426
interfacial stress requires that the barotropic and baroclinic waves are out
of phase, i. e. 'P =I- -a.
With the shorthand notations
(42)
and cP02 and 002 determined from (35) and (36) we find the wave phases
and amplitudes
tan'P
p
A
E8
bolU - VI
28
cos 'P
from the barotropic balance (31) and
tan(.o-'P)
4f.-lCT
- - -
U-,
T
p
IV+,)I
J(4f.-lCT)2 + (U - ,)2
(43)
(44)
(45)
(46)
from the baroclinic balance (33). Without going into more details these
relations obviously reveal similar properties of the wave induced stresses as
the discussed in section 2 for the barotropic CdV model. There is no form
stress for vanishing friction. The barotropic part P sin 'P of the bottom from
stress vanishes for zero bottom friction: for E ---+ 0 we have 'P ---+ 0 from
(43) but P remains finite. The baroclinic part T sin -a vanishes if bottom
and interfacial friction vanish whereas the interfacial form stress vanishes
for zero interfacial friction. Hence, in accordance with the Eliassen-Palm
theorem, it is only through frictional processes that the induced waves feed
back on the mean flow.