ERDC/CHL CHETN-IV-35
June 2001
To proceed, the apportionment of qR must be known. For this purpose, coupling coefficients aαβ
are introduced, where the a's are numbers (which can be expressed as percentages), and
subscripts denote coupling between rate α and rate β:
qbR = abR qR
qdR = adR qR
(6)
qsR = asR qR
These coefficients obey the constraint
abR + adR + asR = 1
(7)
The constraint expresses one equation in three unknowns, requiring two additional equations. To
proceed, in the absence of process-based estimates, one can, for example, specify abR and adR as
inputs and solve for asR as asR = 1 - abR - adR . The determination of the coupling coefficients,
which should be time dependent, in terms of the coastal processes at the site is the subject of
future work. At the moment, values are specified based on experience gained with the model (see
the examples that follow). An estimate for the coupling coefficient adR is given in CHETN-IV-34
(Larson and Kraus 2001), called the "trapping ratio" or p in that Technical Note.
For the channel bottom, the continuity equation gives a change in bottom elevation ∆z in time
interval ∆t as
z
z
W ∆z = ( qdR - qrR ) ∆t = qdR - εrd
qdR ∆t = adR qR 1 - εrd
∆t
za
za
which becomes
z
a
dz
= dR qR 1 - εrd
z(0) = 0
,
(8)
za
dt W0 - x
Similarly, for infilling by growth of the side channel, continuity gives
∆x ( za - z ) = qbR ∆t = abR qR ∆t
which becomes
a
dx
= bR qR ,
x(0) = 0
(9)
dt za - z
Equations 8 and 9 are simultaneous nonlinear equations for channel depth z and width x as a
function of the input rate (which can be time dependent) and time. Equation 8 indicates that z
will increase more rapidly as the width decreases, and Equation 9 indicates that the width W(x)
will increase more rapidly as the channel fills. These equations can be solved numerically for a
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