ERDC/CHL CHETN-IV-32
June 2001
2 g (ζ R - ζ L )
πD 2
Qn =
(16)
fL
4
D
The leaky internal-barrier boundaries retain the same overtopping ability as the standard internal-
barrier boundaries in earlier versions of ADCIRC. The basic assumption for overtopping is that
when surface-water elevation exceeds the height of the internal barrier, hib , the internal-barrier
boundary section overtops. In this case, weir formulae (Chow 1959) are applied to compute
free-surface subcritical or supercritical inflow/outflow across the internal-barrier boundary,
which is added to the cross-barrier pipe flows. The computed normal cross-barrier flows have
been implemented within the framework of normal-flow boundary conditions and it is possible
to specify either one of the following two implementations.
Implementation 1: Essential Leaky Internal-Barrier Normal-Flow Boundary with
Free Tangential Slip Allowed
The portion of the boundary integral in the Generalized Wave-Continuity Equation (GWCE)
(Luettich, Westerink, and Scheffner 1991) corresponding to the leaky internal-barrier boundaries
is evaluated using the calculated nodal cross-barrier flux values. Nodal values of flux are
computed as defined in configurations 1 through 6. Nodal flux is assumed to vary linearly
between nodes on each internal-barrier boundary segment when the flow integral in the GWCE
is computed. Furthermore, the normal-direction velocity component is computed by dividing the
flux by the total water column at the node of interest. This value of normal velocity is enforced
in the momentum equations by eliminating the normal-direction momentum equation at the
internal-barrier boundary nodes (obtained after reorienting the x-y momentum equations into n-t
directions) and replacing this equation with the nodal velocity value. The tangential-direction
momentum equation at internal-barrier boundary nodes is not modified allowing for free
tangential slip. This procedure does result in model-predicted normal flows (computed with the
predicted nodal velocities and elevations) on leaky internal-barrier boundaries exactly matching
the value as computed by summing the Bernoulli-based pipe flow added to the broad-crested
weir formula flow.
Enforcing essential normal-flow boundary conditions on internal barriers can overconstrain the
system and set up local oscillatory modes. This situation has been observed in a variety of
application cases. In practical applications, leaky internal-barrier boundary conditions are
typically implemented as natural conditions as described in the following paragraph.
Implementation 2: Natural Leaky Internal-Barrier Normal-Flow Boundary with Free
Tangential Slip Allowed
The portion of the boundary integral in the GWCE corresponding to the leaky internal-barrier
boundaries is evaluated using the calculated nodal cross-barrier flux values. Nodal values of flux
are computed as defined in configurations 1 through 6. Nodal flux is assumed to vary linearly
between nodes on each internal-barrier boundary segment when the flow integral in the GWCE
is computed. Neither the normal- or tangential-direction momentum equations at internal-barrier
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