Related papers: An Efficient Continuous Data Assimilation Algorith…
Intermittency is one of central obstacles for understanding small-scale dynamics in the fully developed hydrodynamic turbulence. The modern approach is largely based on the multifractal theory of Parisi and Frisch which is, however,…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
This paper studies the role of sparse regularization in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable…
We revisit the two-dimensional SABRA model, in the light of recent results of Frisch {\it et al.} [Phys. Rev. Lett. {\bf 108}, 074501 (2012)] and examine, systematically, the interplay between equilibrium states and cascade (turbulent)…
Data-driven methods have demonstrated strong predictive capabilities in fluid mechanics, yet most current applications still focus on simplified configurations, often characterised by statistical stationarity or limited temporal…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
In this study, we explore data assimilation for the Stochastic Camassa-Holm equation through the application of the particle filtering framework. Specifically, our approach integrates adaptive tempering, jittering, and nudging techniques to…
In this paper we propose the use of a continuous data assimilation algorithm for miscible flow models in a porous medium. In the absence of initial conditions for the model, observed sparse measurements are used to generate an approximation…
When time and velocities are dynamically rescaled relative to the instantaneous turnover time, the Sabra shell model acquires another (hidden) form of scaling symmetry. It has been previously shown that this symmetry is statistically…
Accurate subgrid-scale closures are essential for weather/climate models, where predicting extreme events is critical. Traditional closures have structural errors, e.g., producing excessive diffusion that dampens extremes. Artificial…
There has been a recent surge in development of accurate machine learning (ML) weather prediction models, but evaluation of these models has mainly been focused on medium-range forecasts, not their performance in cycling data assimilation…
This paper proposes a new data assimilation method for recovering high fidelity turbulent flow field around airfoil at high Reynolds numbers based on experimental data, which is called Proper Orthogonal Decomposition Inversion…
Turbulent systems exhibit a remarkable multi-scale complexity, in which spatial structures induce scale-dependent statistics with strong departures from Gaussianity. In Fourier space, this is reflected by pronounced phase synchronization. A…
Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…
The potential for data-driven applications to scale-resolving simulations of turbulent flows is assessed herein. Multigrid sequential data assimilation algorithms have been used to calibrate solvers for Large Eddy Simulation for the…
The main objective of this article is to develop scalable dynamic anomaly detectors when high-fidelity simulators of power systems are at our disposal. On the one hand, mathematical models of these high-fidelity simulators are typically…
The Reynolds-averaged Navier-Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their…
This work integrates ensemble-based data assimilation (DA) with the energy-aware hybrid modeling approach, applied to a three-layer quasi-geostrophic (QG) model of the Gulf Stream flow. Building on prior DA success in the QG channel regime,…
We consider a stabilized nonconforming finite element method for data assimilation in incompressible flow subject to the Stokes' equations. The method uses a primal dual structure that allows for the inclusion of nonstandard data. Error…
Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…