Inertia–gravity waves in a liquid-filled, differentially heated, rotating annulus

Abstract

International audienceDirect numerical simulations based on high-resolution pseudospectral methods are carried out for detailed investigation into the instabilities arising in a differentially heated, rotating annulus, the baroclinic cavity. Following previous works using air (Randriamampianina et al., J. Fluid Mech., vol. 561, 2006, pp. 359–389), a liquid defined by Prandtl number Pr=16 is considered in order to better understand, via the Prandtl number, the effects of fluid properties on the onset of gravity waves. The computations are particularly aimed at identifying and characterizing the spontaneously emitted small-scale fluctuations occurring simultaneously with the baroclinic waves. These features have been observed as soon as the baroclinic instability sets in. A three-term decomposition is introduced to isolate the fluctuation field from the large-scale baroclinic waves and the time-averaged mean flow. Even though these fluctuations are found to propagate as packets, they remain attached to the background baroclinic waves, locally triggering spatio-temporal chaos, a behaviour not observed with the air-filled cavity. The properties of these features are analysed and discussed in the context of linear theory. Based on the Richardson number criterion, the characteristics of the generation mechanism are consistent with a localized instability of the shear zonal flow, invoking resonant over-reflection

Spontaneous inertia–gravity wave emission in the differentially heated rotating annulus experiment

“…After being generated these waves propagate into the interior of the annulus domain. Similar wave characteristics were found by Randriamampianina (2013) and Randriamampianina & Crespo del Arco (2015). However, in contrast to Jacoby et al (2011), the authors assume that a temperature overturn in combination with a flow reversal leads to the formation of a billow similar to that seen in Kevin-Helmholtz instabilities.…”

“…Without doubt, there is a substantial part of IGWs which is generated at the the inner side wall before propagating into the interior of the annulus domain. This mechanism is studied extensively by Jacoby et al (2011) and Randriamampianina & Crespo del Arco (2015). However, both of these studies consider a traditional annulus setup with N/f < 1.…”

“…Previous studies indicate that IGWs in the differentially heated rotating annulus originate both from the jet-front system and from the boundary layer located at the inner side wall of the annulus (Jacoby et al 2011;Randriamampianina 2013;Randriamampianina & Crespo del Arco 2015;Borchert et al 2014). We wish to contribute to the improvement of the physical understanding of the source processes, so that we focus on IGWs originating from the jet-front system.…”

“…The explanation for the absence of WP3 in the linear model is that it is generated by boundary layer instabilities occurring at the inner side wall of the annulus and propagates into the interior of the domain. As mentioned in section 1, proposed generation mechanism for the radiation of such waves are, for instance, discussed in Jacoby et al (2011) and Randriamampianina & Crespo del Arco (2015). Due to the application of the window function implemented in our linear model (see section 2.2.3) we suppress these processes.…”

Baroclinic, Kelvin and inertia-gravity waves in the barostrat instability experiment

“…This particular configuration is not only interesting for investigating the wave regimes that develop in the fluid depth as well as studying inertial Kelvin/baroclinic wave coupling and the coexistence of different baroclinic waves, but also to investigate the occurrence of small-scale waves and in particular inertia gravity waves spontaneously emitted by the baroclinic wave. Recently, several numerical models (Jacoby et al 2011, Borchert et al 2014, Randriamampianina and del Arco 2015 and laboratory experiments (Lovegrove et al 2000, Williams et al 2005 have used different configurations of the rotating annulus experiment to investigate the interaction between largescale 'balanced' flow components (quasi-geostrophic baroclinic waves) and 'fast', small-scale, ageostrophic inertia-gravity waves.…”