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5.10 Exercise 14: Island Wakes 1155.10.4 Stability Criterion for Diffusion TermsThe one-dimensional diffusion equation for a variable ψ can be written as:∂ψ∂t= A h∂ 2 ψ∂x 2 (5.36)where A h is a diffusivity assumed constant. Using an explicit finite-di ference formulationof diffusion term leads to the stability criterion:Δt ≤ (Δx)2A h(5.37)Although the diffusion terms (5.31) and (5.31) in the momentum equations areslightly more complex than assumed here, the latter condition gives a useful upperbound for permitted time steps. If problems persist, the time step should be furtherreduced.5.10.5 Full-Slip, Semi-Slip and No-Slip ConditionsFrictional effects on f ow running parallel to coastlines can be implemented viaspecificatio of the velocity shear near the coast. For, instance, with the choiceof zero-gradient conditions for this velocity component, there is no shear of fl wparallel to the coast and, accordingly, there is no frictional stress imposed on thefl w. This is called the full-slip condition.As another option, fl w vanishes at the coastline under the assumption that thefl w at the grid point on the other side of the coastline is anti-parallel to the coastalfl w, so that the average value vanishes directly at the coast. This is known as theFig. 5.17 Illustration of the full-slip, semi-slip and no-slip conditions used for f ow parallel tocoastlines