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Turbulent cascades in geosciences 100 years after Richardson 1922

In his seminal work "Weather Prediction by Numerical Process" in 1922, Lewis Fry Richardson proposed his famous cascade picture qualitatively, for a turbulent flow where the energy is transferred from large scale structures to small scale ones, until reaching viscosity scales where it is converted to heat. This picture now has been widely adopted to describe different type of turbulent phenomena, for not only the classical hydrodynamic turbulence, but also, not limited to, the movement of atmosphere and oceans.

After 100 years of developments, the concept of cascades has been extended significantly. Now, it describes mainly the nonlinear interactions crossing a large range of scales where scale invariants might emerge spontaneously. More precisely, balances between the external forcing and the dissipation are expected for a turbulent system. However, due to the complexity of atmospheric or oceanic systems, such as earth rotation, stratification, large aspect ratio, mesoscale eddies, ocean current, tidal, waves, etc., the exact balance is still unknown. We still lack an efficient methodology to diagnose the scale-to-scale energy or other physical quantities fluxes to characterize the cascade quantitatively, e.g., strength, direction, etc.

With the increasing capability of remote sensing, computational fluid dynamics, field observation, etc., we have accumulated a large amount of field data. It is now a suitable time to celebrate the 100th Anniversary of Richardson's idea of cascades in the geosciences, and to understand it quantitatively.
This interdisciplinary session welcomes theoretical, methodological, laboratory, data analysis works that aim to characterize the cascade in atmosphere and oceans and other fields.

Co-organized by AS1/OS4/ST3
Convener: Yongxiang Huang | Co-conveners: François G. Schmitt, Shaun Lovejoy, Tommaso AlbertiECSECS, Stéphane Vannitsem
Presentations
| Wed, 25 May, 11:05–11:44 (CEST), 13:20–14:50 (CEST)
 
Room 0.94/95

Wed, 25 May, 10:20–11:50

Chairpersons: Stéphane Vannitsem, Tommaso Alberti, François G. Schmitt

11:05–11:07
Introduction

11:07–11:08
Theories

11:08–11:15
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EGU22-3918
Sébastien Aumaitre and Stéphan Fauve

In his seminal work on turbulence, Kolmogorov made use of the stationary hypothesis to determine the Power Density Spectra of velocity field in turbulent flows. However to our knowledge, the constraints that stationary processes impose on the fluctuations of power have never been used in the context of turbulence. Here we recall that the Power Density Spectra of the fluctuations of the injected power, the dissipated power and the energy flux have to converge to a common value at vanishing frequency. Hence, we show that the intermittent GOY-shell model fulfills these constraints on the power as well as on the energy fluxes. We argue that they can be related to intermittency. Indeed, we find that the constraints on the power fluctuations imply a relation between scaling exponents, which is consistent with the GOY-shell model and in agreement with the She-Leveque formula. It also fixes the intermittent parameter of the log-normal model at a realistic value. The relevance of these results for real turbulence is drawn in the concluding remarks.

How to cite: Aumaitre, S. and Fauve, S.: Turbulent intermittency as a consequence of stationarity of the energy balance, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3918, https://doi.org/10.5194/egusphere-egu22-3918, 2022.

11:15–11:22
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EGU22-3335
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Virtual presentation
Lipo Wang

According to the classic energy cascade notion, large eddies as energy carrier are unstable to break up, through which energy is transferred from large scales till the smallest ones to dissipate the kinetic energy. A fundamental issue hereof is how to quantify the eddies of different sizes, else the energy cascade scenario remains illustrative. A possible remedy is the idea of dissipation element (DE) analysis, which is a topological approach based on extremal points. In this method, starting from each spatial point in a turbulent scalar field ϕ, a local minimum point and a local maximum point will inevitably be reached along the descending and ascending directions of the scalar gradient trajectory, respectively. The ensemble of spatial points whose gradient trajectories share the same pair of minimum and maximum points define a spatial region, called a DE. The entire filed can thus be partitioned into space-filling DEs. Typically, DE can be parameterized with l, the linear distance between the two extremal points, and ∆ϕ = ϕ_max – ϕ_min, the absolute value of the scalar quantity difference between the two extremal points. It needs to mention that dependence of the DE structure on the ϕ field is conformal with the physics that different variable fields are different structured, although related. In the past years, DE analysis has been implemented to understand the turbulence dynamics under different conditions. Since inside each DE, the monotonous change of the field variable (from ϕ_min  to ϕ_max  along the trajectory) depicts a laminar like structure in a local region, the space-filling DEs can be recognized as the smallest eddies.

