Channel flow - Rouse profile

In this scenario, the water depth and the surface slope have been
chosen identical to those in the purely physical
`channel` scenario introduced in section 12.1.2.

Under certain conditions, the suspended matter equation

has an analytical solution:

- Constant settling velocity
- Parabolic eddy diffusivity
- Reflective bottom and surface
- Steady-state solution
- No sources and sinks

Let the eddy diffusivity profile be parabolic with

(276) |

with the depth , the bottom roughness length , the van Karman number and the bottom friction velocity and the vertical coordinate . Then the analytical solution of (275) is

where is the suspended matter concentration at i and depends on the initial conditions for . The Rouse number is then defined as:

(278) |

When running the `rouse` scenario with a two-equation turbulence
closure model, then the analytical solution for the Rouse profile
is only approximated, since the eddy diffusivity deviates from
(277).
In order to be closer to the analytical solution, it is ncessary to chose in
`gotmturb.nml` the analytical parabolic profile for eddy diffusivity,
which is done by the follwing settings in `gotmturb.nml`:

&turbulence turb_method= 2, tke_method= 1, len_scale_method=4, stab_method= 1

This Rouse scenario may be calculated with Eulerian concentrations
or with Lagrangian particles, depending on the setting
of `bio_eulerian` in `bio.nml`.
When using the Lagrangian particle method, it is advisable
to average the concentration over all time steps
which belong to one output time step,
by setting `bio_lagrange_mean=.true.`

It is also possible to include a sink term at the bed
(for simulating the effect of grazing by benthic filter feeder),
the seetings for this have to be made in `mussels.nml`.

Karsten Bolding 2012-12-28