Energy spectrum in the dissipation range of fluid turbulence

High-resolution, direct numerical simulations of three-dimensional incompressible Navier-Stokes equations are carried out to study the energy spectrum in the dissipation range. An energy spectrum of the form A(k/kd)α exp [-βk/kd] is confirmed. The possible values of the parameters α and β, as well as their dependence on Reynolds numbers and length scales, are investigated, showing good agreement with recent theoretical predictions. A 'bottleneck'-type effect is reported at k/kd ≈ 4, exhibiting a possible transition from near-dissipation to far-dissipation.