Circular Basin

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UNDER CONSTRUCTION

Analytical Solution

Dupont (2001) presented an analytical solution for a closed circular domain on an f-plane, with radius , a linear bottom friction, and a spatially variable wind stress equal to , where is the gradient of the wind forcing and is the vertical coordinate. The water surface elevation solution is given by

  (1)

The current velocities are independent of the Coriolis parameter and are given by

  (2)
  (3)

Setup

Figure 1. Computational grid.

The model is run to steady state from zero current and water level initial conditions with , , and . Table 1 shows the general settings used for CMS-Flow. Figure 1 shows the computational grid with 5 levels of refinement from 2000 m to 125 m.


Table 1. General Settings for Wind-driven flow in a circular basin

Parameter Value
Time step 3600 s
Simulation Duration 72 hrs
Ramp Period 24 hrs
Initial Water Depth 10 m
Mixing Terms Off
Wall Friction Off
Linear Bottom Friction Coefficient 0.001



Results

[[Image:CB3_Analytical_Vel_Eta.png|thumb|right|600px| Figure 1. Analytical current velocities and water levels.[[Image:CB3_Calculated_Vel_Eta.png|thumb|right|600px| Figure 1. Calculated current velocities and water levels.

Table 2. Goodness of fit statistics for the current velocity and water level

Variable RRMSE, % RMAE, % R^2 Bias
U-Velocity 3.88 0.64 0.997 -4.06e-5
V-Velocity 3.87 0.64 0.997 4.06e-5
Water Level 0.16 0.13 1.000 -3.56e-6

References

  • Dupont, F., 2001. Comparison of numerical methods for modelling ocean circulation in basins with irregular coasts. Ph.D. thesis, McGill University, Montreal.



Test Cases

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