Hyperviscosity, Galerkin truncation and bottlenecks in turbulence

来自Galerkin正则化非线性色散的长波子

Longons from the nonlinear dispersion of Galerkin regularization

本文提出用Galerkin截断定义的伪微分算子非线性色散来正则化compacton和peakon，揭示了新型行波、孤子结构及长波子现象，并构造准周期解以支持KAM论证。

热化动力学在伽辽金截断的三维欧拉方程中的表现

The dynamics of thermalisation in the Galerkin-truncated, three-dimensional Euler equation

研究了伽辽金截断的三维欧拉方程在热化过程中的动力学行为及其与湍流的关联。

Intermittency and Thermalization in Turbulence

A dissipation rate, which grows faster than any power of the wave number in Fourier space, may be scaled to lead a hydrodynamic system {\it actually} or {\it potentially} converge to its Galerkin truncation. Actual convergence we name for the asymptotic truncation at a finite wavenumber $k_G$ above which modes have no dynamics; and, we define potential convergence for the truncation at $k_G$ which, however, grows without bound. Both types of convergence can be obtained with the dissipation rate $μ[cosh(k/k_c)-1]$ who behaves as $k^2$ (newtonian) and $\exp\{k/k_c\}$ for small and large $k/k_c$ …

不可伸展旋转输流管在销-滚支撑下的大后屈曲动力学：高阶Galerkin与修正Hencky杆链框架

Large post-critical dynamics of an inextensible spinning fluid-conveying pipe with pinned-roller supports: high-order Galerkin and a modified Hencky bar-chain framework

研究不可伸展旋转输流管在销-滚支撑下的稳定性和大后屈曲动力学，通过九阶Galerkin截断和修正Hencky杆链模型揭示了几何刚化效应，并给出了稳定性边界。

Learning Stable Galerkin Models of Turbulence with Differentiable Programming

Turbulent flow control has numerous applications and building reduced-order models (ROMs) of the flow and the associated feedback control laws is extremely challenging. Despite the complexity of building data-driven ROMs for turbulence, the superior representational capacity of deep neural networks has demonstrated considerable success in learning ROMs. Nevertheless, these strategies are typically devoid of physical foundations and often lack interpretability. Conversely, the Proper Orthogonal Decomposition (POD) based Galerkin projection (GP) approach for ROM has been popular in many problems…

Galerkin截断Burgers和Euler方程的共振现象

Resonance phenomenon for the Galerkin-truncated Burgers and Euler equations

研究Galerkin截断的无粘流体方程中，由于截断波与流体粒子运动共振产生的局部短波振荡（“tyger”）现象，并分析其对热化过程及无粘极限行为的影响。