Advanced Ocean Modelling: Using Open-Source Software

3.11 Exercise 6: Kelvin-Helmholtz Instability 513.11.2 Task DescriptionConsider a vertical ocean slice of 500 m in length and 100 m in depth with cycliclateral boundaries (see below) and grid spacings of Δx = 5 m and Δz = 2m.The density interface of two superimposed layers of different densities is locatedat a depth of 50 m. The density of the top layer is set to ρ 1 = 1,027.0kg/m 3 .The bottom layer has a density of ρ 2 = 1,029.0kg/m 3 , yielding a density differenceof Δρ = 2kg/m 3 . Density diffusion is included in the model. Horizontaland vertical density diffusivities are set to small uniform values of K h = K z = 1 ×10 −4 m 2 /s.The initial lateral flow in the top layer has an average speed of 1 m/s, whereasthe lower layer is at rest. Randomly generated values of ±0.01 m/s are added tothe upper-layer flow. This technique promotes the initial growth of disturbances atrandom locations. The random-number generator was taken from Press et al. (1989).With a difference in layer speeds of Δu = 1m/s, Eq. (3.62) suggests that the transitionmixing zone attains a thickness of around 13 m. Equation (3.56) predicts thatmixing is initiated by disturbances of