Advanced Ocean Modelling: Using Open-Source Software

72 3 Basics of Nonhydrostatic Modellingis also encouraged to add the Lagrangian float prediction scheme to the model codeas another means to track movement of the density-driven plume.3.18 Double Diffusion3.18.1 BackgroundMolecules perform random motions, called Brownian motion (Brown, 1866), in theabsence of turbulence. The result of this motion is a slow but continuous moleculardiffusion which operates to smooth curvature in spatial distributions of a property.The rate of molecular diffusion of heat is about 100 times that for salt. Hence, moleculardiffusion in a water column uniform in density but gradients in temperature andsalinity gives rise to local density variations that can trigger the onset of convectionin the interior of the water column (Turner, 1973). The type of instability that developsdepends on the specific shapes of vertical profiles of temperature and salinitythat make up the density stratification.3.18.2 Double-Diffusive InstabilitySuppose there is a warm and saltier layer above cooler, fresher water, with bothlayers having the same density (Fig. 3.40a). The relatively faster molecular diffusionof heat causes the upper layer to cool near the interface. The associated densityincrease creates convective plumes sinking downward across the interface and intothe bottom layer. Similarly, the bottom layer gains heat near the interface whichlowers density. As a consequence of this, convective plumes raise upward and intothe surface layer. The resultant convective mixing is referred to as double-diffusiveinstability or salt fingering.Fig. 3.40 Different stratification scenarios of a water column uniform in density leading to distinctdouble-diffusive processes. Scenario (a) causes double-diffusive mixing across the interface. Scenario(b) leads to isolated convective mixing in each layer and a density contrast develops betweenthe layers