Virial functionals in fluid dynamics

The aim of this paper is to show that functionals similar to the ‘virial’ function of classical mechanics can be introduced for several dynamical systems of fluid mechanics provided that those dynamical systems can be described by Hamilton’s principle of least action. The main requirement to ‘virials’ is their increasing by virtue of equations of motion. Applications of those functionals to hydrodynamic stability theory are reviewed and further perspectives are discussed.