The existing strategies of modelling turbulent two-phase flows can be subdivided into two groups depending on the Lagrangian tracking and Eulerian continuum approaches for handling the particulate phase. In the framework of the Lagrangian method, the particles are assumed to encounter a series of turbulent eddies randomly, and the macroscopic particle properties are determined by solving stocha...

Lagrangian symmetries are found for hydrodynamics and magnetohydrodynamics, which result in conservation of potential vorticity and of cross helicity, respectively. These symmetries, which persist in the reduction from Lagrangian to Eulerian variables, directly give rise to Casimir invariants of the Hamiltonian formalism. The mechanism of spontaneous symmetry breaking in a fluid is also presented.

The increasing realism of ocean circulation models is leading to an increasing use of Eulerian models as a basis to compute transport properties and to predict the fate of Lagrangian quantities. There exists, however, a signiŽ cant gap between the spatial scales of model resolution and that of forces acting on Lagrangian particles. These scales may contain high vorticity coherent structures tha...

This paper describes a motion blur technique which can be applied to rendering fluid simulations that are carried out in the Eulerian framework. Existing motion blur techniques can be applied to rigid bodies, deformable solids, clothes, and several other kinds of objects, and produce satisfactory results. As there is no specific reason to discriminate fluids from the above objects, one may cons...

In hierarchical models of gravitational clustering, virialized haloes are biased tracers of the matter distribution. As discussed by Mo & White (1996), this bias is nonlinear and stochastic. They developed a model which allows one to write down analytic expressions for the mean of the bias relation, in the initial Lagrangian, and the evolved, Eulerian, spaces. We provide analytic expressions fo...