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 (Um/(Nh)<<1), steep (N dh/dx/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/N) > 1•tall topography, U/(Nh) <<1

cmm

myxEzF

),,()(

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.

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/( dh/dx)) calculated on ¼ degree scale

Amplitude of tidal velocity projected onto direction of topographic gradient (cm/s)

Large velocities combined with steep topographymay lead to local overturning in jump-like features: seen in many knife-edge ridges.