GfsSourceCoriolis

From Gerris

As its name suggests, GfsSourceCoriolis adds a Coriolis source term to the components of the velocity or momentum. The object is further generalised and can be used to optionally add a linear friction term (which has a formally similar form to the Coriolis terms).

The syntax in parameter files is

[ GfsSourceVelocity ] [ GfsFunction ] ( [ GfsFunction ] ) ({ x = 0 y = 0 z = 1. })

where the second GfsFunction and the last brackets are optional. The first GfsFunction is the value of the Coriolis coefficient, the second GfsFunction is the value of the linear friction coefficient. The last optional parameter block defines the (x,y,z) coordinates of the rotation axis (default is 0 0 1).

For example

SourceCoriolis 1e-4 3e-3

is formally equivalent to

Source U (-1e-4*V - 3e-3*U)
Source V ( 1e-4*U - 3e-3*V)

but uses a robust implicit discretisation.

Examples

• Lunar tides in Cook Strait, New Zealand

    SourceCoriolis -1e-4

• Coriolis formulation in 3-D

  SourceCoriolis (2.*Omega) 0. { x = 0. y = 1. z = 1. }

• Geostrophic adjustment

  SourceCoriolis F0

• Geostrophic adjustment on a beta-plane

  SourceCoriolis (1. + 0.156246961595*(y + 0.5))

• Geostrophic adjustment with Saint-Venant

  SourceCoriolis F0

• Non-linear geostrophic adjustment

  SourceCoriolis 2.*OMEGA

• Coastally-trapped waves

  SourceCoriolis {} 1.

• Coastally-trapped waves with adaptive refinement

  SourceCoriolis {} 1.

• Oscillations in a parabolic container

    SourceCoriolis 0 tau

• Parabolic container with embedded solid

    SourceCoriolis 0 tau

• Lake-at-rest balance in an inclined domain with cut cells

    SourceCoriolis 0 1.0e-01

• Lake-at-rest balance in an inclined domain with bipolar metric

    SourceCoriolis 0 1.0e-01

• Circular dam break on a rotating sphere

    SourceCoriolis 10.*sin(y*M_PI/180.)

• Rossby--Haurwitz wave

    SourceCoriolis 2.*Omega*sin(y*DTR)

• Rossby--Haurwitz wave with a free surface

    SourceCoriolis 2.*Omega*sin(y*DTR)

• Rossby--Haurwitz wave with Saint-Venant

    SourceCoriolis 2.*Omega*sin(y*DTR)

• Simple example of groundwater flow following Darcy's law

    SourceCoriolis 0 1

• Groundwater flow with piecewise constant permeability

    SourceCoriolis 0 1