ERDC/CHL CHETN-IV-32
June 2001
Elevation (m)
1.75
1.50
1.25
1.00
0.75
0.50
0.25
0.00
-0.25
-0.50
-0.75
-1.00
-1.25
-1.50
-1.75
Figure 25. Grays Harbor elevation and velocity solution at time = 2.05 days
the cross-barrier boundary conditions may feed the oscillations. This situation can readily occur
when the cross-barrier surface-elevation gradients are small, as they are in this example.
To avoid the generation of large localized oscillations, sufficient spatial and temporal resolution
must be specified. In this case, an 80-m spatial resolution in the vicinity of the jetty is sufficient
to resolve the eddies that are formed, and allow for the elimination of spurious modes associated
with under-resolved grids. As a rule of thumb, at least seven nodes should be specified across
any eddies that are formed. Sufficient temporal resolution is another important issue that may
control the smoothness of the solution. Typically, the Courant number based on wave celerity
( CCW = gh∆t / ∆x where CCW = wave celerity based Courant number; g = acceleration due to
gravity; h = water column depth of the flow; ∆t = time-step; ∆x = node to node spacing) and
flow speed ( CU = U∆t / ∆x where CU = flow speed based Courant number and U = flow speed)
should be smaller than 0.25. Wave celerity Courant number is the limiting factor in this domain,
specifically within the channel leading along the jetty into Grays Harbor. A time-step of 1 sec
allows for a maximum wave celerity based Courant number equal to 0.3 in the channel region.
This time-step was sufficient to eliminate spurious modes.
In addition to resolution, the GWCE-based solution requires a proper selection of the numerical
parameter τ0. Typically τ0 should be set small in deep and intermediate tidal waters. Thus,
generally but not always, waters deeper than 5 m should have a τ0 value ranging between 0.0025
and 0.005. In very shallow tidal regions with water column depths less than 5 m and in fast
flowing rivers, a value of τ0 ranging between 0.01 and 0.02 should be specified. Note that if τ0 is
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