Advanced Ocean Modelling: Using Open-Source Software

74 3 Basics of Nonhydrostatic ModellingFig. 3.41 Dynamical regimes for different gradient ratios and Turner angles3.19 Exercise 11: Double-Diffusive Instability3.19.1 AimThe aim of this exercise is to explore the double-diffusive instability mechanismwith application of the nonhydrostatic ocean-slice model.3.19.2 Task DescriptionWe consider a model domain, 200 m in length and 20 m deep, resolved by equidistantgrid spacings of Δx = Δz = 1 m. Lateral boundaries are cyclic. Advectiondiffusionequations for temperature and salinity together with a linearised equationof state are added to the model code. Diffusivity of heat is set to a uniform value of10 −4 m 2 /s and diffusivity of salt is chosen as 10 −6 m 2 /s. These values, exceedingtrue values by a factor of 1,000, are deliberately chosen to speed up the simulation.Rather than full values, we use temperature anomalies T ′ and salinity anomaliesS ′ with reference to constant background values as field variables. Accordingly, thelinearised equation of state can be written as:ρ ′ = ρ − ρ o = ρ o (βS ′ − αT ′ ) (3.77)