the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
The open boundary equation
Abstract. We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection) under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.
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RC C360: 'Revision of the paper 'The open boundary equation'', Anonymous Referee #1, 01 Jul 2015
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AC C412: 'Reply to review 1.', Dirk Diederen, 14 Jul 2015
- SC C526: 'Additional reply to review 1', Marco Toffolon, 07 Aug 2015
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AC C412: 'Reply to review 1.', Dirk Diederen, 14 Jul 2015
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RC C423: 'Revision of "The open boundary equation" by D. Diederen et al. (MS No.: os-2015-29)', Anonymous Referee #2, 15 Jul 2015
- AC C455: 'Reply to review 2.', Dirk Diederen, 26 Jul 2015
- SC C532: 'From the boundary condition to the open boundary equation', Marco Toffolon, 10 Aug 2015
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SC C558: 'Tending to the Open Boundary Equation', Marco Toffolon, 18 Aug 2015
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RC C584: 'Reply to "Tending to the Open Boundary Equation" (SC C558)', Anonymous Referee #2, 20 Aug 2015
- SC C588: 'Other test cases', Marco Toffolon, 21 Aug 2015
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RC C584: 'Reply to "Tending to the Open Boundary Equation" (SC C558)', Anonymous Referee #2, 20 Aug 2015
- RC C604: 'Reply to AC C455, SC C532, SC C558 and SC C588', Anonymous Referee #2, 24 Aug 2015
- EC C620: 'Editor comment', John M. Huthnance, 26 Aug 2015
- AC C855: 'Final Response', Dirk Diederen, 13 Oct 2015
-
RC C360: 'Revision of the paper 'The open boundary equation'', Anonymous Referee #1, 01 Jul 2015
-
AC C412: 'Reply to review 1.', Dirk Diederen, 14 Jul 2015
- SC C526: 'Additional reply to review 1', Marco Toffolon, 07 Aug 2015
-
AC C412: 'Reply to review 1.', Dirk Diederen, 14 Jul 2015
-
RC C423: 'Revision of "The open boundary equation" by D. Diederen et al. (MS No.: os-2015-29)', Anonymous Referee #2, 15 Jul 2015
- AC C455: 'Reply to review 2.', Dirk Diederen, 26 Jul 2015
- SC C532: 'From the boundary condition to the open boundary equation', Marco Toffolon, 10 Aug 2015
-
SC C558: 'Tending to the Open Boundary Equation', Marco Toffolon, 18 Aug 2015
-
RC C584: 'Reply to "Tending to the Open Boundary Equation" (SC C558)', Anonymous Referee #2, 20 Aug 2015
- SC C588: 'Other test cases', Marco Toffolon, 21 Aug 2015
-
RC C584: 'Reply to "Tending to the Open Boundary Equation" (SC C558)', Anonymous Referee #2, 20 Aug 2015
- RC C604: 'Reply to AC C455, SC C532, SC C558 and SC C588', Anonymous Referee #2, 24 Aug 2015
- EC C620: 'Editor comment', John M. Huthnance, 26 Aug 2015
- AC C855: 'Final Response', Dirk Diederen, 13 Oct 2015
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