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

Abstract

The source mechanism of inertia–gravity waves (IGWs) observed in numerical simulations of the differentially heated rotating annulus experiment is investigated. The focus is on the wave generation from the balanced part of the flow, a process presumably contributing significantly to the atmospheric IGW field. Direct numerical simulations are performed for an atmosphere-like configuration of the annulus and possible regions of IGW activity are characterised by a Hilbert-transform algorithm. In addition, the flow is separated into a balanced and unbalanced part, assuming the limit of a small Rossby number, and the forcing of IGWs by the balanced part of the flow is derived rigorously. Tangent-linear simulations are then used to identify the part of the IGW signal that is rather due to radiation by the internal balanced flow than to boundary-layer instabilities at the side walls. An idealised fluid set-up without rigid horizontal boundaries is considered as well, to investigate the effect of the identified balanced forcing unmasked by boundary-layer effects. The direct simulations of the realistic and idealised fluid set-ups show a clear baroclinic-wave structure exhibiting a jet–front system similar to its atmospheric counterparts, superimposed by four distinct IGW packets. The subsequent tangent-linear analysis indicates that three wave packets are radiated from the internal flow and a fourth one is probably caused by boundary-layer instabilities. The forcing by the balanced part of the flow is found to play a significant role in the generation of IGWs, so it supplements boundary-layer instabilities as a key factor in the IGW emission in the differentially heated rotating annulus.

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

“…Although spontaneous imbalance has been documented from a number of numerical simulations also for the annulus configuration (Borchert et al (2014) and Hien et al (2018)) for which Reynolds number like in the experiment was rather small (Re 100) it has never been experimentally observed for the continuously stratified annulus for which in general the Rossby numbers are rather small and the flow is in a nearly balanced state. In our experiments the top layer shows wave packets in the horizontal divergence field travelling mainly with the frontal mean flow and hence much faster than the drift speed of the baroclinic waves.…”

Higher-order compact scheme for high-performance computing of stratified rotating flows

“…This variable is introduced to exhibit the occurrence of small-scale features simultaneously with the large-scale baroclinic waves. In the first plot, the small-scale structures, developing towards the bottom wall, have been identified as inertia gravity waves (IGWs) by different authors [37][38][39] in similar water-filled cavities. The present observed features recall such IGWs reported by these authors.…”

“…Since the pioneering works of Hide [12] , the differentially heated, rotating cylindrical annulus has been an archetypal means of studying the properties of fully-developed baroclinic instability in the laboratory. Recent works mainly based on direct numerical simulations reported the occurrence of IGWs in water-filled baroclinic cavity along the inner cold cylinder [37][38][39] . Moreover, Von Larcher et al [39] observed the presence of additional small-scale ripples resulting from hydrodynamical instability along the hot wall.…”

Efficient Modeling of the Interaction of Mesoscale Gravity Waves with Unbalanced Large-Scale Flows: Pseudomomentum-Flux Convergence versus Direct Approach

“…As one of the most fundamental physical modes in meteorology, gravity waves (GWs) are ubiquitous buoyancy oscillations in the atmosphere. The sources of excited gravity waves include, among others, topographic forcing (Smith 1980;Menchaca and Durran 2017), convection (Alexander et al 1995;Lane et al 2001), the jets Plougonven and Zhang 2014;Hien et al 2018), frontal systems (Snyder et al 1993; Griffiths and Reeder 1996), and shear instability (Bühler et al 1999;Bühler and McIntyre 1999). GW dynamics is also influenced by rotation, especially when the respective waves have relatively long horizontal wavelengths and short vertical wavelengths.…”