only that constant. Using the E equation (6) toeether with the imbalance iind
trailsport models (15) and (17). and the surface-layer constraints (19). we get
for I : :
(21)
Thc remaining u, values were set at 0.15. The neutral calculations shown
later reveal that the structure is not very sensitive to (1,.
(3, = (4 -- 41);12.l = 0.083
4. COMP i ITATION ~ i .
TFC'H N iyu ES
'The rncKlc.1 set was solved numerically with boundary conditions at z = h
and 3 = H. Those at h arc given in Eq. (19). and it is most convenient to
regard 14* and Qo (thc surface heat flux) as inputs and the mean wind and
tcmpcrature at H as dependent variables. 11 is then also convenient to replace the mean cquations ( I ) with their : derivatives. At 2 = H we set the
turhulrnce moments. mean shears. and mean temperature gradient to zero.
For some problems. it is appropriate to treat wind and temperature at H
as inputs. In this case, the mean set ( I ) is carried as written, U, and V, are
spxilied, and the lower boundary conditions (19) are adjusted to account
for the angle between the surfqacc and geostrophic winds. Here it, and Qo are
dependent variables, and u*, for example, can be related to the mean speed
S = (Lf2 + V 2 ) I i 2 at h by
(22)
S = ( i t * / k ) In(h/z,')
Since the equations are tailored to reproduce observed surface-layer structurc, the group h/?~l* need only be chosen small enough that it no longer
affects the solutions. This occurred for hJk, s 0.002. the value used.
i n the unstable case, the boundary at H is interpreted as an inversion lid,
as in Dcurdorff's (1972) study, and in those runs we maintained Hfltc, = 1 .O.
The neutral boundary layer sets its own thickness (Blackadar and
Tennekes, l9flH) to be a multiple of uJ/; so H should be so large compared
to this "natiiral" thickpess that it does not interfere. We chose our value of
Hfjrr, = 1.85 by increasing CI until the neutral structure below no longer
changed. This is four times the height uscd in most of Denrdorffs neutral
calculiitions.
We solved the equation set numerically using the DuFort-Frankel
(DuFort a ~ d
Frankel, 1953) method on a logarithmic height grid with 88
intervals; since the method is "leapfrog," only half the grid points are used in
cacli lime step, Experiments with coarser and finer grids showed this grid to
bc ;I good compromise between accuracy and computation time.
The stcady-state solution5 shown here were found by letting them evolve
from assumed initial states, but they did not depend on the initial state.
trailsport models (15) and (17). and the surface-layer constraints (19). we get
for I : :
(21)
Thc remaining u, values were set at 0.15. The neutral calculations shown
later reveal that the structure is not very sensitive to (1,.
(3, = (4 -- 41);12.l = 0.083
4. COMP i ITATION ~ i .
TFC'H N iyu ES
'The rncKlc.1 set was solved numerically with boundary conditions at z = h
and 3 = H. Those at h arc given in Eq. (19). and it is most convenient to
regard 14* and Qo (thc surface heat flux) as inputs and the mean wind and
tcmpcrature at H as dependent variables. 11 is then also convenient to replace the mean cquations ( I ) with their : derivatives. At 2 = H we set the
turhulrnce moments. mean shears. and mean temperature gradient to zero.
For some problems. it is appropriate to treat wind and temperature at H
as inputs. In this case, the mean set ( I ) is carried as written, U, and V, are
spxilied, and the lower boundary conditions (19) are adjusted to account
for the angle between the surfqacc and geostrophic winds. Here it, and Qo are
dependent variables, and u*, for example, can be related to the mean speed
S = (Lf2 + V 2 ) I i 2 at h by
(22)
S = ( i t * / k ) In(h/z,')
Since the equations are tailored to reproduce observed surface-layer structurc, the group h/?~l* need only be chosen small enough that it no longer
affects the solutions. This occurred for hJk, s 0.002. the value used.
i n the unstable case, the boundary at H is interpreted as an inversion lid,
as in Dcurdorff's (1972) study, and in those runs we maintained Hfltc, = 1 .O.
The neutral boundary layer sets its own thickness (Blackadar and
Tennekes, l9flH) to be a multiple of uJ/; so H should be so large compared
to this "natiiral" thickpess that it does not interfere. We chose our value of
Hfjrr, = 1.85 by increasing CI until the neutral structure below no longer
changed. This is four times the height uscd in most of Denrdorffs neutral
calculiitions.
We solved the equation set numerically using the DuFort-Frankel
(DuFort a ~ d
Frankel, 1953) method on a logarithmic height grid with 88
intervals; since the method is "leapfrog," only half the grid points are used in
cacli lime step, Experiments with coarser and finer grids showed this grid to
bc ;I good compromise between accuracy and computation time.
The stcady-state solution5 shown here were found by letting them evolve
from assumed initial states, but they did not depend on the initial state.