so
J ( M A. BtlSihGEH AND S. P. S. ARYA
The following boui dary coiiditions were used in the solution of
Eqs. (19)-(20).
At ( 3 t o .
(284
T, = exP( - I I’JU, I to)
(2Hb)
T, = 0
At i = &,
(29a)
T, = 0
(29b)
T y = O
Here, the lower and upper boundaries were specified so that to was small
enough and (c”, large enough not to affect the solutions. This occurred when
to 5 0.01H,, and C, 2 H,, H, being the dimensionless boundary layer
height where the fluxes and their gradients becurno vanishingly small (this
implies that T, + 0, TI -+ 0, u + ug and u + vr. as 4 + If,). For a given
stability condition (pJ, the boundary layer would set its own thickness
naturally once the above restrictions on to and f, were satisfied. This
required several trials with different value8 of these oince H, was not known
to begin with.
4. THE MODEL RESULTS AND COMPARISON wrm OTHER STIJDIES
The solution to Eqs. (19). (a), and (26), w&h the bounday-condition as
specified above yields the profiles of K,, dw‘/ui = -%, u’w’/u: = -T,,,
(u, - Z)/U, = -,T,,/dt and (or - b)/u, = aTJd& for different values of p+ .
These are shown in Figs. 3-9. For the neutral cast? (y, = 0) our results are
comptlrd with those obtained by Wyngaard er al. (this volume) using a
higher order closure scheme (see Figs. 3-5). Recognizing that they come
from two basically diflerent models, the good agreement between them is
very encouraging and lends much credence to the simple model used here.
The model calculations were done for various values of p, in the range
0-250. which probably covcn all stable conditbna of practical interest. The
strong effect d stability on eddy viscosity dfstribution can be seen from
Fig. 5. With increasing p* the K, distribution &cornea htter and flatter;
both the maximum value and the dimensionkss height where it occurs
decrease by almost two orders o f magnitude, Following Businger et al.
(1971) we have used here a value of k - 0.35.
The velocity defect profiles are shown in Figs. 6 and 7. Both ii and F
components ovcrshoot their respective geostrophic values before coming
back to geostrophic equilibrium at a greater height. The maximum over-
J ( M A. BtlSihGEH AND S. P. S. ARYA
The following boui dary coiiditions were used in the solution of
Eqs. (19)-(20).
At ( 3 t o .
(284
T, = exP( - I I’JU, I to)
(2Hb)
T, = 0
At i = &,
(29a)
T, = 0
(29b)
T y = O
Here, the lower and upper boundaries were specified so that to was small
enough and (c”, large enough not to affect the solutions. This occurred when
to 5 0.01H,, and C, 2 H,, H, being the dimensionless boundary layer
height where the fluxes and their gradients becurno vanishingly small (this
implies that T, + 0, TI -+ 0, u + ug and u + vr. as 4 + If,). For a given
stability condition (pJ, the boundary layer would set its own thickness
naturally once the above restrictions on to and f, were satisfied. This
required several trials with different value8 of these oince H, was not known
to begin with.
4. THE MODEL RESULTS AND COMPARISON wrm OTHER STIJDIES
The solution to Eqs. (19). (a), and (26), w&h the bounday-condition as
specified above yields the profiles of K,, dw‘/ui = -%, u’w’/u: = -T,,,
(u, - Z)/U, = -,T,,/dt and (or - b)/u, = aTJd& for different values of p+ .
These are shown in Figs. 3-9. For the neutral cast? (y, = 0) our results are
comptlrd with those obtained by Wyngaard er al. (this volume) using a
higher order closure scheme (see Figs. 3-5). Recognizing that they come
from two basically diflerent models, the good agreement between them is
very encouraging and lends much credence to the simple model used here.
The model calculations were done for various values of p, in the range
0-250. which probably covcn all stable conditbna of practical interest. The
strong effect d stability on eddy viscosity dfstribution can be seen from
Fig. 5. With increasing p* the K, distribution &cornea htter and flatter;
both the maximum value and the dimensionkss height where it occurs
decrease by almost two orders o f magnitude, Following Businger et al.
(1971) we have used here a value of k - 0.35.
The velocity defect profiles are shown in Figs. 6 and 7. Both ii and F
components ovcrshoot their respective geostrophic values before coming
back to geostrophic equilibrium at a greater height. The maximum over-