Internal shear layers from librating objects

Abstract

International audienc

Near-field internal wave beams in two dimensions

“…By contrast, for thin forcing, the evolution of the waves is set by the distance normal to the forcing. This can be seen in the inviscid calculations of Oser (1957), Reynolds (1962), Martin & Llewellyn Smith (2011, 2012 b ) and Davis (2012) for a horizontal disc, Hurley (1969) for an inclined plate and Llewellyn Smith & Young (2003) for a vertical plate, or in the viscous calculations of Kistovich & Chashechkin (1999 a , b ) for a two-dimensional inclined plate, Vasil'ev & Chashechkin (2003, 2006 a , b , 2012) for a three-dimensional inclined plate, Tilgner (2000), Bardakov, Vasil'ev & Chashechkin (2007), Davis & Llewellyn Smith (2010), Le Dizès (2015) and Le Dizès & Le Bars (2017) for a horizontal disc, Maurer etal. (2017) and Boury, Peacock & Odier (2019) for a horizontal wave generator and Beckebanze, Raja & Maas (2019) for a vertical wave generator.…”

Reflection of oscillating internal shear layers: nonlinear corrections

“…These beams and their role in the tidal conversion have been studied experimentally (Zhang et al, 2007;King et al, 2009;Echeverri & Peacock, 2010) as well as theoretically (St Laurent et al, 2003;Llewellyn Smith & Young, 2003;Balmforth & Peacock, 2009). Similar concentrated wave beams are also found in rotating fluids (Kerswell, 1995;Le Dizès & Le Bars, 2017). They have mainly been studied in spherical geometries (Calkins et al, 2010;Koch et al, 2013;Cébron et al, 2019;Lin & Noir, 2020) in the context of planetary applications (Le Bars et al, 2015).…”

“…The incident beam is assumed to be described by the similarity solution of Moore & Saffman (1969) and Thomas & Stevenson (1972). Using the notation introduced in Le Dizès & Le Bars (2017), this harmonic solution can be written as X (i) = e((v (i) , b (i) , p (i) )e −iωt ) where the velocity v (i) along the direction Figure 1. Sketches of the typical applications.…”

“…In addition to transporting momentum, they are expected to be involved in mixing and dissipation processes. Of special interest are the viscous harmonic wave beams that are created from critical surfaces, and boundary singularities because they are very thin and possess a universal transverse structure (Moore & Saffman, 1969;Thomas & Stevenson, 1972; Le Dizès & Le Bars, 2017). The goal of the present article is to analyse the reflection of such beams on a flat boundary in order to understand how second-harmonic and meanflow corrections are created during the reflection process.…”

Modeling the effect of centering of a spherical hydrodynamic suspension

“…Experimental data [1] confirm this effect for spherical hydrodynamic suspension. The influence of Coriolis forces of inertia on the dynamics of viscous incompressible fluid increases significantly with increasing oscillatory Reynolds numbers [3][4][5][6][7][8][9]. Nonlinear effects can destabilize the Couette flow in the layers between rotating spheres [10][11][12][13][14], but this is true when their angular velocities are significantly different.…”