Advanced Ocean Modelling: Using Open-Source Software

54 3 Basics of Nonhydrostatic Modelling3.13 Exercise 7: Lee Waves3.13.1 Task DescriptionWe consider a model domain, 500 m in length and 100 m in depth, resolved by ahorizontal grid spacing of Δx = 5 m and a vertical grid spacing of Δz = 2m(Fig. 3.27). Lateral boundaries are cyclic. A small submarine sill is included of aheight of 40 m and a width of about 100 m. A cosine function is used for the creationof this sill. Forcing is provided via prescription of ambient barotropic pressuregradientforce that is added as additional terms in the u-momentum equation as:Forcing term =−g ∂η o∂xwhere ∂η o /∂x is a prescribed ambient sea-level gradient. This forcing, which operatesto gradually accelerate the flow into the positive x-direction, is switched offafter 20 min of simulation.Two different stratification scenarios are considered. The first scenario deals witha water column in which density increases initially linearly with depth (Fig. 3.27a).The background sea level is assumed to vary by 0.5 cm over the length of the modeldomain. The stability frequency (squared) is varied in a range between N 2 = 0.5 ×10 −4 s −2 and N 2 = 5 × 10 −4 s −2 . The second scenario deals with two superimposedlayers of different densities both 50 m in thickness (Fig. 3.27b). Each layer is slightlystratified with a stability frequency squared of N 2 = 0.5 × 10 −4 s −2 . A densityinterface, also called pycnocline, separates both layer. Density stratification acrossthis interface corresponds to a stability frequency (squared) of N 2 = 4.8×10 −3 s −2 ,which is stronger than any stratification considered in Scenario 1. In this scenario,Fig. 3.27 Different initial density configurations used in Exercise 7