Papers by Paula andrea Echeverri
Bulletin of the American Physical Society, Nov 21, 2005
Submitted for the DFD05 Meeting of The American Physical Society Bumps, witches and bouncing beam... more Submitted for the DFD05 Meeting of The American Physical Society Bumps, witches and bouncing beams: lab investigations of internal waves THOMAS PEACOCK, PAULA ECHEVERRI, MIT, NEIL BALM-FORTH, UBC, ALI TABAEI, MIT-There is a great, ongoing effort to better understand the processes surrounding internal wave generation, propagation and dissipation in the oceans. To contribute to this effort, we are in the process of establishing a state-of-the-art experimental facility. The facility, based around the digital schlieren method, is designed to investigate both linear and non-linear phenomena in a laboratory setting. We here report the latest experimental results concerning tidal conversion by typical topographic features, such as a Gaussian bump and a knife-edge. The quantitative results compare very well with theoretical predictions developed from the classic work of Bell and Hurley, and more recent analysis of subcritical topography by Balmforth et al. In addition, we present more details on recently published results concerning the nonlinear generation of second-harmonic wavebeams at reflecting boundaries.
Journal of Physical Oceanography, 2008
Experimental results of internal tide generation by two-dimensional topography are presented. The... more Experimental results of internal tide generation by two-dimensional topography are presented. The synthetic Schlieren technique is used to study the wave fields generated by a Gaussian bump and a knife edge. The data compare well to theoretical predictions, supporting the use of these models to predict tidal conversion rates. In the experiments, viscosity plays an important role in smoothing the wave fields, which heals the singularities that can appear in inviscid theory and suppresses secondary instabilities of the experimental wave field.
Journal of Fluid Mechanics, 2010
To date, analytical models of internal tide generation by two-dimensional ridges have considered ... more To date, analytical models of internal tide generation by two-dimensional ridges have considered only idealized shapes. Here, we advance the Green function approach to address the generation of internal tides by two-dimensional topography of arbitrary shape, employing the Wentzel-Kramers-Brillouin (WKB) approximation to consider the impact of non-uniform stratifications. This allows for a more accurate analytical estimation of tidal conversion rates. Studies of single and double ridges reveal that the conversion rate and the nature of the radiated internal tide can be sensitive to the topographic shape, particularly around criticality and when there is interference between wave fields generated by neighbouring ridges. The method is then applied to the study of two important internal tide generation sites, the Hawaiian and Luzon Ridges, where it captures key features of the generation process.
Journal of Fluid Mechanics, 2009
We analyse the low-mode structure of internal tides generated in laboratory experiments and numer... more We analyse the low-mode structure of internal tides generated in laboratory experiments and numerical simulations by a two-dimensional ridge in a channel of finite depth. The height of the ridge is approximately half of the channel depth and the regimes considered span sub- to supercritical topography. For small tidal excursions, of the order of 1% of the topographic width, our results agree well with linear theory. For larger tidal excursions, up to 15% of the topographic width, we find that the scaled mode 1 conversion rate decreases by less than 15%, in spite of nonlinear phenomena that break down the familiar wave-beam structure and generate harmonics and inter-harmonics. Modes two and three, however, are more strongly affected. For this topographic configuration, most of the linear baroclinic energy flux is associated with the mode 1 tide, so our experiments reveal that nonlinear behaviour does not significantly affect the barotropic to baroclinic energy conversion in this regi...
Journal of Fluid Mechanics, 2011
A study is presented of the generation of internal tides by barotropic tidal flow over topography... more A study is presented of the generation of internal tides by barotropic tidal flow over topography in the shape of a double ridge. An iterative map is constructed to expedite the search for the closed ray paths that form wave attractors in this geometry. The map connects the positions along a ray path of consecutive reflections from the surface, which is double-valued owing to the presence of both left- and right-going waves, but which can be made into a genuine one-dimensional map using a checkerboarding algorithm. Calculations are then presented for the steady-state scattering of internal tides from the barotropic tide above the double ridges. The calculations exploit a Green function technique that distributes sources along the topography to generate the scattering, and discretizes in space to calculate the source density via a standard matrix inversion. When attractors are present, the numerical procedure appears to fail, displaying no convergence with the number of grid points u...
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Papers by Paula andrea Echeverri