• Physics of fractals and spirals.
  • Dissipation properties of near-singular flow structures and their crucial dependence on the geometry of these structures.
  • Direct numerical simulations and investigations of small-scale near-singular structures, for example in vortex tubes. The theorem of self-similar streamlines relates the Kolmogorov capacity of spiral-helical streamlines to singularity properties of vortex tubes. Geometrical eduction of vortex tubes independently of their enstrophy levels.
  • Scalar interfaces and Eulerian and Lagrangia n statistics in various flows with va rious spatial and time structures: superpositions of random Fourier modes, steady and unsteady vortex tubes, DNS turbulence, chaotic advection.
  • Large-eddy simulations, kinematic simulations and stochastic models of turbulent diffusion in homogeneous and stratified turbulence. Fluid elements and inertial particles.
  • Wind tunnel experiments.
  • Combustion: flamelet-vortex interactions and reaction-diffusion systems. G-equation.
  • Ocean waves: geometry and equilibrium range wind-wave spectra.
  • Fractals, spirals, wavelets and intermittency. Burgers turbulence. Energy transfer during shear-layer instabilities.
  • Financial fluctuations.
  • Fundamental, experimental studies in fluid mechanics with particular emphasis on turbulence.
  • Turbulent shear layers with changing boundary conditions such as Reynolds number, roughness.
  • Control of wall-bounded and separating shear layers.
  • Pressure fluctuations.
  • Superfluid turbulence, particularly the energy and pressure spectra.
  • Mathematical tools for turbulence studies.