In a more general sense, a newly defined multi-level DE structure has been developed. Introducing the size of the observation window S, extremal points are multi-level, based on which the DE structure can be extended to multi-level. At each S-level, the turbulent field can be decomposed into space-filling DEs, which makes it possible to understand to entire field from the properties of such individual units. In this sense, it is tentatively possible to define turbulent eddies of different scales as DEs at different S-levels. Conventional analyses based on “turbulent eddies” can be implemented using such idea. For instance, during energy cascade, eddy breakup corresponds to the splitting of DEs at higher levels (with larger S) to smaller ones at lower levels (with smaller S). Because of DE can be exactly defined, eddies can be quantified as well, but not just demonstrative. Such kind of multi-level DE structure is uniquely different from other existing approaches (e.g. vortex tube, PoD, Fourier analysis etc.) in the following senses. First, DEs at any S-level are quantitatively defined, rather than qualitatively visualized. Second, DEs at any S-level are space-filling.  The multi-level DE approach is generally applicable in turbulence analysis.

How to cite: Wang, L.: Quantification of “turbulent eddies” in energy cascade based on the multi-level dissipation element structure, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3335, https://doi.org/10.5194/egusphere-egu22-3335, 2022.

11:22–11:29
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EGU22-9028
Milan Palus

Big whirls have little whirls that feed on their velocity,

and little whirls have lesser whirls and so on to viscosity.

These famous words written in 1922 by Lewis Fry Richardson have become inspiration for intensively developing scientific field studying scales of climate variability and their interactions. In spite of ever growing interest in this research area, the description of this session states: ”We still lack an efficient methodology to diagnose the scale-to-scale energy or other physical quantities fluxes to characterize the cascade quantitatively, e.g., strength, direction, etc. ”  In this contribution we would like to remind the methodology able to identify causal relations and information transfer between dynamical processes on different time scales and even to quantify the effect of such causal influences. Moreover, in macroscopic systems the information transfer is tied to the transfer of mass and energy [1].

The detection of cross-scale causal interactions [2] starts with a wavelet (or other scale-wise) decomposition of a multi-scale signal into quasi-oscillatory modes of a limited bandwidth, described using their instantaneous phases and amplitudes. Then their statistical associations are tested in order to search interactions across time scales. An information-theoretic formulation of the generalized, nonlinear Granger causality [3] uncovers causal influence and information transfer from large-scale modes of climate variability, characterized by time scales from years to almost a decade, to regional temperature variability on short time scales.  In particular, a climate oscillation with the period around 7-8 years has been identified as a factor influencing variability of surface air temperature (SAT) on shorter time scales.  Its influence on the amplitude of the SAT annual cycle was estimated in the range 0.7-1.4 °C, while its strongest effect was observed in the interannual variability of the winter SAT anomaly means where it reaches 4-5 °C in central European stations and reanalysis data [4].  In the dynamics of El Niño-Southern Oscillation (ENSO), three principal time scales - the annual cycle (AC), the quasibiennial (QB) mode(s) and the low-frequency (LF) variability – and their causal network have been identified [5]. Recent results show how the phases of ENSO QB and LF oscillations influence amplitudes of precipitation variability in east Asia in the annual and QB scales.

Support from the Czech Science Foundation (GA19-16066S) and the Czech Academy of Sciences (Praemium Academiae) is gratefully acknowledged.

[1] J. Hlinka et al., Chaos 27(3), 035811 (2017)

[2] M. Palus, Phys. Rev. Lett. 112, 078702 (2014)

[3] M. Palus, M. Vejmelka, Phys. Rev. E 75, 056211  (2007)

[4] N. Jajcay, J. Hlinka, S. Kravtsov, A. A. Tsonis, M. Palus, Geophys. Res. Lett. 43(2), 902–909 (2016)

[5] N. Jajcay, S. Kravtsov, G. Sugihara, A. A. Tsonis, and M. Palus, npj Climate and Atmospheric Science 1, 33 (2018).  doi:10.1038/s41612-018-0043-7, https://www.nature.com/articles/s41612-018-0043-7

How to cite: Palus, M.: Big whirls talking to smaller whirls: detecting cross-scale information flow, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9028, https://doi.org/10.5194/egusphere-egu22-9028, 2022.

11:29–11:30
Observations, data analyses and models in the atmosphere

11:30–11:37
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EGU22-5934
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On-site presentation
Ivana Stiperski et al.

The turbulent energy cascade is one of the most recognizable characteristics of turbulent flow. Still, representing this tendency of large-scale anisotropic eddies to redistribute their energy content with decreasing scale, a phenomenon referred to as return to isotropy, remains a recalcitrant problem in the physics of turbulence. Atmospheric turbulence is characterised by large scale separation between production and viscous destruction of turbulent kinetic energy making it suitable for exploring such scale-wise redistribution of energy among velocity components.  Moreover, real-world atmospheric turbulence offers an unprecedentedly diverse source of inhomogeneity and large-scale anisotropy (caused by shear, buoyancy, terrain-induced pressure perturbations, closeness to the wall) while maintaining a high Reynolds number state. It may thus be assumed that relaxation through the energy cascade may be dependent on the anisotropy source, thus adding to the ways that atmospheric turbulence differs from canonical turbulent boundary-layers.

