Advanced Ocean Modelling: Using Open-Source Software

52 3 Basics of Nonhydrostatic Modelling3.11.4 ResultsThe flow becomes dynamically unstable owing to the Kelvin-Helmholtz instabilitymechanism after 45 min of simulation and creates vigorous internal wavebreaking at the density interface (Fig. 3.24). Disturbances attain vertical speeds of> 30 cm/s. Equation (3.60) suggests that disturbances are confined to a layer ofabout 13 m in thickness, such that Re ≈ 0.25 establishes in this layer. The simulationproduces a transition zone of around 25 m in thickness, characterised bya Richardson number of Ri ≈ 0.5 (Figs. 3.25 and 3.26). This discrepancy by afactor of two is presumably caused by inertia effects followed by continued mixingafter onset of dynamical instabilities. Another source of bias could be the relativelycoarse grid spacing, which the reader may verify via the choice of finer gridspacings.Vortices involved in the instability process do neither fully mix density normomentum. The final result is rather a transition zone over which both densityand the horizontal flow vary approximately linearly. Hence, it is a misconceptionto assume that the Kelvin-Helmholtz mechanism fully mixes portions of the fluidcolumn. In model applications that cannot resolve the Kelvin-Helmholtz instabilitymechanism, this process is often parameterised by means of vertical turbulentdiffusion in which the coefficient is a function of the Richardson number.Fig. 3.24 Exercise 6. The onset of Kelvin-Helmholtz instabilities after 50 min of simulation.Shown are the density distribution (shading and contours) and the flow field (arrows, averagedover 5 × 5 grid cells)Fig. 3.25 Exercise 6. Same as Fig. 3.24, but after 100 min of simulation