Principles for capturing the upstream effects of deep sills in low resolution ocean models |
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| Institution: | 1. State Key Lab of Fine Chemicals, School of Chemical Engineering, Liaoning Key Lab for Energy Materials and Chemical Engineering, Faculty of Chemical, Environmental and Biological Science and Technology, Dalian University of Technology, Dalian, 116024, Liaoning, China;2. Key Laboratory of Energy Materials Chemistry, Ministry of Education, Institute of Applied Chemistry, Xinjiang University, Urumqi, 830046 Xinjiang, China;3. Institute of Applied Chemistry, Xinjiang University, Urumqi, 830046, Xinjiang, China |
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| Abstract: | Principles for incorporating the upstream effects of deep sills into numerical ocean circulation models using nonlinear analytical hydraulic models are discussed within the context of reduced gravity flow. A method is developed allowing the upstream influence of a numerically unresolvable deep sill or width contraction to be reproduced. The method consists of placing an artificial boundary in the numerical model's overflowing layer at some distance upstream of the actual sill or width contraction of the deep strait. Given the model state at time t, the dependent flow variables are then predicted at the artificial boundary at time t + Δt by using the method of characteristics in combination with quasi-steady hydraulic laws. The calculation requires the use of Riemann invariants and examples are given for a simple nonrotating flow and for rotating channel flow with uniform potential vorticity. The computation is considerably simplified by linearizing the relevant equations in the vicinity of the artificial boundary, resulting in a linear wave reflection problem. The reflection coefficients for the two cases are calculated and these can be used directly to numerically satisfy the boundary condition in a straightforward way. |
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