(1970a) in which
19
Tbz = pF |uorl| U
(2.4)
Tiv = pF |uori| V
(2.5)
where F is a drag coefficient (of the order of .01) and |uorj,| is the time average over a wave
period of the absolute value of the wave orbital velocity at the bottom. From linear wave
theory it is found that
O IT
|Uort| = T sinh kh (2,6)
where H is the wave height and T is the wave period, k is the wavenumber, and h = D is
the total water depth. Ebersole and Dalrymple used a more complete quadratic formulation
Tb = pF *|t|
(2.7)
where the overbar represents the time average over a wave period and ut is comprised of both
the mean current and the wave orbital velocities. The total velocity vector tiĀ” is expressed
as
ui = (U + ticos#) + (V + sin0),7 (2.8)
so that its magnitude is given by
|u*| = Vu2 + V2 + 2 + 2U cos 9 + 2 V sin 6 (2.9)
The wave orbital velocity is expressed as
um cos at
(2.10)
where um is the maximum wave orbital velocity at the bottom which is found to be
xH
T sinh kh
The x and y components of the time averaged bottom friction are thus
rhx = ^ Jq {U+ mcos0coeat)-\ut\d{at)
Hv = (p-/ [V + sin icos at) |tT{|d(o-t)
X Jo
(2.11)
(2.12)
(2.13)