Reflections and focusing of inertial waves in a librating cube with the rotation axis oblique to its faces

Wu, Ke; Welfert, Bruno D.; Lopez, Juan M.

doi:10.1017/jfm.2020.328

Cited by 10 publications

(43 citation statements)

References 22 publications

(47 reference statements)

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“…At sufficiently large , the wave beams originating from the edges are only weakly damped as they propagate along straight lines, and eventually reflect on the walls of the container. The reflection laws for internal waves in stratified fluids are similar to those for inertial waves in rotating fluids, and are in general different from standard Euclidean reflection laws (Phillips 1963; Wu, Welfert & Lopez 2020), unless the reflecting surface is parallel or perpendicular to the direction of stratification (or the axis of rotation), as is the case here for all walls of the container. Figure 2 illustrates the patterns of the beams in three planes, (vertical streamwise midplane), (vertical, spanwise in the slat boundary layer) and (horizontal, at roughly 3/4 height), at two forcing frequencies .…”

Section: Response Flowsmentioning

confidence: 65%

Oblique instability of a stratified oscillatory boundary layer

2021

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The instability and dynamics of a vertical oscillatory boundary layer in a container filled with a stratified fluid are addressed. Past experiments have shown that when the boundary oscillation frequency is of the same order as the buoyancy frequency, the system is unstable to a herringbone pattern of oblique waves. Prior studies assuming the basic state to be a unidirectional oscillatory shear flow were unable to account for the oblique waves. By accounting for confinement effects present in the experiments, and the ensuing three-dimensional structure of the basic state, we are able to numerically reproduce the experimental observations, opening the door to fully analysing the impacts of stratification on such boundary layers.

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Section: Response Flowsmentioning

confidence: 65%

Oblique instability of a stratified oscillatory boundary layer

2021

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“…These beams usually originate from localized forcings and are aligned with the characteristics, typically forming a St Andrew's cross pattern (Görtler 1943; Mowbray & Rarity 1967; Voisin 2003). The piecewise constant vorticity solutions obtained here constitute a more regular class of beams, with energy distributed over the container rather than focused in rays or sheets, and can be overshadowed by these stronger beams when the latter are present, as happens, for example, in numerical simulations of parametrically forced rotating flows (Wu et al 2020).…”

Section: Discussionmentioning

confidence: 75%

“…Maas & Lam 1995; Wotherspoon 1995), there is still much to learn (e.g. Bajars et al 2013; Pillet et al 2018; Pillet, Maas & Dauxois 2019), and approaches from the study of how inertial waves reflect in the obliquely rotating cube (Wu et al 2020) can be adapted for the internal wave problem.…”

Section: Summary Discussion and Perspectivesmentioning

confidence: 99%

“…Smooth intrinsic modes which are not completely separable have also been found, for example, in rotating rectangular containers (Maas 2003; Wu, Welfert & Lopez 2018 b ). However, one should in general expect singular (non-smooth) solutions (Aldridge 1975; Maas & Lam 1995; Rieutord, Georgeot & Valdettaro 2000; Harlander & Maas 2007; Swart et al 2007; Bajars, Frank & Maas 2013; Borcia, Abouzar & Harlander 2014; Pillet et al 2018; Rieutord & Valdettaro 2018; Wu, Welfert & Lopez 2020). These non-smooth solutions, which can be described as the superposition of an infinite number of regular ‘modes’ (and as such are non-separable), have been found in the inviscid limit in geometries where some or all of the container boundaries are neither parallel nor orthogonal to gravity or the mean rotation.…”

Section: Introductionmentioning

confidence: 99%

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Stably stratified square cavity subjected to horizontal oscillations: responses to small amplitude forcing

et al. 2021

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“…1997; Manders & Maas 2003; Klein et al. 2014; Wu, Welfert & Lopez 2020 b ). Of particular interest is the latter configuration in the context of the present paper.…”

Section: Introductionmentioning

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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Reflections and focusing of inertial waves in a librating cube with the rotation axis oblique to its faces

Cited by 10 publications

References 22 publications

Oblique instability of a stratified oscillatory boundary layer

Oblique instability of a stratified oscillatory boundary layer

Stably stratified square cavity subjected to horizontal oscillations: responses to small amplitude forcing

Vortex cluster arising from an axisymmetric inertial wave attractor

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