Diffusivity and Dynamics of Linear Internal Waves from a Lagrangian Perspective

Tracer release experiments conducted just below a shallow pycnocline during the 2011 ONR LatMix campaign reveal a diffusivity of O(1) m^2/s at scales of O(1) km, while simultaneously released surface drifters drogued to the same depth yield a diffusivity of O(0.1) m^2/s. We show that this discrepancy in diffusivity can be explained by the fact that linear internal waves act on the dye and drifters in physically different ways.

An analytical linear internal wave model is constructed using a realistic stratification profile and Garrett-Munk energy spectrum matching the ambient conditions during the field experiments. The analytical model is then used to advect synthetic dye-like particles, which follow isopycnal displacements, and drifter-like particles, which are constrained to a horizontal plane. The results show that not only are the observed diffusivities explained by linear internal waves, but that there also exists a strong dependence on location in the stratification profile. Analytical results from estimates of Stokes' drift are shown to be consistent. The Lagrangian frequency spectrum of the particles from this system is computed analytically and shown to be consistent with the observed spectrum from the surface drifters in the field campaign. Finally, these results from the analytical linear internal-wave model are complemented with nonlinear simulations.