Spectral Energy Transfer in Geophysical Turbulence Based on Structure Functions

Abstract:

Energy transfer across scales is fundamental for geophysical turbulence, and to obtain a sound understanding we need consistent information obtained from both measurements and numerical simulations. Measurements provide limited oceanic information, while numerical simulations give information with full details, but we need to find suitable conditions to set up numerical systems, e.g. at which scales simulation is forced. This work uses the latest third-order structure function theory that extends the Kolmogorov's classical inertial range result by its ability to capture forcing scales and bidirectional transfer. We first analyze the third-order structure function obtained from surface drifters of the Grand Lagrangian Deployment experiment in the Gulf of Mexico. The results reveal that the energy injection peaks around 1 km, and below 1km energy transfers downscale and above 1km energy transfers upscale. Also, the ratio between the magnitude of the upscale and downscale energy transfer is around three. In a rotating stratified turbulence simulation, we consider an external forcing centred around one spatial scale, and we find a third-order structure function which is consistent with that obtained from the measurement and therefore justify our numerical setup. In addition, the buoyancy data in the numerical simulation helps us to identify an energy conversion from kinetic to potential energy in the regime of downscale energy flux.