Advanced Ocean Modelling: Using Open-Source Software

164 5 3D Level Modelling5,000 Lagrangian floats are initialised at random locations of the model domain. Thetotal simulation time is 50 days with data outputs at 12-hrs intervals. The pressureaccuracy of the S.O.R. iteration is set to ɛ =0.01Pa.5.12.3 The Smagorinsky Turbulence Closure SchemeThe turbulence closure scheme proposed by Smagorinsky (1963) reads:√ (∂u ) 2 ( ) ∂v 2 ( ∂uA h = c 1 ΔxΔy + + 0.5∂x ∂y ∂y + ∂v ) 2(5.37)∂xwhere c 1 is a parameter often set to values between 0.1 and 0.2.5.12.4 WarningCompletion of this simulation might take one or more days. Also, SciLab mightcrash occasionally owing to memory limitations. To avoid these problems, the readermight double lateral grid spacings to Δx = Δy = 40 km using half the number ofgrid points for both the x- and the y-direction. This, however, will incur a severeloss in spatial resolution.5.12.5 ResultsThe westerly wind burst creates an initial depression of the thermocline travellingeastward along the equator over a distance of 2000 km in form of an equatorialKelvin Wave (Fig. 5.29). The phase speed of this wave is approximately 66 cm/s,which is slightly less than predicted by theory (take Eq. 3.63). The imprint ofthe Kelvin Wave is a circular patch in the Eulerian tracer concentration field and,accordingly, in the density field. This imprint is associated with transient downwardpumping of the pycnocline whereby the wave depresses the pycnocline by 30–50 m.The radius of the circular patch is 200 km, being of the order of the equatorial radiusof deformation. A second wave develops behind the trailing wave.As the trailing wave meets the eastern coastline, it disintegrates into two coastalKelvin waves propagating away from the equator in the respective hemisphere.Turbulence-enhanced vertical mixing leaves behind some perturbation in the densityfield and weak currents in the western equatorial region of the model domain. With acloser inspection, we can also spot planetary Rossby waves not far from the westernboundary slowly propagating westward.Owing to the trade winds and the Coriolis parameter changing sign across theequator, equatorial regions are generally prone to upwelling which operates to