MOI )EI.INCi A ('0NVECTIVEI.Y UNSTABLE B O U N D A R Y LAYER
121
the simple thermal model, i.e.. A in tlie thermodynamic model is a function
of time.
Figures 4b and 4c show the evolutions of A0 and [O,(t) - U,] for both
models and again they exhibit similar trends.
The nature of these provisional results for the trial values of u and K
provide encouragement for following up these ideas. In particular we await
further observational data such that we can determine values of a and K
directly and compare the computed evolutions with the actual ones.
APPENDIX
Details of the Nirmerical Intcgrat iorr Procedure
Substitution of Eqs. (20t(23) into Eq. (19) gives
(A I )
CD V ( V' - A V cos p) - (dh/dt) A V cos /I = .j71 A C' sin /Iq
and
(A2)
CD I' A V sin /? + (dh/dr) A V sin j = j h A V cos /I.
If we now introduce the nondiniensional variables,
( A 3
V = V l V , ,
(A4)
1: = AV/V,,
(A5)
rt =.fh!C,V,.
and
(Ah)
1 = (dh/dt)/CD 5,
then Eq. (A2) implies
647)
which with Eq. (A I ) gives
tan /? = q/(v + A),
v2 = &2[$ + (v + A)'].
Further, Eqs. (24). (A7). and (AS) give