EI)l)Y DIFFUSION COEFFICIENTS
z+ x :
409
Y -+ Y ( L x , A A , i.).)
(9b 1
Y-0
Y - , K 2 j.).(j.: + A:)'"
(9c)
K , + 0
k', - , L', (A: +
K , - + K , ( L , ix, i.")
Lz,
h?
(9d 1
L -+ 0
L . 4 L ,
L - + L ( L , . A, , A).)
-+
v
f
--v(Sa)
(5b). ( 5 c )
(Sd)
The boundary conditions (8a). (Xb) show that the coordinate system is
orientated with the s axis parallel to the surface stress.
An iterative method for solving the system of the equations (1)-(4) with
the boundary conditions (8a)-(8d). (9a)- (9d) has been given by Wippermann (197 I b).
Three free parameters appear in the equations: one for the thermal
stratification ( L , or 1 1 ) and two for the baroclinicity (Ax and iY). These three
parameters are internal ones; they do not contain any external parameter.
Only in the boundary conditions (Xc) and (8d) does an external parameter
appear, namely Z,, , the nondimensional roughness length, which is according to the definitions made
(10)
Z o = ( K C ~
Roo)-'
I t reflects thc influence of the external parameters I G
,
, I , j ; z o . However. for
Z 9 Z 0 , thc solutions become independent of Z o , i t . , independent of any
external parameter (Rossby number similarity); they depend only on the
three intern;il parameters p. A x , A,:
X ( Z . p, A., . A).)
Y (Z, 11. A.v , I,")
K , ( Z . p, A x . i.).)
L ( Z . p ) or L(Z, 11. A x . A,,,)
z % ZO
and are called universal. From these, the universal profiles ofother variables
(for instancc the velocity defect or the energy dissipation rate) can be
derived.
We notc. that in ;i PBL the profile k',,(Z) is universal for Z 3 Z 0 : such
protiles will bc studied in the following sections.