APPENDIX B
DERIVATION OF THE RADIATION STRESS TERMS
The basis of the derivation is to use the definition of the velocity potential to substitute
for the wave induced velocities in the definition for the radiation stresses.
d
, d
Ufi~dZ
w =
zp dz
where is expressed in terms of the general complex amplitude function B as
_ 1 (_il cosh k(h0 + z) _iut
2 V a
B cosh kh
+ cc)
where c.c. represents the complex conjugate term. Also r¡' is expressed as
r,' = i(Be-iut + c.c)
where the prime is used to denote wave induced quantities.
For convenience Eq. (2.50) of Section 2.2 is reproduced below.
Sap = pLh u'aU'pdz + 6a0 [J_h ?dz h+ ^)2 + y fa')2
An expression for p is obtained in Section 2.2 and is reproduced below
OlL.W1
dz p(w'y
Substituting Eq. (B.5) into Eq. (B.4) gives
Sap = P I uau'pdz + 6ap
/l o
(B.l)
(B.2)
(B.3)
(B.4)
(B.5)
ri c* ( r* du'w' \
J ^ pg(r) z)dz +J ^ Ip J Ldz) dz
' .. * '
-/
p[w'Y dz yOK + + y fa')2
-O L
_x2 P9-.
(B.6)
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