Proceedings: Mathematical and physical sciences, Том 434

A. N. Kolmogorov a₁ amplitude approximation asymptotic attractor behaviour boundary conditions calculated cascade coefficients combustion components computed constant correlations crack crystal curve decay defined density derived diffusion dimension direct numerical simulations dissipation rate dynamics eddies effects elastic energy equations experimental exponents figure finite fluctuations Fluid Mech fractal function gradient half-spaces high Reynolds number homogeneous hypothesis inertial range integral interaction intermittency internal waves isotropic Kolmogorov Kraichnan laminar flame length scale linear log-normal Lond Malliavin calculus Mandelbrot matrix measurements motion multifractal Navier-Stokes Navier-Stokes equations nonlinear normalized obtained parameters Phys pore problem Proc random random variable ratio regions Reynolds number scalar fields shear similar simulations small-scale solution spectra spectrum Sreenivasan statistical strain stress structure structure functions surface Temam temperature theorem theory turbulent flow universal values variable vector velocity field viscous vorticity wave numbers wavenumber zero