Possible Explanation of the Atmospheric Kinetic and Potential Energy Spectra

Vallgren, Andreas; Deusebio, Enrico; Lindborg, Erik

doi:10.1103/physrevlett.107.268501

Cited by 42 publications

(60 citation statements)

References 29 publications

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“…In three dimensions (3D), energy is transferred in a direct cascade towards small scales [1,2], whereas in two dimensions (2D) energy undergoes an inverse cascade towards large scales [3,4]. Numerical simulations have confirmed this picture in both 3D [5] and 2D turbulence [6,7] but they have also shown that the two processes are not mutually exclusive and the coexistence of both a downscale and upscale energy transfer has been observed [8][9][10][11][12].…”

Section: Introductionsupporting

confidence: 55%

Dimensional transition in rotating turbulence

et al. 2014

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In this work we investigate, by means of direct numerical hyperviscous simulations, how rotation affects the bidimensionalization of a turbulent flow. We study a thin layer of fluid, forced by a two-dimensional forcing, within the framework of the "split cascade" in which the injected energy flows both to small scales (generating the direct cascade) and to large scale (to form the inverse cascade). It is shown that rotation reinforces the inverse cascade at the expense of the direct one, thus promoting bidimensionalization of the flow. This is achieved by a suppression of the enstrophy production at large scales. Nonetheless, we find that, in the range of rotation rates investigated, increasing the vertical size of the computational domain causes a reduction of the flux of the inverse cascade. Our results suggest that, even in rotating flows, the inverse cascade may eventually disappear when the vertical scale is sufficiently large with respect to the forcing scale. We also study how the split cascade and confinement influence the breaking of symmetry induced by rotation.

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Section: Introductionsupporting

confidence: 55%

Dimensional transition in rotating turbulence

et al. 2014

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“…h to a k −5/3 h spectrum have been simulated both in idealized numerical simulations (Kitamura & Matsuda 2006;Bartello 2010;Vallgren, Deusebio & Lindborg 2011) and atmospheric models (Skamarock 2004;Takahashi, Hamilton & Ohfuchi 2006;Hamilton, Takahashi & Ohfuchi 2008;Waite & Snyder 2009). Bartello (2010) simulated a strongly stratified and rotating flows in a triply periodic domain forced only at large scales.…”

Section: Introductionmentioning

confidence: 99%

The route to dissipation in strongly stratified and rotating flows

2013

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We investigate the route to dissipation in strongly stratified and rotating systems through high-resolution numerical simulations of the Boussinesq equations (BQs) and the primitive equations (PEs) in a triply periodic domain forced at large scales. By applying geostrophic scaling to the BQs and using the same horizontal length scale in defining the Rossby and the Froude numbers, Ro and Fr, we show that the PEs can be obtained from the BQs by taking the limit Fr 2 /Ro 2 → 0. When Fr 2 /Ro 2 is small the difference between the results from the BQ and the PE simulations is shown to be small. For large rotation rates, quasi-geostrophic dynamics are recovered with a forward enstrophy cascade and an inverse energy cascade. As the rotation rate is reduced, a fraction of the energy starts to cascade towards smaller scales, leading to a shallowing of the horizontal spectra from kat the small-scale end. The vertical spectra show a similar transition as the horizontal spectra and we find that Charney isotropy is approximately valid also at larger wavenumbers than the transition wavenumber. The high resolutions employed allow us to capture both ranges within the same simulation. At the transition scale, kinetic energy in the rotational and in the horizontally divergent modes attain comparable values. The divergent energy is several orders of magnitude larger than the quasi-geostrophic divergent energy given by the Ω-equation. The amount of energy cascading downscale is mainly controlled by the rotation rate, with a weaker dependence on the stratification. A larger degree of stratification favours a downscale energy cascade. For intermediate degrees of rotation and stratification, a constant energy flux and a constant enstrophy flux coexist within the same range of scales. In this range, the enstrophy flux is a result of triad interactions involving three geostrophic modes, while the energy flux is a result of triad interactions involving at least one ageostrophic mode, with a dominant contribution from interactions involving two ageostrophic and one geostrophic mode. Dividing the ageostrophic motions into two classes depending on the sign of the linear wave frequency, we show that the energy transfer is for the largest part supported by interactions within the same class, ruling out the wave-wave-vortex resonant triad interaction as a mean of the downscale energy transfer. The role of inertia-gravity waves is studied through analyses of time-frequency spectra of single Fourier modes. At large scales, distinct peaks at frequencies predicted for linear waves are observed, whereas at small scales no clear wave activity is observed. Triad interactions show a behaviour which is consistent with turbulent dynamics, with a large exchange of † Email address for correspondence: deusebio@mech.kth.se The route to dissipation in strongly stratified and rotating flows 67 energy in triads with one small and two large comparable wavenumbers. The exchange of energy is mainly between the modes with two comparable wavenumbers.

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“…In the first, which we call Q-forcing, the forcing is restricted to the q-equation. This is the same scheme as used in Vallgren et al (2011) and Deusebio et al (2013). In the second scheme, which we call mixed forcing or M-forcing, the forcing is applied to all three equations, with about twothirds of the energy injection into the ageostrophic modes, a 1 and a 2 .…”

Section: Simulationsmentioning

confidence: 99%

“…It has also been demonstrated that the strongly stratified turbulence regime can be obtained in the presence of system rotation (Lindborg 2005;Waite & Bartello 2006), provided that the rotation is not too strong. Recently, Vallgren, Deusebio & Lindborg (2011) and Deusebio, Vallgren & Lindborg (2013) carried out numerical simulations of strongly stratified turbulence at strong system rotation, that is at small Rossby number Ro = U/f L, where f is the Coriolis parameter. They showed that even for very small Ro a substantial part of the injected energy cascades towards small scales.…”

Section: Introductionmentioning

confidence: 99%

Third-order structure functions in rotating and stratified turbulence: a comparison between numerical, analytical and observational results

2014

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International audienceFirst, we review analytical and observational studies on third-order structure functions including velocity and buoyancy increments in rotating and stratified turbulence and discuss how these functions can be used in order to estimate the flux of energy through different scales in a turbulent cascade. In particular, we suggest that the negative third-order velocity–temperature–temperature structure function that was measured by Lindborg & Cho (Phys. Rev. Lett., vol. 85, 2000, p. 5663) using stratospheric aircraft data may be used in order to estimate the downscale flux of available potential energy (APE) through the mesoscales. Then, we calculate third-order structure functions from idealized simulations of forced stratified and rotating turbulence and compare with mesoscale results from the lower stratosphere. In the range of scales with a downscale energy cascade of kinetic energy (KE) and APE we find that the third-order structure functions display a negative linear dependence on separation distance r, in agreement with observation and supporting the interpretation of the stratospheric data as evidence of a downscale energy cascade. The spectral flux of APE can be estimated from the relevant third-order structure function. However, while the sign of the spectral flux of KE is correctly predicted by using the longitudinal third-order structure functions, its magnitude is overestimated by a factor of two. We also evaluate the third-order velocity structure functions that are not parity invariant and therefore display a cyclonic–anticyclonic asymmetry. In agreement with the results from the stratosphere, we find that these functions have an approximate r2-dependence, with strong dominance of cyclonic motions

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Possible Explanation of the Atmospheric Kinetic and Potential Energy Spectra

Cited by 42 publications

References 29 publications

Dimensional transition in rotating turbulence

Dimensional transition in rotating turbulence

The route to dissipation in strongly stratified and rotating flows

Third-order structure functions in rotating and stratified turbulence: a comparison between numerical, analytical and observational results

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