MIKE 21 BW - Chezy Number; Long Periodic Waves

Calibration Parameters
133
Long periodic waves
For modelling of long wave transformation (e.g. harbour resonance and
seiching) the effect of bottom friction may be important.
Wave-induced currents
As opposed to the shore-normal case (1DH applications) steady solutions for
the wave-induced mean flow can only exists when the forcing by radiation
stress is balanced by bottom friction and mixing processes. Therefore you
need to include bottom friction in simulations of wave-induced flow fields, see
examples in Section 4.2.6 (Island), Section 4.2.7(Rip channel) and 4.2.8
(Detached breakwater).
The bottom friction can be formulated using
 Chezy number formulation
 Manning number formulation
Chezy number
The bottom friction formulation used in MIKE 21 BW has been set up using
the Chezy bed friction rule.
With the Chezy bed friction rule, the shear stress at the bed can be
expressed in terms of the Chezy number, C, as
(5.1)
where U is the depth-averaged velocity, is the water density, and g is grav-
ity. The unit of the Chezy number is m
1/2
/s.
The Chezy number may be approximated by the following expression:
(5.2)
where U
b
is the velocity at the bed, and f
w
is the wave friction factor appearing
in the bottom shear stress.
For small waves the wave friction factor may be determined by:
(5.3)
where a
b
is the amplitude of the wave particle motion at the bed, and k
N
is the
bed roughness parameter (Svendsen and Jonsson (1980)).

b
gU U
C
2
-------------------=
C
U
U
b
------
2g
f
w
------=
f
w
5.977– 5.213+ a
b
k
N

0.194–
exp=