On Variational Principles for Coherent Vortex Structures

Abstract

Abstract. Different approaches are discussed of variational principles characterizing coherent vortex structures in two-dimensional flows. Turbulent flows seem to form ordered structures in the large scales of the motion and the self-organization principle predicts asymptotic states realizing an extremal value of the energy or a minimum of enstruphy. On the other hand the small scales take care of the increase of entropy, and asymptotic results can be obtained by applying the theory of equilibrium statistical mechanics.

Low-dimensional model for vortex merging in the two-dimensional temporal mixing layer

“…• The presented method can be extended to analyze other types of coherent structures. Many coherent structures, such as monopoles, dipoles and tripols, can be described using few parameters, see Van de Fliert, [23]. These descriptions can be used to design a model manifold.…”

Coherent hydrodynamic structures and vortex dynamics

“…Дадим основное определение когерентности в системе, базирующееся на идеологии вариации функционалов в пуассоновых системах [96]- [97]: когерентной структурой (КС) для (обобщенной) гидродинамической системы будем называть обобщенное состояние относительного равновесия (элементарная КС) либо упорядоченную определенным образом совокупность обобщенных СОР (составная КС) задачи на вариацию выделенного инварианта Казимира (энергии, псевдоэнтропии и т. д.)…”

Differential Quadrature Method to Examine the Dynamical Behavior of Soliton Solutions to the Korteweg-de Vries Equation

“…Sarma [29] provided a solitary wave solution for this equation. Van de Fliert and Groesen [30] used a variational methodology, which was further investigated by Yuliawati et al using the steepest descent approach, to study the solution of the KDV equation in the Hamiltonian condition. In addition, there have been several other successful numerical approaches to the KdV equation, including the spectral method [31], the pseudospectral method, and the collocation method [32].…”