Contents

174 IndexFFinite differencesexplicit, implicit, 8, 9forward, backward, centred, 66Flooding algorithm, 73, 77–82, 84, 93, 94, 120,157, 163Flowanticyclonic, 124, 156, 160baroclinic, 43barotropic, 43, 124cyclonic, 124, 149, 152, 156, 160, 161frontal, 153, 154, 156, 158, 159, 160geostrophic, 122–128, 129, 130, 132, 137,140, 141, 142, 143, 144, 146, 148, 150,154, 155, 157, 158quasi-geostrophic, 127, 129, 157, 158shear, 58, 132–134, 135, 136Forceapparent, 28, 43–44, 45buoyancy, 34–36, 37, 38, 39centrifugal, 43–45, 46–47, 50, 51centripetal, 44–45, 46, 47, 51, 52coriolis, 28, 43–57, 62, 63, 68, 91, 99,119–120, 121, 122, 123, 137, 139, 152,164, 165, 166gravity, 35, 41, 50, 51, 165, 166pressure-gradient, 41–43, 46, 47, 50, 51,79, 119, 123, 130, 137, 148reduced-gravity, 165, 166Froude number, 62GGeostrophicadjustment, 151–157equations, 123–124method, 124HHydrostatic balance, 41, 42, 47, 123IInertialoscillations, 48, 50, 51, 55, 56–57, 156period, 50, 63, 68, 91, 121, 123, 152, 154radius, 50Instabilitybaroclinic, 157–158barotropic, 132, 133, 134–137, 157, 158,162Internal wave, 86, 87, 151, 154, 156KKelvin wave, 120–122LLagrangian trajectory, 28Lateralfriction, 99, 112, 113–114, 117, 119, 149,154, 159momentum diffusion, 112, 113, 117, 118,130, 135, 144, 145, 147, 148, 149, 159Level of no motion, 149Local vertical, 50–51, 52MMerian’s formula, 87NNavier–Stokes equations, 60–61, 63, 68Nonlinear terms, 29, 30, 60, 62, 68, 70, 91, 99,111–112, 113, 119, 122, 123, 138, 145,147, 148, 149, 156, 159Numerical diffusion, 77, 104, 106, 107, 112,117, 122Numerical stability criterionfor advection, 106for diffusion, 115Numerical waves, 73PPermanent thermocline, 148, 150Phase speed, 21, 24, 25, 62, 68, 70, 85, 86, 87,88, 91, 96, 97, 98, 106, 121, 128, 131,151, 154, 155Prandtl’s mixing length, 59RReduced-gravityconcept, 149–151, 153plume, 162, 163–167Reynoldsapproach, 57–58number, 113, 117Richardson number, 58, 59Rossbynumber, 63, 122, 123, 127, 129, 132, 135,138(internal) radius of deformation, 121, 122,128, 153, 154, 155wave, 127–128, 130, 131, 132SScaling, 61–63, 68, 122–123, 133, 139Semi-implicit approachfor bottom friction, 99–100, 120for Coriolis force, 53–54, 120