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Parameterizing tidal mixing at tall steep isolated ridges Legg and Klymak, 2008, JPO; Klymak, Legg and Pinkel, 2009, JFM in press; Klymak, Legg and Pinkel, 2010, JPO in prep. Velocity/buoyancy fields for U 0=5 cm/s, M 2 tidal forcing. MITgcm simulation for Hawaiian ridge parameters. For tall (Um/(Nh)<<1), steep (N dh/dx/w>1) topography, transient internal jump-like lee waves are generated, with vertical wavenumber m ~ N/Um. 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/(w/N) > 1 • tall topography, U/(Nh) <<1 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. F(z) = vertical distribution function, dependent on lengthscale U/N mc= mode number corresponding to arrested wave: all energy at higher mode numbers is dissipated locally. mc~(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/(w 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.