We propose a novel gauge fluid solver based on Clebsch wave functions to solve
incompressible fluid equations. Our method combines the expressive power of Clebsch …

The use of potential fields in fluid dynamics is retraced, ranging from classical potential
theory to recent developments in this evergreen research field. The focus is centred on two …

For a strictly inviscid barotropic flow with conservative body forces, the Helmholtz vorticity
theorem shows that material or Lagrangian surfaces which are vortex surfaces at time t= 0 …

We propose a theoretical method for constructing an initial two-component wave function
that can be transformed into a knotted velocity field with finite kinetic energy and enstrophy …

Clebsch maps encode velocity fields through functions. These functions contain valuable
information about the velocity field. For example, closed integral curves of the associated …

We develop a general method for constructing knotted flux tubes with finite thickness,
arbitrary shape and tunable twist. The central axis of the knotted tube is specified by a …

A recently proposed variational principle with a discontinuous Lagrangian for viscous flow is
reinterpreted against the background of stochastic variational descriptions of dissipative …

We report a systematic study on the construction of the explicit, general form of vortex-
surface fields (VSFs) and Clebsch potentials in the initial fields with the zero helicity density …

The discontinuous Lagrangian approach, allowing for a variational description of irreversible
phenomena in continuum theory such as viscosity and thermal conductivity, is utilised for the …

Detailed analyses of the Navier–Stokes equations on the basis of the Euler–Lagrangian
formalism are presented with the use of numerical simulations. A singular perturbation …