Structure-function scaling of bounded two-dimensional turbulence

Krämer, Werner; Keetels, GH Geert; Clercx, Hjh Herman; Heijst, van Gjf Gert-Jan

doi:10.1103/physreve.84.026310

Cited by 8 publications

(5 citation statements)

References 37 publications

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“…As follows from the theory of 2‐D turbulence, both energy cascade and the enstrophy cascade can be split into two subranges that have the opposite directions of energy fluxes. While at larger scales the inverse energy cascade where energy transfers from smaller scales to larger ones takes place, at smaller scales there is a direct energy cascade [e.g., Kramer et al , 2011]. The estimations show that the boundary between the two subranges corresponds to the scale of several hundred meters, which in our case are the smallest convective scales.…”

Section: The Applicability Of 2‐d Cloud Models To Describe 3‐d Convecmentioning

confidence: 76%

Turbulent effects on the microphysics and initiation of warm rain in deep convective clouds: 2‐D simulations by a spectral mixed‐phase microphysics cloud model

Benmoshe¹,

Pinsky²,

Pokrovsky³

et al. 2012

J. Geophys. Res.

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[1] The spectral bin microphysics Hebrew University cloud model with the spatial resolution of 50 Â 50 m is used to simulate the evolution of isolated deep mixed phase convective clouds under different meteorological conditions and at different aerosol concentrations. The model takes into account the effects of turbulence on droplet collision rate. Turbulent collision kernels are calculated at each time step and at each grid point. The turbulence-induced collision rate enhancement is determined by means of lookup tables calculated in the recent studies for different values of turbulent dissipation rate and the Taylor microscale Reynolds numbers. Deep convective clouds observed during the Large-Scale Biosphere-Atmosphere Experiment in Amazonia-Smoke, Aerosols, Clouds, Rainfall and Climate campaign in the Amazon region are simulated at different aerosol concentrations. Turbulence intensity in the simulated clouds is spatially inhomogeneous and reaches its maximum at the tops of multiple bubbles forming the clouds. It is shown that polluted clouds are more turbulent than those developing in the clean atmosphere. An agreement of the calculated droplet size distributions with those measured in situ is demonstrated. It is shown that turbulence accelerates formation of raindrops, especially in polluted clouds. At the same time, turbulence-induced collision enhancement lessens the amount of ice and leads to a decrease in the net accumulated rain from mixed-phase clouds. To a certain degree the effects of turbulence on precipitation counteract the aerosol effects. Since no turbulence effects on collisions of drops larger than 22 mm in radius as well as on drop ice and ice collisions are considered in this study, and taking into account that a 2-D model geometry is used, the results of the study should be considered as preliminary. Additional numerical and theoretical investigations are required to quantify the turbulent effects.Citation: Benmoshe, N., M. Pinsky, A. Pokrovsky, and A. Khain (2012), Turbulent effects on the microphysics and initiation of warm rain in deep convective clouds: 2-D simulations by a spectral mixed-phase microphysics cloud model,

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Section: The Applicability Of 2‐d Cloud Models To Describe 3‐d Convecmentioning

confidence: 76%

Turbulent effects on the microphysics and initiation of warm rain in deep convective clouds: 2‐D simulations by a spectral mixed‐phase microphysics cloud model

Benmoshe¹,

Pinsky²,

Pokrovsky³

et al. 2012

J. Geophys. Res.

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“…From Fig. 6, we can see that the model M FI-CNN is successful in producing the r 3/2 scaling [90] for the vorticity structure function at small scales and it gradually flattens near the large scales. The excessive dissipation of DSM is also illustrated in Fig.…”

Section: B a Posteriori Deploymentmentioning

confidence: 87%

Frame invariant neural network closures for Kraichnan turbulence

Pawar,

San,

Rasheed

et al. 2022

Preprint

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Numerical simulations of geophysical and atmospheric flows have to rely on parameterizations of subgrid scale processes due to their limited spatial resolution. Despite substantial progress in developing parameterization (or closure) models for subgrid scale (SGS) processes using physical insights and mathematical approximations, they remain imperfect and can lead to inaccurate predictions. In recent years, machine learning has been successful in extracting complex patterns from high-resolution spatio-temporal data, leading to improved parameterization models, and ultimately better coarse grid prediction. However, the inability to satisfy known physics and poor generalization hinders the application of these models for real-world problems. In this work, we propose a frame invariant closure approach to improve the accuracy and generalizability of deep learning-based subgrid scale closure models by embedding physical symmetries directly into the structure of the neural network. Specifically, we utilized specialized layers within the convolutional neural network in such a way that desired constraints are theoretically guaranteed without the need for any regularization terms. We demonstrate our framework for a two-dimensional decaying turbulence test case mostly characterized by the forward enstrophy cascade. We show that our frame invariant SGS model (i) accurately predicts the subgrid scale source term, (ii) respects the physical symmetries such as translation, Galilean, and rotation invariance, and (iii) is numerically stable when implemented in coarse-grid simulation with generalization to different initial conditions and Reynolds number. This work builds a bridge between extensive physics-based theories and data-driven modeling paradigms, and thus represents a promising step towards the development of physically consistent data-driven turbulence closure models.

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“…While single-point velocity fluctuations are often close to a Gaussian distribution (e.g. LaCasce, 2005), this is often not true for two-point statistics (e.g. Tsinober, 2001, his Fig.…”

Section: Velocity Increments and Structure Functionsmentioning

confidence: 99%

Submesoscale dispersion of surface drifters in a coastal sea near offshore wind farms

et al. 2019

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Abstract. We analysed relative dispersion of surface drifters released as pairs (six instances) or triplets (two instances) during three field experiments conducted in the German Bight in close proximity to wind farms. There is some tentative evidence that nearly exponential growth of relative dispersion (non-local dispersion) preferably occurs for drifter pairs that are most exposed to the influence of a wind farm. Kinetic energy spectra and velocity structure functions are analysed with regard to the assumption that turbulent energy could be injected by tides, possibly also via an interaction between tidal currents and wind turbine towers. Applicability of inertial range turbulence theory, however, can be doubted given distinct peaks of overtides observed in velocity power spectra. More comprehensive studies would be needed to better separate submesoscale effects of wind farms, tides and possibly baroclinic instabilities on observed drifter behaviour in a complex coastal environment.

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Structure-function scaling of bounded two-dimensional turbulence

Cited by 8 publications

References 37 publications

Turbulent effects on the microphysics and initiation of warm rain in deep convective clouds: 2‐D simulations by a spectral mixed‐phase microphysics cloud model

Turbulent effects on the microphysics and initiation of warm rain in deep convective clouds: 2‐D simulations by a spectral mixed‐phase microphysics cloud model

Frame invariant neural network closures for Kraichnan turbulence

Submesoscale dispersion of surface drifters in a coastal sea near offshore wind farms

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