Optimal combination of spatial basis functions for the model reduction of nonlinear distributed parameter systems

M Jiang, H Deng - Communications in Nonlinear Science and Numerical …, 2012 - Elsevier
Spectral methods are among the most extensively used techniques for model reduction of
distributed parameter systems in various fields, including fluid dynamics, quantum …

Logarithmic discretization and systematic derivation of shell models in two-dimensional turbulence

ÖD Gürcan, P Morel, S Kobayashi, R Singh, S Xu… - Physical Review E, 2016 - APS
A detailed systematic derivation of a logarithmically discretized model for two-dimensional
turbulence is given, starting from the basic fluid equations and proceeding with a particular …

Turbulence as a network of Fourier modes

ÖD Gürcan, Y Li, P Morel - Mathematics, 2020 - mdpi.com
Turbulence is the duality of chaotic dynamics and hierarchical organization of a field over a
large range of scales due to advective nonlinearities. Quadratic nonlinearities (eg …