EGU General Assembly 2020
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the Creative Commons Attribution 4.0 License.

Transition from geostrophic flows to inertia-gravity waves in the spectrum of a differentially heated rotating annulus experiment.

Costanza Rodda and Uwe Harlander
Costanza Rodda and Uwe Harlander
  • BTU Cottbus-Senftenberg, Department of Aerodynamics and Fluid Mechanics, Cottbus, Germany (

Inertia-gravity waves (IGWs) are known to play an essential role in the terrestrial atmospheric dynamics as they can lead to energy and momentum flux when they propagate upwards. An open question is to which extent nearly linear IGWs contribute to the total energy and to flattening of the energy spectrum observed at the mesoscale.
In this work, we present an experimental investigation of the energy distribution between the large-scale balanced flow and the small-scale imbalanced flow. Weakly nonlinear IGWs emitted from baroclinic jets are observed in the differentially heated rotating annulus experiment. Similar to the atmospheric spectra, the experimental kinetic energy spectra reveal the typical subdivision into two distinct regimes with slopes k-3 for the large scales and k-5/3 for smaller scales. By separating the spectra into a vortex and wave part, it emerges that at the largest scales in the mesoscale range the gravity waves observed in the experiment cause a flattening of the spectra and provide most of the energy. At smaller scales, our data analysis suggests a transition towards a turbulent regime with a forward energy cascade up to where dissipation by diffusive processes occurs.

How to cite: Rodda, C. and Harlander, U.: Transition from geostrophic flows to inertia-gravity waves in the spectrum of a differentially heated rotating annulus experiment., EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9374,, 2020


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displays version 1 – uploaded on 10 Apr 2020
  • CC1: Comment on EGU2020-9374, Paul PUKITE, 10 May 2020

    Isn't the Nastrom and Gage wavenumber spectrum more easily modelled as a Cauchy-like distribution? The inflection point breaks are a consequence of the shape of that curve and derived from the likelihood of a preferred wavenumber (see Mathematical Geoenergy (Wiley, 2019) chapter 11 ) 

    • AC1: Reply to CC1, Costanza Rodda, 11 May 2020

      Thank you very much for your interest in our work and for the reference. You are right, the data of Nastrom and Gage can be fitted to model distributions and we certainly can learn a lot from this approach. From the picture you provided the two different slopes in the spectrum are rather clear and your distribution smoothly connects the "two" curves. The question we are focusing on is why do we see the two slopes, no matter whether there is a smooth transition or whether one considers this as two curves covering different phenomena. The pressing issue for us is to physically and not statistically interpret the data. According to this, there are different and controversial ideas for the meso-scale part of the spectrum (3D turbulence, wave processes,...) and we think our experiment points to gravity waves and weak interactions of such waves as an explanation for the slope of the meso-scale.

      • CC2: Reply to AC1, Paul PUKITE, 11 May 2020

        Another suggestion is to model the spectrum in your slide 7 more realistically. There is clearly a strong periodic component in the wavetrain data. This is my attempt at extracting what appears to be a semi-random  sawtooth wave from the spectra (the method is described in my book Mathematical Geoenergy).   The point is that the more you can characterize the data the better that you can extract and discriminate the finer structure that you are interested in -- in your case the high wavenumber turbulence.

        • CC3: Reply to CC2, Paul PUKITE, 12 May 2020

          The width of the spectral lobes is due to the sampling being limited to a few cycles. By fitting to a cusped asymmetric sawtooth waveform of ~4 cycles, the power spectra can be duplicated precisely. 

          • AC2: Reply to CC3, Uwe Harlander, 12 May 2020

            Dear Paul,

            thank you very much for your interesting comments. You are right, due to the length of the measured time series the low-frequency wave part is indeed limited to a few waves and also the skewness of the wave form you have shown seems to be rather realistic to me. The low-frequency part consists of Rossby waves (or their relatives, Eady waves) and the cold front is usually steeper as the warm front of the wave.

            Thanks a lot. We are not familiar with the techniques you use but we will take a closer look to your book. Would be great to stay in contact.

            Best wishes,