eTheses Repository - University of Birmingham

The boundary conditions used for this work are described in Table 3.2. These are selected
in the m3tras_TAPE5 file before running the model. Only pressure boundary conditions are
automatically prescribed, since they are coupled with other boundary conditions.
Table 3.2: Summary of the boundary conditions used for all METRAS model runs
Variable Lower boundary Upper boundary Lateral boundaries
Wind vector
Temperature
Fixed value
prescribed
Model energy
budget equation
used
Large scale values are
prescribed for wind
components normal to the
boundary. Zero gradient for
wind components parallel to
the boundary.
Direct calculation for wind
components normal to the
boundary. Zero gradient for
wind components parallel to
the boundary.
Zero gradient at boundary Zero gradient at boundary
The upper boundary of the model has no physical boundary, and therefore the boundary
conditions must permit vertically propagating waves to leave the model volume without
reflections. Therefore it is assumed that the gradients of horizontal wind components
normal to the boundary will be zero and the vertical wind component will vanish. For the
temperature field, the boundary conditions results in zero fluxes at the model top.
At the lower boundary the wind velocity vector has a ‘no slip’ boundary condition at the
ground. This means the wind velocity parallel to the surface is zero at the ground, which
results in the following conditions at the boundary:
w(0,j,i) = 0
u(0,j,i) = -u(1,j,i)
v(0,j,i) = -v(1,j,i)
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