Experimental evidence of internal wave attractor signatures hidden in large-amplitude multi-frequency wave fields

Beckebanze, F.; Grayson, Katherine; Maas, Leo R. M.; Dalziel, Stuart B.

doi:10.1017/jfm.2021.24

Cited by 6 publications

(5 citation statements)

References 34 publications

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“…Thus, both TRI and the two-wave interactions (Beckebanze et al. 2021; Boury, Peacock & Odier 2021) are present in the system and play a role. The corresponding energy spectrum shown in figure 9 demonstrates that the linear dispersion relation attracts the energy maxima.…”

Section: Numerical Resultsmentioning

confidence: 99%

Vortex cluster arising from an axisymmetric inertial wave attractor

et al. 2021

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We present an experimental and numerical study of the nonlinear dynamics of an inertial wave attractor in an axisymmetric geometrical setting. The rotating ring-shaped fluid domain is delimited by two vertical coaxial cylinders, a conical bottom and a horizontal wave generator at the top: the vertical cross-section is a trapezium, while the horizontal cross-section is a ring. Forcing is introduced via axisymmetric low-amplitude volume-conserving oscillatory motion of the upper lid. The experiment shows an important result: at sufficiently strong forcing and long time scale, a saturated fully nonlinear regime develops as a consequence of an energy transfer draining energy towards a slow two-dimensional manifold represented by a regular polygonal system of axially oriented cyclonic vortices undergoing a slow prograde motion around the inner cylinder. We explore the long-term nonlinear behaviour of the system by performing a series of numerical simulations for a set of fixed forcing amplitudes. This study shows a rich variety of dynamical regimes, including a linear behaviour, a triadic resonance instability, a progressive frequency enrichment reminiscent of weak inertial wave turbulence and the generation of a slow manifold in the form of a polygonal vortex cluster confirming the experimental observation. This vortex cluster is discussed in detail, and we show that it stems from the summation and merging of wave-like components of the vorticity field. The nature of these wave components, the possibility of their detection under general conditions and the ultimate fate of the vortex clusters at even longer time scale remain to be explored.

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Section: Numerical Resultsmentioning

confidence: 99%

Vortex cluster arising from an axisymmetric inertial wave attractor

et al. 2021

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“…Along a 1 m section of the tank floor, 2.5 m from the left-hand wall of the tank, sits the Arbitrary Spectrum Wave Maker (ASWaM), also known as the 'magic carpet'. This flexible horizontal boundary can generate sinusoidal forcing (Beckebanze et al 2021;Dobra, Lawrie & Dalziel 2021, 2022 (as well as aperiodic configurations (Dobra, Lawrie & Dalziel 2019)), with the ability to vary amplitude, frequency and wavenumber in both the temporal and spatial domains. The wavemaker is composed of a series of 96 computer-controlled linear actuators that sit below the tank.…”

Section: Experimental Set-upmentioning

confidence: 99%

The long view of triadic resonance instability in finite-width internal gravity wave beams

2022

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This article presents our exploration into how a finite-width internal gravity wave beam is modified by triadic resonance instability. We present both experimental and weakly nonlinear modelling to examine this instability mechanism, in which a primary wave beam generates two secondary wave beams of lower frequencies and shorter length scales. Through a versatile experimental set-up, we examine how this instability evolves over hundreds of buoyancy periods. Unlike predictions from previous zero-dimensional weakly nonlinear theory, we find that the wave does not monotonically approach a saturated equilibrium of triadic interactions; rather, the amplitudes and structures of the constituent beams continue to modulate without ever reaching a steady equilibrium. To understand this behaviour, we develop a weakly nonlinear approach to account for the spatiotemporal evolution of the amplitudes and structures of the beams over slow time scales and long distances, and explore the consequences using a numerical scheme to solve the resulting equations. Through this approach, we establish that the evolution of the instability is remarkably sensitive to the spatiotemporal triadic configuration for the system and how part of the observed modulations can be attributed to a competition between the linear growth rate of the secondary wave beams and the finite residence time of the triadic perturbations within the underlying primary beam.

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“…2014; Jouve & Ogilvie 2014; Beckebanze et al. 2021; Ryazanov et al. 2021) and instabilities (Brouzet et al.…”

Section: Introductionmentioning

confidence: 99%

“…However, the picture seems more complex in a spherical shell owing to the presence of the rotation axis in the domain and of a critical latitude singularity issued from the inner sphere (Rieutord & Valdettaro 2010He et al 2022He et al , 2023. The robustness of attractors has been analysed with respect to wall friction (Beckebanze et al 2018), nonlinearity (Grisouard et al 2008;Favier et al 2014;Jouve & Ogilvie 2014;Beckebanze et al 2021;Ryazanov et al 2021) and instabilities (Brouzet et al 2016b(Brouzet et al , 2017Dauxois et al 2018). The 2-D framework has also been used to obtain most of the available mathematical results (Maas & Lam 1995;Manders, Duistermaat & Maas 2003;Maas 2009;Bajars, Frank & Maas 2013;Beckebanze & Keady 2016;de Verdière & Saint-Raymond 2020;Dyatlov, Wang & Zworski 2022;Makridin et al 2023).…”

Section: Introductionmentioning

confidence: 99%

Inertial wave super-attractor in a truncated elliptic cone

Favier,

Le Dizès

2024

J. Fluid Mech.

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We consider inertial waves propagating in a fluid contained in a non-axisymmetric three-dimensional rotating cavity. We focus on the particular case of a fluid enclosed inside a truncated cone or frustum, which is the volume that lies between two horizontal parallel planes cutting an upright cone. While this geometry has been studied in the past, we generalise it by breaking its axisymmetry and consider the case of a truncated elliptic cone for which the horizontal sections are elliptic instead of circular. The problem is first tackled using ray tracing, where local wave packets are geometrically propagated and reflected within the closed volume without attenuation. We complement these results with a local asymptotic analysis and numerical simulations of the original linear viscous problem. We show that the attractors, well known in two dimensional or axisymmetric domains, can be trapped in a particular plane in three dimensions provided that the axisymmetry of the domain is broken. Contrary to previous examples of attractors in three-dimensional domains, all rays converge towards the same limit cycle regardless of initial conditions, and it is localised in the bulk of the fluid.

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Experimental evidence of internal wave attractor signatures hidden in large-amplitude multi-frequency wave fields

Abstract: Abstract

Cited by 6 publications

References 34 publications

Vortex cluster arising from an axisymmetric inertial wave attractor

Vortex cluster arising from an axisymmetric inertial wave attractor

The long view of triadic resonance instability in finite-width internal gravity wave beams

Inertial wave super-attractor in a truncated elliptic cone

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