Here, we examine the scalewise return to isotropy for an unprecedented dataset of atmospheric turbulence measurements covering flat to mountainous terrain, stratification spanning convective to very stable conditions, surface roughness ranging over several orders of magnitude, various distances from the surface, and Reynolds numbers that far exceed the limits of direct numerical simulations and laboratory experiments.  The results indicate that irrespective of the complexity of the dataset examined, the return-to-isotropy trajectories that start from specific initial anisotropy at large scales show surprising scalewise universality in their trajectories towards isotropy. This novel finding suggests that the effects of boundary conditions, once accounted for in the starting anisotropy of the trajectory in the cascade, cease to be important at much smaller scales. It can therefore be surmised that large-scale anisotropy encodes the relevant information provided by the boundary conditions, adding to the body of evidence that the information on anisotropy is a missing variable in understanding and modelling atmospheric turbulence [1-3].

 

[1]  Stiperski I, and M Calaf. Dependence of near-surface similarity scaling on the anisotropy of atmospheric turbulence. Quarterly Journal of the Royal Meteorological, 144, 641-657, 2017.

[2]  Stiperski I, M Calaf and MW Rotach. Scaling, anisotropy, and complexity in near-surface atmospheric turbulence. Journal of Geophysical Research: Atmospheres, 124, 1428-1448, 2019.

[3] Stiperski I, GG Katul, M Calaf. Universal return to isotropy of inhomogeneous atmospheric boundary layer turbulence. Physical Review Letters, 126 (19), 194501, 2021

How to cite: Stiperski, I., Katul, G. G., and Calaf, M.: Scalewise Universal Relaxation to Isotropy of Inhomogeneous Atmospheric Boundary Layer Turbulence, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5934, https://doi.org/10.5194/egusphere-egu22-5934, 2022.

11:37–11:44
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EGU22-9270
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ECS
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Virtual presentation
Serhat Can

In recent years a consensus has been reached regarding the direction of the energy cascade in the mesoscales in the Upper Tropospheric-Lower Stratospheric (UTLS) altitudes. Numerous measurements and model results confirm the existence of a predominantly forward spectral energy flux from low to high horizontal wavenumbers. However, the details to explain the observed -5/3 power law for Kinetic and Available Potential Energy (KE and APE) are still being debated.

In this study we performed simulations using the dry version of the Kühlungsborn Mechanistic general Circulation Model (KMCM) with high horizontal and vertical resolution for permanent January conditions. Horizontal diffusion schemes for horizontal momentum and sensible heat satisfy the Scale Invariance Criterion (SIC) using the Dynamic Smagorinsky Model (DSM). We investigated the simulated KE and APE spectra with regard to the scaling laws of Stratified Macro-Turbulence (SMT). Zonally and temporally averaged dissipation rates for KE & APE and SMT statistics correlate highly in subtropical mid-latitudes and the UTLS levels. Particularly the characteristic dimensionless numbers of Buoyancy Reynolds Number and turbulent-Rossby Number are pronounced in the regions, where the maximum of the forward spectral fluxes of nonlinear interactions are also found. During this process the spectral contribution of the negative buoyancy production term plays an important role by converting KE to APE. These findings are entirely in line with the spectral and statistical predictions of idealized Stratified Turbulence (ST) and confirms that the energy cascades that give rise to the simulated mesoscale shallowing are strongly nonlinear.

Furthermore level by level analyses of the horizontally averaged spectral tendencies and fluxes of both KE and APE reservoirs in this specific region revealed that there is a non-negligible spectral contribution by the energy deposition term of upward propagating Gravity Waves (GW). Further investigation indicate the dynamics of these resolved GWs look like a superposition of westward Inertia GWs that are subject to a Lindzen-type saturation condition. Their vertical propagation in UTLS heights is non-conservative above their generation level. These results associate directly for the first time ST and GW dynamics, which were thought to be distinct in character. Finally we present simulations with different diffusion schemes and show that the previously mentioned energy deposition contribution was only identified if both horizontal momentum and sensible heat diffusion schemes fulfill the SIC.

How to cite: Can, S.: Macro-Turbulent Energy Cascades in UpperTropospheric-Lower Stratospheric Mesoscales, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9270, https://doi.org/10.5194/egusphere-egu22-9270, 2022.

Wed, 25 May, 13:20–14:50

Chairpersons: Tommaso Alberti, Shaun Lovejoy, Stéphane Vannitsem

13:20–13:27
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EGU22-8277
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Virtual presentation
Yang Gao et al.

