Parameterizing tidal mixing at tall steep isolated ridges Velocity/buoyancy fields for U0=5cm/s, M2 tidal forcing. MITgcm simulation for Hawaiian ridge parameters. Legg and Klymak, 2008, JPO; Klymak, Legg and Pinkel, 2009, JFM in press; Klymak, Legg and Pinkel, 2010, JPO in prep. For tall (U m /(Nh)<<1), steep (N dh/dx/  topography, transient internal jump-like lee waves are generated, with vertical wavenumber m ~ N/U m. These arrested waves overturn and break when flow relaxes, leading to local mixing.

Local dissipation due to breaking arrested wave Conditional on: steep topography, dh/dx  /N) > 1 tall topography, U/(Nh) <<1 F(z) = vertical distribution function, dependent on lengthscale U/N E(x,y,m) = energy extracted from barotropic tide, as a function of vertical mode number m, found from analytic model for tall steep topography (e.g. Llewellyn Smith and Young, 2003), given topographic height, N, tidal velocities U. m c = mode number corresponding to arrested wave: all energy at higher mode numbers is dissipated locally. m c ~(N/U)/H. Energy at lower mode numbers is assumed to propagate away as linear waves. Fraction of energy dissipated locally increases as U increases. No arbitrary dimensional parameters.

Do tidally-driven transient overturns matter on a global scale? (N/(  dh/dx)) calculated on ¼ degree scale Amplitude of tidal velocity projected onto direction of topographic gradient (cm/s) Large velocities combined with steep topography  may lead to local overturning in jump-like features: seen in many knife-edge ridges.