Related papers: Extracting self-similarity from data
In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…
Processing the data from a large variety of zero-pressure-gradient boundary layer flows shows that the Reynolds-number-dependent scaling law, which the present authors obtained earlier for pipes, gives an accurate description of the…
We obtain, by extensive direct numerical simulations, time-dependent and equal-time structure functions for the vorticity, in both quasi-Lagrangian and Eulerian frames, for the direct-cascade regime in two-dimensional fluid turbulence with…
Reconstructing flow fields from sparse measurements is a fundamental problem in fluid mechanics with broad implications for modeling, control, and design. In this work, we propose a novel operator learning framework that leverages the…
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…
Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the…
Simulating turbulence to stationarity is a major bottleneck in many engineering problems of practical importance. The problem can be cast as a multiscale problem involving energy redistribution processes that take place on the long large…
The single droplet under shear is a foundational problem in fluid mechanics. In computational fluid dynamics, the two-dimensional (2D) formulation offers advantages in both computational efficiency and relevance, yet its theoretical…
A millimetre-size superhydrophobic sphere impacting on the free surface of a quiescent bath can be propelled back into the air by capillary effects and dynamic fluid forces, whilst transferring part of its energy to the fluid. We report the…
For any $\alpha \in (0,1/3)$, we construct exact $C^{\alpha}$ self-similar blowup profiles for the vorticity of the 3D incompressible Euler equation without swirl, and build on them to prove asymptotically self-similar blowup from…
We investigate time-irreversibility from the point of view of a single particle in Burgers turbulence. Inspired by the recent work for incompressible flows [Xu et al., PNAS 111.21 (2014) 7558], we analyze the evolution of the kinetic energy…
Despite its great scientific and technological importance, wall-bounded turbulence is an unresolved problem in classical physics that requires new perspectives to be tackled. One of the key strategies has been to study interactions among…
Data-driven modeling of fluid dynamics has advanced rapidly with neural PDE solvers, yet a fair and strong benchmark remains fragmented due to the absence of unified PDE datasets and standardized evaluation protocols. Although architectural…
Modern machine-learning techniques are generally considered data-hungry. However, this may not be the case for turbulence as each of its snapshots can hold more information than a single data file in general machine-learning settings. This…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
The Hamiltonian dynamics of a compressible inviscid fluid is formulated as a gauge theory. The idea of gauge equivalence is exploited to unify the study of apparantly distinct physical problems and solutions of new models can be generated…
Modeling and simulation of complex fluid flows with dynamics that span multiple spatio-temporal scales is a fundamental challenge in many scientific and engineering domains. Full-scale resolving simulations for systems such as highly…
This work is a review with proofs of a group of results on the stochastic Burgers equation with small viscosity, obtained during the last two decades. These results jointly show that the equation makes a surprisingly good model of…
This work proposes two algorithmic approaches to extract critical dynamical mechanisms in wall-bounded turbulence with minimum human bias. In both approaches, multiple types of coherent structures are spatiotemporally tracked, resulting in…