| Popis: |
Turbulent two-dimensional fluids support an inverse cascade of energy, in which eddies transfer energy to successively larger scales. Systems experiencing differential rotation also admit a class of plane-wave solutions called Rossby waves. The excitation of Rossby waves leads to an anisotropisation of the energy cascade such that most of the turbulent energy is funnelled towards zonal modes. This manifests as alternating zonal jets with meridional widths that scale according to the Rhines scale. It is this phenomenon that is thought to be the origin of spontaneous jet formation that has been observed in many systems of geophysical interest, such as the World Ocean and Jovian atmospheres. In this thesis, we study jets using a barotropic channel model on the β-plane. Jets are known to be supported by the divergence of Reynolds stresses in the underlying eddy fields. This relationship can be visualised using the geometric eddy ellipse formulation, in which the average direction of momentum flux is given by the tilt angle of these ellipses. This formulation is introduced by studying the interaction of shear instabilities with a barotropically unstable jet profile. We demonstrate how, in more turbulent systems, we can filter the flow fields to recover ellipse patterns of the most dominant modes. We then study jet formation in β-plane turbulence from physical and spectral perspectives and show that these may be unified by finding the location an energy front in wavenumber space and studying how it propagates. Then, using the geometric eddy ellipse formulation, we show how the underlying eddy field is arranged by the anisotropisation process. We find that there are strong momentum fluxes at low-wavenumber, occupying the most energetic scales. These mask a regular underlying pattern of momentum fluxes at intermediate scales that correlate with the jet structure. To reveal this structure we develop a formulation for evaluating two-point correlations in which the energy spectrum is expanded on a series of angular Fourier modes. We show that the zeroth and second angular modes contain all of the eddy ellipse information. In particular, we find that the tilt angle can be recovered from the quotient of the real and imaginary parts of the second mode. |