Turbulence theory essentially describes energy and enstrophy flows crossing scales or a balance between input and output. A famous example is the Richardson-Kolmogorov forward energy cascade picture for three-dimensional homogeneous and isotropic turbulence. However, due to the complexity of turbulent systems, and the lack of an efficient method to describe the cascade quantitatively, the factual cascade features for most fluids are still unknown. In this work, an improved Filter-Space-Technique (FST) is proposed to extract the energy flux ΠE, and enstrophy flux ΠΩ between different scales for the ocean surface wind field which was remotely sensed by the China-France Oceanography Satellite (CFOSAT). With the improved FST method, ΠE and ΠΩ can be calculated for databases which contain gaps or with irregular boundary conditions. Moreover, the local information of the fluxes are preserved. A case study of the typhoon Maysak (2020) shows both inverse and forward cascades for the energy and enstrophy around the center of the typhoon, indicating a rich dynamical pattern. The global views of ΠE and ΠΩ for the wind field are studied for scales from 12.5 to 500 km. The results show that both ΠE and ΠΩ are hemispherically symmetric, with evident spatial and temporal variations for all the scales. More precisely, positive and negative ΠE  are found for the scales less and above 60 km, respectively. As for ΠΩ, the transition scale is around 150 km, forward and backward cascades are corresponding to the scales below and above this scale. In the physical space, stronger fluxes are occurring in midlatitudes than the ones in tropical regions, excepts for a narrow region around 10oN, where strong fluxes are observed. In the temporal space, the fluxes in winter are stronger than the ones in summer. Our study provides an improved approach to derive the local energy and enstrophy fluxes with complex field observed data. The results presented in this work contribute to the fundamental understanding of ocean surface atmospheric motions in their multiscale dynamics, and also provide a benchmark for atmospheric models.

 

Ref. 

Alexakis, A., & Biferale, L. (2018). Cascades and transitions in turbulent flows. Phys. Rep., 767, 1-101.

Dong, S., Huang, Y.X., Yuan, X., Lozano-Durán, A. (2020). The coherent structure of the kinetic energy transfer in shear turbulence. J. Fluid Mech., 892, A22.

Frisch, U., Kolmogorov, A. N. (1995). Turbulence: the legacy of AN Kolmogorov. Cambridge University Press.

Gao, Y. , Schmitt, F.G., Hu,  J.Y. &  Huang, Y.X. (2021) Scaling analysis of the China France Oceanography Satellite along-track wind and wave data. J. Geophys. Res. Oceans, 126:e2020JC017119

 

How to cite: Gao, Y., Schmitt, F. G., Hu, J., and Huang, Y.: Scale-to-Scale Energy and Enstrophy Fluxes of Atmospheric Motions via CFOSAT, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8277, https://doi.org/10.5194/egusphere-egu22-8277, 2022.

13:27–13:34
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EGU22-1089
Nathan Paldor et al.

Variability in the tropical atmosphere is concentrated at wavenumber–frequency combinations where linear theory indicates wave modes can freely propagate, but with substantial power in between. This study demonstrates that such a power spectrum can arise from small-scale convection triggering large-scale waves via wave–wave interactions in a moderately turbulent fluid. Two key pieces of evidence are provided for this interpretation of tropical dynamics using a nonlinear rotating shallow-water model: a parameter sweep experiment in which the amplitude of an external forcing is gradually ramped up, and also an external forcing in which only symmetric or only antisymmetric modes are forced. These experiments do not support a commonly accepted mechanism involving the forcing projecting directly onto the wave modes with a strong response, yet still simulate a power spectrum resembling that observed, though the linear projection mechanism could still complement the mechanism proposed here in observations. Interpreting the observed tropical power spectrum using turbulence offers a simple explanation as to why power should be concentrated at the theoretical wave modes, and also provides a solid footing for the common assumption that the background spectrum is red, even as it clarifies why there is no expectation for a turbulent cascade with a specific, theoretically derived slope such as −5/3. However, it does explain why the cascade should be toward lower wavenumbers, that is an inverse energy cascade, similar to the midlatitudes even as compressible wave modes are important for tropical dynamics.
It also explains why  in satellite observations and reanalysis data, the symmetric component is stronger than the anti-symmetric component, as any bias in the small-scale forcing from isotropy, whether symmetric or antisymmetric, leads to symmetric bias in the large-scale spectrum regardless of the source of variability responsible for the onset of the asymmetry.


