On the generation mechanisms of short-scale unbalanced modes in rotating two-layer flows with vertical shear

Abstract

We report on the results of a laboratory investigation using a rotating two-layer annulus experiment, which exhibits both large-scale vortical modes and short-scale divergent modes. A sophisticated visualization method allows us to observe the flow at very high spatial and temporal resolution. The balanced long-wavelength modes appear only when the Froude number is supercritical (i.e. F > F critical ≡ π 2 /2), and are therefore consistent with generation by a baroclinic instability. The unbalanced shortwavelength modes appear locally in every single baroclinically unstable flow, providing perhaps the first direct experimental evidence that all evolving vortical flows will tend to emit freely propagating inertia-gravity waves. The short-wavelength modes also appear in certain baroclinically stable flows. We infer the generation mechanisms of the short-scale waves, both for the baroclinically unstable case in which they co-exist with a large-scale wave, and for the baroclinically stable case in which they exist alone. The two possible mechanisms considered are spontaneous adjustment of the large-scale flow, and Kelvin-Helmholtz shear instability. Short modes in the baroclinically stable regime are generated only when the Richardson number is subcritical (i.e. Ri < Ri critical ≡ 1), and are therefore consistent with generation by a Kelvin-Helmholtz instability. We calculate five indicators of shortwave generation in the baroclinically unstable regime, using data from a quasi-geostrophic numerical model of the annulus. There is excellent agreement between the spatial locations of shortwave emission observed in the laboratory, and regions in which the model Lighthill/Ford inertia-gravity wave source term is large. We infer that the short waves in the baroclinically unstable fluid are freely propagating inertia-gravity waves generated by spontaneous adjustment of the large-scale flow.

Spontaneous Gravity Wave Radiation in a Shallow Water System on a Rotating Sphere

“…This was because U 0 and H 0 are constant for the cases of fixed Fr, and an unsteady jet flow is qualitatively the same for all cases. The shift of the dominant source term, which agrees with a previous laboratory study (Williams et al 2005(Williams et al , 2008, may cause an amplification of the gravity wave flux for smaller Ro. It is probable that there is a lo- cal maximum in the gravity wave flux for the cases of smaller Fr for Ro ∼ 10.…”

“…In contrast, in the process of spontaneous emission, gravity waves are radiated from unsteady rotational flows at any stage of time evolution. Although there are several theoretical (Vanneste and Yavneh 2004;Vanneste 2008) and experimental (Williams et al 2005;Afanasyev et al 2008) studies on spontaneous emission, the radiation processes of gravity waves are not fully understood.…”

Increased light, moderate, and severe clear-air turbulence in response to climate change

“…The hypothesis also concurs with evidence that eastbound transatlantic flights, being closer to the strong tailwinds in the core of the jet stream, encounter more clear-air turbulence than westbound transatlantic flights . Gravity waves, including those generated as the atmosphere adjusts to a loss of balance (Williams et al, 2003(Williams et al, , 2005, may play a role by initiating the Kelvin-Helmholtz instability in an otherwise stable part of the atmosphere (Knox et al, 2008;McCann et al, 2012).…”

Application of the Lighthill–Ford Theory of Spontaneous Imbalance to Clear-Air Turbulence Forecasting

“…Even weak gravity waves can have sizable impacts on the background flow (Williams et al 2003). In this paper, we emphasize that weak gravity waves can modify the local environmental stability and wind shear to reduce the Richardson number (section 6.3 of Nappo 2003) to values that allow for turbulence production (Roach 1970;McCann 2001).…”