A Semi-Implicit, Three-Dimensional Model for Estuarine ... - USGS
A Semi-Implicit, Three-Dimensional Model for Estuarine ... - USGS
A Semi-Implicit, Three-Dimensional Model for Estuarine ... - USGS
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142 A <strong>Semi</strong>-<strong>Implicit</strong>, <strong>Three</strong>-<strong>Dimensional</strong> <strong>Model</strong> <strong>for</strong> <strong>Estuarine</strong> Circulation<br />
u VELOCITY COMPONENT,<br />
IN CENTIMETERS PER SECOND<br />
WATER SURFACE ELEVATION,<br />
IN CENTIMETERS<br />
w VELOCITY COMPONENT,<br />
IN CENTIMETERS PER SECOND<br />
28<br />
24<br />
20<br />
16<br />
12<br />
8<br />
4<br />
0<br />
-4<br />
30<br />
25<br />
20<br />
15<br />
10<br />
5<br />
0<br />
-5<br />
-10<br />
0.005<br />
0.000<br />
-0.005<br />
-0.010<br />
-0.015<br />
Node i = 13, j = 5 (middle of basin)<br />
Nonhomogeneous fluid<br />
Analytical solution<br />
(non-viscous, homogeneous fluid)<br />
Node i = 2, j = 5 (west end of basin)<br />
Analytical solution<br />
(non-viscous, homogeneous fluid)<br />
Computed solution<br />
(viscous, nonhomogeneous fluid)<br />
Node i = 2, j = 5, k = 3 (west side of basin, third layer)<br />
Δ t = 3 minutes<br />
<strong>Semi</strong>-implicit, leapfrog-trapezoidal<br />
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7<br />
TIME, IN HOURS<br />
Computed solution<br />
(viscous fluid)<br />
k = 1<br />
k = 2<br />
k = 3<br />
k = 4<br />
k = 5<br />
k = 6<br />
Analytical solution<br />
(non-viscous, homogeneous fluid)<br />
Computed solution<br />
(viscous, nonhomogeneous fluid)<br />
Figure 5.33. Computed solution of the 3-dimensional (3-D) seiching problem using a viscous fluid of nonhomogeneous density.<br />
For comparison, the analytical solution <strong>for</strong> an ideal (non-viscous, homogeneous) fluid is shown. The computed solution is determined<br />
using the 3-D, semi-implicit, leapfrog-trapezoidal scheme and a time step of 3 minutes. k, layer number; Δt, time step.