Shamir, O., C. Schwartz, C.I. Garfinkel, and N. Paldor, The power distribution between symmetric and anti-symmetric components of the tropical wavenumber-frequency spectrum, JAS, https://doi.org/10.1175/JAS-D-20-0283.1 .
Garfinkel, C.I., O. Shamir, I. Fouxon, and N. Paldor, Tropical background and wave spectra: contribution of wave-wave interactions in a moderately nonlinear turbulent flow, JAS, https://doi.org/10.1175/JAS-D-20-0284.1.
Shamir, O., C.I. Garfinkel, O. Adam, and N. Paldor, A note on the power distribution between symmetric and anti-symmetric components of the tropical Brightness Temperature spectrum in the wavenumber-frequency plane , JAS,doi: 10.1175/JAS-D-21-0099.1.

How to cite: Paldor, N., Garfinkel, C. I., and Shamir, O.: Tropical Background and Wave Spectra: Contribution of Wave–Wave Interactions in a Moderately Nonlinear Turbulent Flow, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1089, https://doi.org/10.5194/egusphere-egu22-1089, 2022.

13:34–13:35
Convection and applications

13:35–13:42
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EGU22-7557
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ECS
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Virtual presentation
Vincent Böning et al.

In this study, we analyse the non-linear transfer of kinetic energy in simulations of convection in a 3D rotating shell. Our aim is to understand the role of upscale transfer of kinetic energy and a potential inverse cascade for the formation of zonal jets and large vortices on the giant planets Jupiter and Saturn. We find that the main driving of the jets is associated with upscale transfer directly from the convection scale to the jets. This transfer of energy is mediated by Reynolds stresses, i.e. statistical correlations of velocity components of the small-scale flow.  Intermediate scales are mostly not involved, therefore strictly speaking the jets are not powered by an inverse energy cascade. To a much smaller degree, energy is transferred upscale from the convective scale to large vortices. However, these vortices also receive energy from the jets, likely due to an instability of the jet flow.  Concerning transport in the forward direction, we find as expected that the 3D convective motions transfer energy to the even smaller dissipation scales in a forward cascade.

How to cite: Böning, V., Wulff, P., Dietrich, W., Christensen, U. R., and Wicht, J.: Upscale and forward transfer of kinetic energy: Impact on giant planetary jet and vortex formation, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7557, https://doi.org/10.5194/egusphere-egu22-7557, 2022.

13:42–13:49
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EGU22-2192
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ECS
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On-site presentation
Tobias Sternberg and Andrew Jackson
Fluids that are subject to temperature gradients (or internal heating) and a gravity force will begin convecting when the thermal forcing, conventionally measured by the nondimensional Rayleigh number Ra exceeds a critical value. The critical value RL for the transition from a static, purely conductive state to an advective state can be determined by linearising the equations of motion and formulating an associated characteristic value problem. We discuss two aspects of fluid behaviour away from this point:
(i) Highly supercritical behaviour, and the asymptotic behaviour of heat transport in the highly nonlinear regime. (ii) Subcritical behaviour for Ra<RL, which may be possible for finite amplitude fluid motions. We work in both full sphere and shell geometries, with various forms of heating and gravitational profiles. We report on both theoretical developments and direct numerical simulations using highly accurate fully spectral methods for solving the relevant equations of motion and of heat transfer.

How to cite: Sternberg, T. and Jackson, A.: Nonlinear subcritical and supercritical thermal convection in a sphere, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2192, https://doi.org/10.5194/egusphere-egu22-2192, 2022.

13:49–13:56
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EGU22-7115
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Virtual presentation
Tinghui Yan et al.

Recently, multiscale statics is found to be relevant in description of the lithosphere deformation of the Tibetan Plateau (Jian et al, Phys. Rev. E, 2019). More precisely, a dual-power-law behavior is observed respectively on the spatial scale range of  50≤ r≤ 500km and 500≤ r ≤2000km, which coincidently agrees well with the one reported for the atmospheric movement (Nastrom et al., Nature, 1984). The corresponding high-order scaling exponents demonstrated a nonlinear shape, showing multifractality nature of the underlying dynamics. To diagnose further whether the lithosphere deformation is turbulent or not, the third-order longitudinal structure-function SLLL(r)=< ΔuL(r)3> is estimated, where r is the modulus of the distance vector  r, and  ΔuL is the velocity component that paralleling with r.  Due to the finite sample size, the experimental SLLL(r) is not reliable when r≤200km. The measured SLLL(r) is scaled as  -r4±0.2 on the spatial scale range of 500≤ r ≤ 2000km, indicating the existence of a turbulent cascade. Because of the complexity of the geodynamics, e.g., Coriolis force, mantle convection, India-Eurasia collision, to list a few, the exact force balance is remained unknown. Therefore, the full interpretation of the current observation is not feasible.

 

Ref.

