gradient¶
If
abl_driver_type == "PressureGradient"
then
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.
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.