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Model Response to Tidal Propagation

This is a test case for the accuracy of the time integration scheme implemented in representing the propagation of an undamped sine wave in a rectangular channel.

Reference

  • Taylor, C and Davis, J (1975). "Tidal and Long Wave Propagation", Elsevier, pp 111.

Domain

  • Cuboid flume 60 m (length), 15 m (width) and 9.81 m (depth)
  • Open at one end, enclosed on all others
  • "Free-slip" velocity condition is assumed on all internal walls

Tidal propagation domain

Initial Conditions

  • Initial depth = 9.81 m

Boundary Conditions

  • h = (1.0)Sin(t) ; where h is water surface displacement and t is time

Results

  • Taylor and Davis 1975 reports the analytic solution as:
  • h = (1.0)Sin(t - x/9.81) ; where x is the longitudinal distance from the open boundary
  • Analytic versus model water surface elevation results at X=30 m and Y = 15 m

periodic forcing result

  • Error between analytic and model results at X=30 m and Y = 15 m

periodic forcing result error