A. Alexakis, &  L. Biferale (2018). Cascades and transitions in turbulent flows, Phys. Rep., 767, 1-101.

U. Frisch, (1995) Turbulence: The Legacy of A.N. Kolmogorov, Cambridge University Press

X. Jian, W. Zhang, Q. Deng & Y.X. Huang (2019) Turbulent lithosphere deformation in the Tibetan Plateau, Phys. Rev. E, 99:062122

G.D. Nastrom, K.S Gage & Jasperson (1984) Kinetic energy spectrum of large- and mesoscale atmospheric processes, Nature, 310:36

How to cite: Yan, T., Ma, Y., Hu, J., and Huang, Y.: Turbulent Cascade of  the Lithosphere Deformation in the Tibetan Plateau, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7115, https://doi.org/10.5194/egusphere-egu22-7115, 2022.

13:56–13:57
Observations, data analyses and models in the ocean

13:57–14:04
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EGU22-2238
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ECS
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Virtual presentation
Jin-Han Xie et al.

Ocean turbulence causes flows to split into smaller whirls or merge to make larger whirls, cascading energy to small or large scales respectively. Conventional ocean dynamics dictates that the kinetic energy in the ocean will cascade primarily to larger scales, via the inverse energy cascade, and has raised the question of how the kinetic energy in the ocean dissipates, which would necessarily require the transfer towards the molecular scales. However, so far no clear observational quantification of the energy cascade at the scales where these mechanisms are potentially active has been made. By using forcing-scale resolving third-order structure-function theory, which captures bidirectional energy fluxes and is applicable beyond inertial ranges, we analyse data from surface drifters, released in dense arrays in the Gulf of Mexico, to obtain the kinetic energy flux magnitude and directions along with the energy injection scales. We provide the first direct observational verification that the surface kinetic energy cascades to both small and large scales, with the forward cascade dominating at scales smaller than approximately 1-10km. Our results also show that there is a seasonality in these cascades, with winter months having a stronger injection of energy into the surface flows and a more energetic cascade to smaller scales. This work provides exciting new opportunities for further probing the energetics of ocean turbulence using non-gridded sparse observations, such as from drifters, gliders, or satellites.

How to cite: Xie, J.-H., Balwada, D., Marino, R., and Feraco, F.: Direct evidence of an oceanic dual kinetic energy cascade and its seasonality from surface drifters, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2238, https://doi.org/10.5194/egusphere-egu22-2238, 2022.

14:04–14:11
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EGU22-7004
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Virtual presentation
Yinxiang Ma et al.

Due  to the extreme complexity of the oceanic dynamics, e.g., stratification, air-sea interaction,  waves, current, tide, etc., the corresponding turbulent cascade remains unknown. The third-order longitudinal structure-function is often employed to diagnose  the cascade direction and intensity, which is written as  SLLL(r)=< Δ uL3(r)>, where Δ uL is the  velocity increment along the distance vector r, and r is the modulus of r. In the case of  three-dimension homogeneous and isotropic turbulence, SLLL(r) is scaled as -4/5εr in the inertial range, where ε is the energy dissipation rate per unit.  In this work, SLLL(r) is estimated for two experimental velocities that obtained in the Gulf of Mexico, namely Grand LAgrangian Deployment (GLAD) and the LAgrangian Submesoscale ExpeRiment (LASER). The experimental SLLL(r) for both experiments shows a transition from negative values to a positive one roughly at rT=10km, corresponding to a timescale  around τT=12-hour (e.g., τT=rT/urms with urms ≈0.24m/s.  Power-law is evident for the scale on the range 0.01≤ r≤1km as SLLL(r)∼ -r1.45±0.10, and for the scale on the range 30≤ r≤300km as SLLL(r)∼ r1.45±0.10. Note that a weak stratification with depth of 10∼15m has been reported for the GLAD experiment, indicating a quasi-2D flow topography. The scaling ranges are above this stratification depth. Hence, the famous Kraichnan's 2D turbulence theory or the geostrophic turbulence proposed by Charney are expected to be applicable. However, due to the complexity of real oceanic flows, hypotheses behind these theories cannot be verified either directly or indirectly. To simplify the situation, we still consider here the sign of  SLLL(r) as an indicator of the energy cascade. It thus suggests a possible forward energy cascade below the spatial scale rT, and an inverse one above the scale  spatial rT.  While, the scaling exponents 1.45 are deserved more studied in the future if more data is available.

 

Ref.

Charney, J. G. (1971). Geostrophic turbulence. J. Atmos. Sci., 28(6), 1087-1095.

Frisch, U., & Kolmogorov, A. N. (1995). Turbulence: the legacy of AN Kolmogorov. Cambridge University Press.

Alexakis, A., & Biferale, L. (2018). Cascades and transitions in turbulent flows. Phys. Rep., 767, 1-101.

Dong, S., Huang, Y., Yuan, X., & Lozano-Durán, A. (2020). The coherent structure of the kinetic energy transfer in shear turbulence. J. Fluid Mech., 892, A22.

