PRINCIPLES FOR CAPTURING THE UPSTREAM EFFECTS OF DEEP SILLS IN LOW-RESOLUTION OCEAN MODELS

Principles for incorporating the upstream effects of deep sills into n umerical ocean circulation models using nonlinear analytical hydraulic models are discussed within the context of reduced gravity flow. A me thod is developed allowing the upstream influence of a numerically unr esolvable deep sill or width contraction to be reproduced. The method consists of placing an artificial boundary in the numerical model's ov erflowing layer at some distance upstream of the actual sill or width contraction of the deep strait, Given the model state at time t, the d ependent flow variables are then predicted at the artificial boundary at time t + Delta t by using the method of characteristics in combinat ion 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 tw o cases are calculated and these can be used directly to numerically s atisfy the boundary condition in a straightforward way.