neutral and unstable results with those from the three-dimensional numeric;rl mcxlcl of Deardorff( 1972). Thc stably stratified case can be done with the
model. and this work will be covered in a future paper.
2. THE PROBLEM
Wc have liinited our study to a horizontally homogeneous planetary
boundary liiyer with the s direction (the direction of the surface-layer wind)
positive to the east, J* positivc to the north. and : positive upward. I n this
cc)ordin:itr system. the unit vector tii along the earth's rotation axis is
(0, cos 4, sin 4). where 4 is latitude. Denoting mean and fluctuating wind
vectors by U i --= ( U , k', 0) and tii = ( I I , P , w), mean and fluctuating temperatures by @ and 0, the mean field equations. for a dry atmosphere without
rddialiw flux divergence, are
i.U/t?r + 2unq:'k = ,f ( V - <)
i7Vii-t + ?iw;/(7z =,f(tr, - U )
(1)
(mlc't + cfi)i/?: = o
Here Ifl and 5 are the geostrophic wind components defined by
( 3
I;, = -(I$) (7P/?J-; v, = (l/f) ?P/i?X ,
whew P is the mean kinematic pressure andj; the Coriolis parameter, is
30 sin 4 with (tj the earth's rotation rate. The turbulence covariance equations arc
where we have indicated differentiation by a comma and repeated indices
arc summed; the other notation is standard. In writing Eqs. (3)-(5), we
assume the turbulence Reynolds number is so large that molecular diffusion
can be neglected and locally isotropic forms can be used for the molecular
Jcstrwfion terms.