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In this article we detail the use of machine learning for spatiotemporally dynamic turbulence model classification and hybridization for the large eddy simulations (LES) of turbulence. Our predictive framework is devised around the determination of local conditional probabilities for turbulence models that have varying underlying hypotheses. As a first deployment of this learning, we classify a point on our computational grid as that which requires the functional hypothesis, the structural hypothesis or no modeling at all. This ensures that the appropriate model is specified from emph{a priori} knowledge and an efficient balance of model characteristics is obtained in a particular flow computation. In addition, we also utilize the conditional probability predictions of the same machine learning to blend turbulence models for another hybrid closure. Our test-case for the demonstration of this concept is given by Kraichnan turbulence which exhibits a strong interplay of enstrophy and energy cascades in the wave number domain. Our results indicate that the proposed methods lead to robust and stable closure and may potentially be used to combine the strengths of various models for complex flow phenomena prediction.
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A computationally efficient model is introduced to account for the sub-grid scale velocities of tracer particles dispersed in statistically homogeneous and isotropic turbulent flows. The model embeds the multi-scale nature of turbulent temporal and spatial correlations, that are essential to reproduce multi-particle dispersion. It is capable to describe the Lagrangian diffusion and dispersion of temporally and spatially correlated clouds of particles. Although the model neglects intermittent corrections, we show that pair and tetrad dispersion results nicely compare with Direct Numerical Simulations of statistically isotropic and homogeneous $3D$ turbulence. This is in agreement with recent observations that deviations from self-similar pair dispersion statistics are rare events.
A new method for the localization of the regions where small scale turbulent fluctuations are present in hypersonic flows is applied to the large-eddy simulation (LES) of a compressible turbulent jet with an initial Mach number equal to 5. The localization method used is called selective LES and is based on the exploitation of a scalar probe function $f$ which represents the magnitude of the stretching-tilting term of the vorticity equation normalized with the enstrophy (Tordella et al. 2007). For a fully developed turbulent field of fluctuations, statistical analysis shows that the probability that $f$ is larger than 2 is almost zero, and, for any given threshold, it is larger if the flow is under-resolved. By computing the spatial field of $f$ in each instantaneous realization of the simulation it is possible to locate the regions where the magnitude of the normalized vortical stretching-tilting is anomalously high. The sub-grid model is then introduced into the governing equations in such regions only. The results of the selective LES simulation are compared with those of a standard LES, where the sub-grid terms are used in the whole domain, and with those of a standard Euler simulation with the same resolution. The comparison is carried out by assuming as reference field a higher resolution Euler simulation of the same jet. It is shown that the selective LES modifies the dynamic properties of the flow to a lesser extent with respect to the classical LES. In particular, the prediction of the enstrophy, mean velocity and density distributions and of the energy and density spectra are substantially improved.
The representation of nonlinear sub-grid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but only for short-term simulations of at most a few years because of computational limitations. Here we demonstrate that deep learning can be used to capture many advantages of cloud-resolving modeling at a fraction of the computational cost. We train a deep neural network to represent all atmospheric sub-grid processes in a climate model by learning from a multi-scale model in which convection is treated explicitly. The trained neural network then replaces the traditional sub-grid parameterizations in a global general circulation model in which it freely interacts with the resolved dynamics and the surface-flux scheme. The prognostic multi-year simulations are stable and closely reproduce not only the mean climate of the cloud-resolving simulation but also key aspects of variability, including precipitation extremes and the equatorial wave spectrum. Furthermore, the neural network approximately conserves energy despite not being explicitly instructed to. Finally, we show that the neural network parameterization generalizes to new surface forcing patterns but struggles to cope with temperatures far outside its training manifold. Our results show the feasibility of using deep learning for climate model parameterization. In a broader context, we anticipate that data-driven Earth System Model development could play a key role in reducing climate prediction uncertainty in the coming decade.
MHD turbulence is likely to play an important role in several astrophysical scenarios where the magnetic Reynolds is very large. Numerically, these cases can be studied efficiently by means of Large Eddy Simulations, in which the computational resources are used to evolve the system only up to a finite grid size. The resolution is not fine enough to capture all the relevant small-scale physics at play, which is instead effectively modeled by a set of additional terms in the evolution equations, dubbed as sub-grid-scale model. Here we extend such approach, commonly used in non-relativistic/non-magnetic/incompressible fluid dynamics, applying the so-called gradient model to a general set of balance-law equations, that includes the relevant case in which a non-trivial inversion of conserved to primitive fields is needed. In particular, we focus on the relativistic compressible ideal MHD scenario, providing for the first time (and for any equation of state) all the additional sub-grid-scale terms. As an application, we consider box simulations of the relativistic Kelvin-Helmholtz instability, which is also the first mechanism responsible for the magnetic field amplification in binary neutron star mergers and cannot yet be fully captured by the finest-grid and longest simulations available. The performance of our model is numerically assessed by comparing it to the residuals arising from the filtering of high-resolution simulations. We find that the model can fit very well those residuals from resolutions a few times higher. Although the application shown here explicitly considers the Minkowski metric, it can be directly extended to general relativity, thus settling the basis to implement the gradient sub-grid model in a GRMHD binary merger. Our results suggest that this approach will be potentially able to unveil much better the small-scale dynamics achievable in full GRMHD simulations.
Hydroelastic surface waves propagate at the surface of water covered by a thin elastic sheet and can be directly measured with accurate space and time resolution. We present an experimental approach using hydroelastic waves that allows us to control waves down to the sub-wavelength scale. We tune the wave dispersion relation by varying locally the properties of the elastic cover and we introduce a local index contrast. This index contrast is independent of the frequency leading to a dispersion-free Snell-Descartes law for hydroelastic waves. We then show experimental evidence of broadband focusing, reflection and refraction of the waves. We also investigate the limits of diffraction through the example of a macroscopic analog to optical nanojets, revealing that any sub-wavelength configuration gives access to new features for surface waves.
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