Inertial waves in rapidly rotating flows: a dynamical systems perspective

Abstract

Abstract.An overview of recent developments in a wide variety of enclosed rapidly rotating flows is presented. Highlighted is the interplay between inertial waves, which have been predicted from linear inviscid considerations, and the viscous boundary layer dynamics which result from instabilities as the nonlinearities in the systems are increased. Further, even in the absence of boundary layer instabilities, nonlinearity in the system often leads to complicated interior flows due to subcritical instabilities, Eckhaus bands and heteroclinic dynamics. The ensuing spatio-temporally complex dynamics are analysed in terms of equivariant dynamical systems, providing a general perspective for the wide range of dynamics involved.

Rapidly rotating precessing cylinder flows: forced triadic resonances

“…One of the goals is to understand what aspects of the dynamics observed in the previous studies are specific to the Kelvin triadic resonances, and which are generic in precessing flows. In rotating cylinder flows, the boundary layers provide the localized driving that generates inertial wave beams, particularly near the corners where the cylinder endwalls meet the sidewall (Lopez & Marques 2011Lopez & Gutierrez-Castillo 2016;Lopez & Marques 2016a). In precessing flows, these wave beams are not axisymmetric due to the presence of the overturning flow, which completely breaks the rotational symmetry.…”

Superharmonic and triadic resonances in a horizontally oscillated stably stratified square cavity

“…Very-low-frequency states may appear in autonomous (unforced) systems after a sequence of bifurcations introducing new frequencies into the flow (Lopez & Marques 2003; Abshagen et al. 2005), but in the context of the present study, they have also been found to play important dynamical roles in parametrically forced flows, particularly in parameter regimes involving triadic resonances (Marques & Lopez 2015; Lopez & Marques 2016 a , b , 2018).…”