Poje, A. C., Özgökmen, T. M., Bogucki, D. J., & Kirwan, A. D. (2017). Evidence of a forward energy cascade and Kolmogorov self-similarity in submesoscale ocean surface drifter observations. Phys. Fluids, 29(2), 020701.

How to cite: Ma, Y., Hu, J., and Huang, Y.: Turbulent Energy Cascade in the Gulf of Mexico, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7004, https://doi.org/10.5194/egusphere-egu22-7004, 2022.

14:11–14:18
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EGU22-13450
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On-site presentation
Joe LaCasce and Thomas Meunier

The relative dispersion of pairs of particles was first considered in a seminal article by Richardson (1926). The dispersion subsequently was subsequently linked to turbulence, and pair separation statistics can advantageously be used to deduce energy wavenumber spectra. Thus one can, for example, employ surface drifters to identify turbulent regimes at scales well below those resolved by satellite altimetry. The identification relies on knowing how dispersion evolves with a specific energy spectrum. The analytical predictions commonly used apply to infinite inertial ranges, i.e. assuming the same dispersive behavior over all scales. With finite inertial ranges, the metrics are less conclusive, and often are not even consistent with each other.

We examine this using pair separation probability density functions (PDFs), obtained by integrating a Fokker-Planck equation with different diffusivity profiles. We consider time-based metrics, such as the relative dispersion, and separation-based metrics, such as the finite scale Lyapunov exponent (FSLE). As the latter cannot be calculated from a PDF, we introduce a new measure, the Cumulative Inverse Separation Time (CIST), which can. This behaves like the FSLE, but advantageously has analytical solutions in the inertial ranges. This allows establishing consistency between the time- and space-based metrics, something which has been lacking previously.

We focus on three dispersion regimes: non-local spreading (as in a 2D enstrophy inertial range), Richardson dispersion (as in the 3D and 2D energy inertial ranges) and diffusion (for uncorrelated pair motion). The time-based metrics are more successful with non-local dispersion, as the corresponding PDF applies from the initial time. Richardson dispersion is barely observed, because the self-similar PDF applies only asymptotically in time. In contrast, the separation-based CIST correctly captures the dependencies, even with a short (one decade) inertial range, and is superior to the traditional FSLE at large scales. Furthermore, the analytical solutions permit reconciling the CIST with the other measures, something which is generally not possible with the FSLE.

How to cite: LaCasce, J. and Meunier, T.: Relative Dispersion with Finite Inertial Ranges, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-13450, https://doi.org/10.5194/egusphere-egu22-13450, 2022.

14:18–14:25
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EGU22-8564
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ECS
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Virtual presentation
Jingjing Song et al.

In his seminal work "Weather Prediction by Numerical Process" in 1922, Lewis Fry Richardson proposed the famous cascade picture qualitatively for a turbulent flow that energy transferring from large to small scale  structures, until the viscosity one where the kinetic energy is converted  into heat. This picture has been recognized further as the forward energy  cascade.  But, it cannot be applied directly to the real atmospheric  or oceanic motions. Whatever, the global circulation model is indeed established within this framework by considering more complex situations, e.g., earth rotation, stratification, tide, mesoscale eddies, to list a few. In  this work, an improved Filter-Space-Technique (FST) is applied to a reanalysis product provided by the CMEMS global ocean eddy-resolving (1/12o degree horizontal resolution).   The FST provides a global view of the  energy flux ΠE  that associated with the oceanic cascades for all resolved  scales, e.g., from mesoscale eddies to global circulations. For instance, at scale r=160 km (i.e., radius of the Gaussian filter kernel), a rich dynamic pattern is observed for an instantaneous flow filed. Both forward (ΠE>0, energy transferring from large scale to small scale structures) and inverse (ΠE<0, energy transferring from small scale to large scale structures) cascades are evident in the equator, western boundary current regions, Antarctic Circumpolar Current region, to name a few. While, the long-term averaged flux field show mainly a negative ΠE (inverse energy cascade) except for the equatorial region. Moreover, a high intensity negative flux is found for both the Loop Current and Kuroshio Current, indicating that the mesoscale eddies might be absorbed by the main flow.

 

Ref.

Charney, J. G. (1971). Geostrophic turbulence. J. Atmos. Sci., 28(6), 1087-1095.

Frisch, U.,  Kolmogorov, A. N. (1995). Turbulence: the legacy of AN Kolmogorov. Cambridge University Press.

Alexakis, A.,  Biferale, L. (2018). Cascades and transitions in turbulent flows. Phys. Rep., 767, 1-101.

Dong, S., Huang, Y.X., Yuan, X., & Lozano-Durán, A. (2020). The coherent structure of the kinetic energy transfer in shear turbulence. J. Fluid Mech., 892, A22.

