Energy Spectra Of Strongly Stratified And Rotating Turbulence

Author : Hossein Amini Kafiabad
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)

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Download or read book Spontaneous Imbalance in Rotating Stratified Turbulence written by Hossein Amini Kafiabad and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Whereas high-frequency waves are valid solutions to the Boussinesq equations in certain limits, their amplitudes are generally observed to be small in large-scale atmospheric and oceanic data. Traditionally, this has led to the development of balance models, reducing the dynamics to only the slow subset. Their solutions, however, can spontaneously generate imbalance in the context of the full equations. To study this phenomenon, we perform high-resolution turbulence simulations of the non-hydrostatic Boussinesq equations, starting with a high-order nonlinearly balanced initial condition. To produce this initial condition, we employ the nonlinear normal mode initialization scheme that was introduced by Baer and Tribbia (1977) up to second order in the Rossby number as the next-order improvement to quasigeostrophic theory. This initialisation is devised to limit the growth of high-frequency modes initially. To keep the flow predominantly balanced, we set the initial Rossby, Ro, and Froude, Fr, numbers to small values. By increasing these dimensionless parameters slightly, we investigate at what scales balance breaks down and after how long. Our results show that the balanced initial condition displays a steep geostrophic energy spectrum and an even steeper ageostrophic energy spectrum. However, a shallow tail later develops in the ageostrophic energy spectrum at small scales if Ro and the Reynolds number, Re, are large enough. This shallow range moves toward smaller wavenumbers if Ro is increased. Increasing N/f (while f is held nearly constant) leads to a shift of the shallow tail to smaller scales due to lower amplitudes of the unbalanced modes. By implementing a Baer-Tribbia-based balance/imbalance decomposition at the end of the integration time, we show that the unbalanced component of the dynamics accounts for the shallow range in the energy spectrum. This breakdown of balance, which leads to a change of slope in the energy spectrum, is consistent with observed atmospheric and oceanic spectra. The disparity between the fast and slow timescales, which is a requirement of balance, is shown to break down at scales where the energy spectrum is still steep and the scale-dependent Ro and Fr are small. Spontaneous imbalance, which is the energy transfer from the balanced to the unbalanced modes, is also quantified in this study. More particularly, the scale at which it occurs and its dependence on the flow parameters are investigated. In our simulations, this quantity is shown to scale approximately as Ro^4.4 for our decomposition, accurate to second order in Ro. However, the wavenumber at which the maximum energy transfer from balance to imbalance occurs is invariant to Ro and Fr but dependent on the large-scale flow characterised by the Rossby radius of deformation. This wavenumber is found to be smaller than the wavenumber characterising the transition between the large scales and the shallow tail but larger than the peak of the energy spectrum. By comparing the results at different orders of balance, it is determined that all qualitative conclusions of this study are robust to the precise definition of balance. " --