238
R.H, Charlier and Chr. P. De Meyer
r = kau2,ve
(11)
where k = constant (a/R) 3/4, a is the length of the ripple marks and R, the
half amplitude of the oscillating water motion at the bottom (R>>a).
Calculations then give :
y3/2 = p (y < about Lot8)
(12)
This profile is similar to the one above. Certainly the profile depends on the
wave period T, but as the profile is shaped mainly by storm waves and as
the variation in T for these is small, the profile in reality will be the same as
that given by (10).
Value of p is calibrated to local environmental conditions (waves,
materials).
Pier Vellinga (Beach and Dune Erosion during Storm Surges, Delft
University, Holland, 1986) found the following model law for profiles in the
surf zone :
no/n a =(no /n2w) °'26
(13)
where no is the length scale, i~ is the vertical scale and nw is the settling
velocity scale. Transforming this expression according to Stokes law for
settling velocities, one has where D is grain size diameter, thence
n I • nD TM ---~-nd 5/4
In the prototype n~ = nd= 1
(14)
one therefore has
nlnw °s --rid 5/4
(14')
Putting n~ = x and na = y one gets
X" nw °s ___=_y5/4
(14")
A profile, however, has different grain sizes varying with depth and actual
exposure. The k-value in the above expression [cf. (11)] for shear stresses =
kou "~2 (Um~x = max velocity of the orbital flow at the bottom) varies with
grain size.
R.H, Charlier and Chr. P. De Meyer
r = kau2,ve
(11)
where k = constant (a/R) 3/4, a is the length of the ripple marks and R, the
half amplitude of the oscillating water motion at the bottom (R>>a).
Calculations then give :
y3/2 = p (y < about Lot8)
(12)
This profile is similar to the one above. Certainly the profile depends on the
wave period T, but as the profile is shaped mainly by storm waves and as
the variation in T for these is small, the profile in reality will be the same as
that given by (10).
Value of p is calibrated to local environmental conditions (waves,
materials).
Pier Vellinga (Beach and Dune Erosion during Storm Surges, Delft
University, Holland, 1986) found the following model law for profiles in the
surf zone :
no/n a =(no /n2w) °'26
(13)
where no is the length scale, i~ is the vertical scale and nw is the settling
velocity scale. Transforming this expression according to Stokes law for
settling velocities, one has where D is grain size diameter, thence
n I • nD TM ---~-nd 5/4
In the prototype n~ = nd= 1
(14)
one therefore has
nlnw °s --rid 5/4
(14')
Putting n~ = x and na = y one gets
X" nw °s ___=_y5/4
(14")
A profile, however, has different grain sizes varying with depth and actual
exposure. The k-value in the above expression [cf. (11)] for shear stresses =
kou "~2 (Um~x = max velocity of the orbital flow at the bottom) varies with
grain size.