Numerical simulation of a two-dimensional internal wave attractor

Grisouard, Nicolas; Staquet, Chantal; Pairaud, Ivane

doi:10.1017/s002211200800325x

Cited by 47 publications

(94 citation statements)

References 19 publications

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“…height, 17 cm. In our recent work [17] we examined 3D effects on the dynamics of attractor and we showed very good correspondence of experiments and 3D numerical simulation, and we explained discrepancies observed in previous 2D numerical simulation [14].…”

Section: Mathematical Setupsupporting

confidence: 73%

“…The experimental setup possess very large scales interval because of very high Prandtl-Schmidt number. This is why till recently such numerical research were not possible, and numerical modelling dealt with linear modes only, as in ( [14,15]). In these works finite volume method was used for numerical simulation, and realisation of finite volume method was based on MIT code of general circulation model.…”

Section: Introductionmentioning

confidence: 99%

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High-Resolution Simulation of Internal Waves Attractors and Impact of Interaction of High Amplitude Internal Waves With Walls on Dynamics of Waves Attractors

Sibgatullin¹,

Kalugin²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract.Internal wave attractors have received great attention since its discovery in 1995 by Leo Maas ([1, 2]). Now convectional theory describing the formation of attractors is generally accepted, and the principal interest of researchers in recent years is focused on nonlinear interactions. A number of theories had been proposed and now nonlinear interaction due to triadic resonance is accepted as a principle cause of instability of attractors, in which case the parent wave of large amplitude gives birth to two daughter waves, such that conditions of triadic resonance are fulfilled for all the three waves [3]. All this presumes that wave-wall interaction participate in the process only by focusing-defocusing of energy on the inclined boundaries. Here we address interactions of large amplitude internal waves with the boundaries in real laboratory conditions, where Prandtl-Schmidt number is equal to 700. We show that large amplitude waves produce folded structures which are clearly visible on density-gradient images, as if produced by "kneading the dough". These structures are not quickly dissipated due to high Schmidt number and with time they propagate to the interior of the domain, as was shown by our numerical simulation. These structures have visible impact on the instability of attractor and the whole picture of turbulent motion for large amplitudes. The mechanism of interaction of these structures with internal gravity waves structures is the subject of further research. Numerical simulation is quite challenging due to high Prandtl-Schmidt number and small scale of the folded structures in highly nonlinear regimes. Also study is performed on large time scales. As a consequence most of conventional computational approaches give unreliable results. We have applied spectral element approach base on code nek5000 by Paul Fischer. It allowed us to carefully follow the fine space structures on large time scales.

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Section: Mathematical Setupsupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

High-Resolution Simulation of Internal Waves Attractors and Impact of Interaction of High Amplitude Internal Waves With Walls on Dynamics of Waves Attractors

Sibgatullin¹,

Kalugin²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…In order to extract the spatial structure of the different components of the flow, we follow the approach used by several authors [39][40][41] in the context of internal gravity or inertial wave attractors. The velocity field is filtered at a particular frequency ω f according tô…”

mentioning

confidence: 99%

Generation and maintenance of bulk turbulence by libration-driven elliptical instability

et al. 2015

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Longitudinal libration corresponds to the periodic oscillation of a body’s rotation rate and is, along with precessional and tidal forcings, a possible source of mechanically-driven turbulence in the fluid interior of satellites and planets. In this study, we present a combination of direct numerical simulations and laboratory experiments, modeling this geophysically relevant mechanical forcing. We investigate the fluid motions inside a longitudinally librating ellipsoidal container filled with an incompressible fluid. The elliptical instability, which is a triadic resonance between two inertial modes and the oscillating base flow with elliptical streamlines, is observed both numerically and experimentally. The large-scale inertial modes eventually lead to small-scale turbulence, provided that the Ekman number is small enough. We characterize this transition to turbulence as additional triadic resonances develop while also investigating the properties of the turbulent flow that displays both intermittent and sustained regimes. These turbulent flows may play an important role in the thermal and magnetic evolution of bodies subject to mechanical forcing, which is not considered in standard models of convectively driven magnetic field generation.

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“…The experiments performed confirm that internal tide energy can be focused by an internal wave attractor in a double-ridge configuration, and also serve to test the analytical model. This study differs from previous studies of attractors ([56], [35], [31]) as it considers an open domain where it is possible for internal wave rays to escape, so a method was developed to assess the existence and stability of attractors in double ridge systems as a function of the geometric configuration parameters. Using ray tracing, 1-D maps of subsequent internal wave ray reflections on the topography were constructed.…”

Section: Discussion and Contributionsmentioning

confidence: 99%

“…If the geometry is right, it is possible that internal wave rays converge into closed trajectories between the two ridges. Attractive orbits of 125 internal wave rays are also called internal wave attractors and have only been studied previously in closed basins (by Maas et al [56], Hazelwinkel et al [35] and Grisouard et al [31]). These considerations motivate the investigations of chapter 5.…”

mentioning

confidence: 99%

Internal tide generation by tall ocean ridges

Mondragón¹

2009

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Internal tides are internal waves of tidal period generated by tidal currents flowing over submarine topography. Tall ridges that are nominally two-dimensional (2-D) are sites of particularly strong generation. The subsequent dissipation of internal tides contributes to ocean mixing, thereby playing an important role in the circulation of the ocean. Strong internal tides can also evolve into internal wave solitons, which affect acoustic communication, offshore structures and submarine navigation. This thesis addresses the generation of internal tides by tall submarine ridges using a combined analytical and experimental approach.The first part of the thesis is an experimental investigation of a pre-existing Green function formulation for internal tide generation by a tall symmetric ridge in a uniform density stratification. A modal decomposition technique was developed to characterize the structure of the experimental wave fields generated by 2D model topographies in a specially configured wave tank. The theory accurately predicts the low mode structure of internal tides, and reasonably predicts the conversion rate of internal tides in finite tidal excursion regimes, for which the emergence of non-linearities was notable in the laboratory.In the second part of the thesis, the Green function method is advanced for asymmetric and multiple ridges in weakly non-uniform stratifications akin to realistic ocean situations. A preliminary investigation in uniform stratification with canonical asymmetric and double ridges reveals asymmetry in the internal tide that can be very sensitive to the geometric configuration. This approach is then used with realistic topography and stratification data to predict the internal tide generated by the ridges at Hawaii and at the Luzon Strait. Despite the assumption of two-dimensionality, there is remarkably good agreement between field data, simulations and the new theory for the magnitude, asymmetry and modal content of the internal tide at these sites.The final part of the thesis investigates the possibility of internal wave attractors in the valley of double-ridge configurations. A one-dimensional map is developed to identify the existence and stability of attractors as a function of the ridge geometry. The Green function method is further advanced to include a viscous correction to balance energy focusing and dissipation along an attracting orbit of internal wave rays, and very good agreement is obtained between experiment and theory, even in the presence of an attractor.

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Numerical simulation of a two-dimensional internal wave attractor

Cited by 47 publications

References 19 publications

High-Resolution Simulation of Internal Waves Attractors and Impact of Interaction of High Amplitude Internal Waves With Walls on Dynamics of Waves Attractors

High-Resolution Simulation of Internal Waves Attractors and Impact of Interaction of High Amplitude Internal Waves With Walls on Dynamics of Waves Attractors

Generation and maintenance of bulk turbulence by libration-driven elliptical instability

Internal tide generation by tall ocean ridges

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