How to cite: Song, J., Zhang, D., Peng, Y., Gao, Y., and Huang, Y.: Global view of oceanic cascades from the Global Circulation Model, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8564, https://doi.org/10.5194/egusphere-egu22-8564, 2022.

14:25–14:32
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EGU22-9226
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ECS
Ashwita Chouksey et al.

The ocean is densely populated with energetic coherent vortices of different sizes. Mesoscale and submesoscale vortices contribute to stirring of the ocean, transporting and redistributing water masses and tracers (active and passive), affecting ventilation pathways and thus impacting the large-scale circulation. Submesoscale Coherent Vortices (SCVs), i.e. vortices with radii between 1-30 km have been detected via satellite and in-situ measurements at surface or at depth (usually not more than ~2000 m depth). They are found to be of different shapes and sizes depending upon latitude and place of origin. Previous studies mostly describe the surface mesoscale and submesoscale eddies rather than the deep SCVs (> 2000 m). This study focuses on SCVs below the mixed layer along four different isopycnal surfaces: 26.60, 27.60, 27.80, and 27.86, which lie in the depth range of 10-500 m, 200-2000 m, 1200-3000 m, and 1800-4500 m, respectively. We aim to quantify their physical characteristics (radius, thickness, bias in polarity: cyclones versus anticyclones) in different parts of the Atlantic ocean, and analyze the dynamics involved in the generation and destruction of the SCVs throughout their life-cycle. We use the Coastal and Regional Ocean COmmunity model (CROCO) ocean model in a high resolution setup (3 km) of the Atlantic Ocean. The detection of SCVs are done every 12 hr using the Okubo-Weiss parameter along the isopycnal surfaces using the eddy-tracking algorithm by Mason et al., 2014. We consider only structures living for more than 21 days. The census of SCVs shows that there are in total more cyclonic than anticyclonic SCV detections. However cyclones are on average smaller and shorter lived, such that there is a dominance of anticyclones while considering long-lived and larger distance travelling SCVs. We concentrate on the strongest and longest lived SCVs among which meddies that we compare to previous in-situ observations. This study is the first step in the understanding of the formation, occurrences and structure of SCVs in the Atlantic Ocean, and their impact on the large-scale ocean circulation.

How to cite: Chouksey, A., Carton, X., and Gula, J.: Study of Submesoscale Coherent Vortices (SCVs) in the Atlantic Ocean along different isopycnals, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9226, https://doi.org/10.5194/egusphere-egu22-9226, 2022.

14:32–14:39
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EGU22-9329
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ECS
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On-site presentation
Pauline Tedesco et al.

Western boundary currents are hotspots of the mesoscale oceanic variability and of energy transfers, channeled by topography, toward smaller scales and eventually down to dissipation. Here, we assess the main mesoscale eddies energy sinks in the Agulhas Current region, with an emphasize on the different paths of energy toward smaller scales, from a regional numerical simulation. 

We derive an eddy kinetic energy (EKE) budget in the framework of the vertical modes. This comprehensive method accounts for energy transfers between energy reservoirs and vertical modes, including transfers channeled by topography and by a turbulent vertical cascade. 

The variability is dominated by mesoscale eddies (barotropic and 1st baroclinic modes) in the path of intense mean currents. Eddy-topography interactions result in a major mesoscale eddy energy sink (50 % of the total EKE sink). They represent energy transfers both toward higher baroclinic modes (27 % of the total EKE sink) and mean currents (23 % of the total EKE sink). Energy transfers toward higher baroclinic modes take different forms in the Northern Agulhas Current, where it corresponds to non-linear transfers to smaller vertical eddies on the slope (5 % of the total EKE sink), and in the Southern Agulhas Current, where it is dominated by a (linear) generation of internal-gravity waves over topography (22 % of the total EKE sink). The vertical turbulent cascade is significant in offshore regions, away from topography and intense mean currents. In these regions the direction of the turbulent vertical cascade is inverse - energy transferred from higher baroclinic modes toward mesoscale eddies - and it can locally amounts for most of the mesoscale eddies energy gain (up to 68 % of the local EKE source).

However, the Agulhas Current region remains a net source of mesoscale eddy energy due to the strong generation of eddies, modulated by the topography, especially in the Southern Agulhas Current. In the complex Agulhas Current system, which includes an intense mean oceanic current and mesoscale eddies field as well as strong topographic constraint and stratification gradients, the local generation of mesoscale eddies dominates the net EKE budget. It is in contrast with the paradigm of mesoscale eddies decay upon western boundaries, suggested as being due to topographically-channeled interactions triggering a direct energy cascade.

How to cite: Tedesco, P., Gula, J., Penven, P., and Ménesguen, C.: Mesoscale Eddy Kinetic Energy budgets and transfers between vertical modes in the Agulhas Current, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9329, https://doi.org/10.5194/egusphere-egu22-9329, 2022.

14:39–14:50
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