Tidal Diffusivity: A Mechanism for Frontogenesis*

Abstract

It is hypothesized that tidal mixing may provide a ''diffusivity'' mechanism for frontogenesis. It stems from the fact that tidal diffusivity varies in the opposite sense from the water depth, so the vertically integrated diffusivity may exhibit a minimum at midshelf, thus giving rise to a maximum in the property gradient-even in the absence of flow convergence. An analytical model assuming a tidal diffusivity dominated by shear dispersion is used to elucidate the mechanism, which shows additionally that the front is located at a water depth that is about twice the tidal frictional depth-a prediction not inconsistent with some observed fronts. The proposed frontogenesis is demonstrated by numerical calculations using the Princeton Ocean Model (POM), which show the emergence of a front from an initial field of uniform gradient after tides are switched on, and the diagnosis of the numerical solution and its parameter dependence has corroborated the analytical model. It is suggested moreover that this diffusivity mechanism may be extended to the wind-induced mixing to explain the shelfbreak front off of the northeastern United States.

A numerical study of the Magellan Plume

“…Strong vertical mixing associated to large tidal amplitudes homogenizes the MP vertically and keep it as a bottom‐trapped plume against other forcing factors (e.g., winds). The spatial inhomogeneity in the tidal mixing associated with strong cross‐shore motions appears to drive the offshore displacement of the plume front at Grande Bay [ Ou et al , 2003]. The analytical model of Ou et al appears to be particularly relevant to this region because the MP plume is vertically homogeneous, and the region has large M 2 currents that are strongly polarized in the cross‐shelf direction.…”

“…The observed offshore displacement of the MP front in EXP6 (Figure 7a) appears to be related to the “tidal diffusivity” mechanism postulated by Ou et al [2003]. They argued that cross‐shelf variations of tidal mixing leads to an offshore displacement of the maximum density gradient until it reaches twice the frictional depth ( h f ), defined as where Cd is the bottom friction coefficient (∼2 × 10 −3 ) and U is the magnitude of the cross‐shelf transport tidal‐driven transport.…”

A model of tidally dominated ocean processes near ice shelf grounding lines

“…Similarly to uniform K h reductions, the tidal front is unaffected but transport toward the grounding line is reduced. Experimentation with different vertical diffusivities and tidal periods shows that the O67 formulation can only give dispersion rates approaching those listed by Fischer et al [1979] when combined with the assumption of a (high) constant volume flux, as used by Ou et al [2003], but these velocities become excessive as the grounding line is approached. Therefore, using a constant dispersion coefficient to crudely represent unspecified mixing processes appears to be more reasonable than assuming that vertical shear dispersion is dominant.…”

Horizontal mixing of Great Barrier Reef waters: Offshore diffusivity determined from radium isotope distribution

“…In effect, if one presumes that eddy diffusivity is due to fluctuating flows then the condition that there be no flow through the coast implies that diffusivity must reduce to zero there. The onshore‐offshore component of the tidal volume flux must necessarily approach zero as the coast is approached, and so we might expect that diffusivity associated with tidal shear would also diminish to zero as x → 0 [ Ou et al , 2003].…”

“…The onshoreoffshore component of the tidal volume flux must necessarily approach zero as the coast is approached, and so we might expect that diffusivity associated with tidal shear would also diminish to zero as x ! 0 [Ou et al, 2003].…”