Chapter 1: INTRODUCTION
break off the Rayleigh-jet column and enter the ocean at lower velocities
allowing them to penetrate to deeper levels.
Remarkably, the formation of vortex rings is associated with drop
oscillations. The best coalescence of an oscillating drop with the ocean
occurs when the drop is spherical and changing from an oblate to a prolate
spheroid at the moment of contact with the surface (Chapman and Critchlow,
1967).
Natural rain is an ensemble of raindrops. The penetration depth of
primary and secondary drops depends not only on the behavior of single
events, as mostly analyzed in laboratory studies, but is also governed by the
interaction of raindrops with the vortex rings and surface waves generated by
them. For natural rain, Maxworthy (1972) concluded that the depth p
z
reached by the vortex rings is proportional to the initial drop radius 0
r . The
constant of proportionality is large ( 1
0
/
300
p
a z r |
) for single drops but
decreases to
100
a |
for a drop ensemble (Manton, 1973).
The kinetic energy of a falling drop entering the ocean is large compared
with the potential energy reached at p
z ; respectively, the buoyancy effects
on the penetration depth can be ignored. The freshwater flux due to rain
decreases the near-surface salinity and, thereby, further (though only
slightly) reduces the buoyancy effect on the submerging drops.
1.5.2 Surface flux of freshwater due to rain
The total volume of the rainwater is
3
0
0
0
0
0
4
3
u
V V
r n r dr
S
f
³
,
(1.64)
where
1
u
V m3 is the unit volume included by Schl ssel et al. (1997) for
dimensional correctness of the equation, and
0
n r
is the raindrop
distribution expressed in the number of drops per (volume) unit of air per
equivalent drop radius. The dimension of
0
n r is m
-3 m
-1 , and is commonly
described by the Marshall-Palmer distribution (Marshall and Palmer, 1948)
0
0
0
0
exp 2
dN
n r
n
r
dr
/ ,
(1.65)
35
ü