Waves and eddies on a β plane: experiments with altimetry

Zhang, Yang (2016) Waves and eddies on a β plane: experiments with altimetry. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

This study investigated problems related to beta-plane turbulence and wave radiation by a vortex drifting on a beta plane using laboratory experiments supplemented by numerical simulations and analytic methods. An optical system Altimetric Imaging Velocimetry was employed in the study. It directly measures geostrophic currents and then calculates the total current using the quasi-geostrophic approximation under a small Rossby number assumption. The first part of the dissertation investigated the barotropic β-plane turbulence. In the first experiment, an electromagnetic method was employed to generate barotropic turbulent ows consisting of cyclones and prevalent anti-cyclones. Zonal jets were formed in both the forced-dissipative regime and the free-decaying regime. In the former case, jets are latent, are obscured by the strong vortices and are only visible after time averaging of the observed fields. In the second experiment, Thermal convection played the role of forcing with scales confined by the baroclinic deformation radius, which was much smaller than the scale of the electromagnetic forcing. The jets were more distinctive in this experiment. In both cases, an anisotropic energy spectrum was observed, where less energy was located inside a dumbbellshaped area near the origin, whose boundary corresponds to the Rhines scale. Rather than arresting the inverse cascading energy, the dumbbell redirected energy to the zonal modes of approximately the forcing scale. The theoretical spectrum evolution showed that the zonal modes can be fed by an isotropic forcing through only linear dynamics. The westpropagating Rossby waves caused the asymmetry in the frequency-wavenumber spectrum with an energetic plume directing towards the west with a slope Vrmsk, where Vrms is the root mean square velocity of the turbulent ow and k is the isotropic wavenumber. The second part of the dissertation presented the results from a series of experiments on baroclinic β-plane turbulence where a shear between two layers generated meanders, waves, eddies and filaments interacting with each other. The small eddies and thin filaments in these experiments are ageostrophic and can be related to the submesocale dynamics in the ocean, where energy slowly released from baroclinic instability cascades to smaller scales. Dynamics in spectral spaces were emphasized, and a normal Fourier transform in a local Cartesian coordinate system together with a Fourier-Bessel transform in a global polar coordinate system were employed. Rhines arguments hold on both spectra, which showed anisotrophy during a quasi-stationary regime. High energy concentration on the zonal modes larger than the Rhines scale, as well as low energy concentration below a threshold scale, represented by the dumbbell-shaped curve in the Fourier spectrum, were observed as well. In frequencywavenumber space, prominent signatures due to the westward-propagating Rossby waves and the eastward-propagating baroclinic instability waves were revealed by dispersion relations. Encouraged by the significance of the linear dynamics in β-plane turbulence, the third part of the dissertation extended the β-plume theory to an idealized scenario, i.e. wave radiation by a drifting vortex on a β-plane. In a series of experiments, a cyclonic vortex was generated by siphoning water out of the tank. A northwestward-propagating cyclone radiating Rossby waves (long waves to the west and short waves to the east) was observed in the experiments as well as in the pseudo-spectral simulation. Distinct inertial waves were obvious in the altimetric images. Decomposing the vortex into a primary monopole and a secondary dipole showed that the vortex translation speed was indeed determined by its dipole component (β-gyres). In the far field the linear dynamics played a dominant role. Laboratory experiments, numerical simulation and a linear theory showed a similar wave pattern where the long wave crests aligned in a quasi-zonal direction to the west of the cyclone. A linear analogue of the Rhines wavenumber is proposed as kRhines = [square root of] β/Ut, which qualitatively described the energy distribution of large-scale dynamics in the spectrum, where Ut is the vortex translation speed. This result might be applied to the ocean, where sparsely distributed eddies interact with each other through Rossby waves.

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