Observations on the robustness of internal wave attractors to perturbations

Abstract

Previously, internal wave attractors have been studied in the laboratory in idealized situations. Here, we present a series of experiments in which these conditions are modified. Modifications are made by varying the forcing frequency, by using a nonuniform stratification, by introducing finite amplitude perturbations to the trapezoidal domain, and by using a parabolic domain. All these new experiments reveal the persistence of internal wave attractors that remain reasonably well predictable by means of ray tracing. We conclude that the occurrence of wave attractors is likely to be more general than has previously been thought. The fundamental response of the confined, continuously stratified fluids studied in this paper to a sustained forcing has to be described in terms of internal wave attractors.

Nonlinear Fate of Internal Wave Attractors

“…The profile (1) is reproduced in discrete stepwise form by the motion of 51 horizontal plates driven by the rotation of a vertical camshaft. Since the thickness of each plate is small compared to the width of the wave-attractor beams, the discretization does not produce any secondary perturbations to the wave field, in agreement with [8,15]. The perturbations of the density gradient are evaluated with the synthetic schlieren technique [17] from apparent displacements of elements of the background random dot pattern placed behind the test tank.…”

“…Numerically, nearly all studies of wave attractors solve linear equations of motion as stressed in [6]. Experimentally, attractors are usually generated by low-amplitude vertical or horizontal oscillations of test tanks filled with stratified fluids [5,7,8] or by a modulation of the angular velocity in rotating fluids [12]. Oscillations of small objects have also been used to produce internal waves forming attractor-like patterns in 2D [11] and 3D [13] geometries.…”

“…In reality, a finite width of wave beams is set by the balance between geometric focusing and viscous broadening [6,7]. Attractors were shown to be sufficiently robust to be observable in a non-uniform stratification and in test tanks with corrugated walls [8] as well as in laterally infinite fluid domains with appropriate bottom topography [9]. The significance of wave attractors has been recognized in rotating fluids [10] and proposed for magnetized materials [11].…”

Vertical propagation of lakewide internal waves

“…In this case, waves propagate ever closer to trajectories called 'Internal Wave Attractors' (IWAs) [Maas and Lam, 1995]. To date, IWAs have been identified in the laboratory [Maas et al, 1997;Hazewinkel et al, 2010] but not in the field.…”

A conundrum in conversion

“…Lam & Maas 2008) although the problem goes back to John (1941). The peculiar nature of the Poincaré equation leads to the existence of wave attractors, which are seen in experiments (Maas et al 1997;Hazewinkel et al 2010). To quote the title of one such paper, these problems are linear yet nonlinear: the field equations are linear but the boundary conditions on finite topography lead to nonlinear problems.…”