Geostrophic turbulence

Two-layer quasi-geostrophic (QG) turbulence has been studied as an idealization for atmospheric and oceanic eddies. It is simple in the sense that fast waves are filtered out, thereby allowing for efficient numerical integrations and parameter space exploration. Yet, key features of geostrophically balanced motion with stratification (represented by two vertical modes) are built into the QG formulations. 

On this subject, an overarching goal is to better understand the equilibrated scales of baroclinc eddies in turbulent flows. It has been argued that the equilibration may be thought of as the arrest of barotropic inverse cascade (i.e., an important phenomenology in 2D turbulence), and the arrest is accomplished by two main mechanisms: bottom drag and beta effect (i.e., via excitation of Rossby waves). Understanding the arrest processes is important because the arrest scale is also the most energetic range and thus governs the eddy heat transport.

We have studied the baroclinic eddy scaling in two-layer QG turbulence under the following conditions:

Bottom-drag only

Bottom drag + Beta effect

The tool we use is an open-source, spectral PDE solver, called Dedalus.

In the examples below, we can see the well known result that, as the strength of beta (i.e. meridional gradient of the background rotation rate) increases, eddies transition from being largely isotropic to zonally elongated, with banded zonal jets (5 jets in this case) emerging in the bottom right panel. We are examining the dependence of this transition on environmental parameters (i.e. drag strength and beta) as well as the amount of dissipation that is associated with the jets.

Images below offer examples of zonal jets emerged in turbulent flows. Left is a new image of Jupiter from NASA's James Webb Space Telescope. Right is the AVISO-derived, 10-year anomalies of surface geostrophic current from Maximenko et al. (2005). Multiple zonal jets are ubiquitous in both Pacific and Atlantic basins.