Structural studies of decaying fluid turbulence: Effect of initial conditions

Abstract

We present results from a systematic numerical study of structural properties of an unforced, incompressible, homogeneous, and isotropic three-dimensional turbulent fluid with an initial energy spectrum that develops a cascade of kinetic energy to large wave numbers. The results are compared with those from a recently studied set of power-law initial energy spectra [C. Kalelkar and R. Pandit, Phys. Rev. E 69, 046304 (2004)] which do not exhibit such a cascade. Differences are exhibited in plots of vorticity isosurfaces, the temporal evolution of the kinetic energy-dissipation rate, and the rates of production of the mean enstrophy along the principal axes of the strain-rate tensor. A crossover between "non-cascade-type" and "cascade-type" behavior is shown numerically for a specific set of initial energy spectra.

Statistics of pressure fluctuations in decaying isotropic turbulence

“…The plots are equispaced in time with a temporal separation of τ = 0.24. The plot with open circles is calculated at cascade completion at the dimensionless time τ = τ c = 0.71, and shows a wavenumber range (for 1 k 10) that exhibits the well-known −5/3 power-law [11,17,18]. Upon cascade completion, the shape of the energy spectrum does not change appreciably (except at large wavenumbers where it falls), but the kinetic energy decays monotonically.…”

“…as a function of the dimensionless time τ . The kinetic energy-dissipation rate peaks [17,18] at τ = τ c , corresponding to cascade completion in the kinetic energy spectrum, and decreases thereafter. The turbulence may be considered as 'fully developed' at τ = τ c and our spatial results (see below) will be calculated at this instant of time.…”

Effect of initial conditions on electron–plasma turbulence: a multiresolution analysis

“…The influence of initial conditions on the evolution of fluid turbulence has been pointed out in several studies (Benzi, Patarnello & Santangelo 1988; Santangelo, Benzi & Legras 1989; Driscoll et al. 2000; Yin, Montgomery & Clerckx 2003; Kalelkar 2005; van Bokhoven et al. 2007).…”

“…On the other hand, the initial vortex distribution may affect the time evolution of the decaying 2D turbulence, since the vortex interactions strongly depend on vortex size, vorticity amplitude, separation distance of the vortex centres, and background shear induced by the surrounding vortices (Melander, Zabusky & McWilliams 1988;Dritschel & Waugh 1992;Waugh 1992;Amoretti et al 2001;Trieling, Velasco Fuentes & van Heijst 2005). The influence of initial conditions on the evolution of fluid turbulence has been pointed out in several studies (Benzi, Patarnello & Santangelo 1988;Santangelo, Benzi & Legras 1989;Driscoll et al 2000;Yin, Montgomery & Clerckx 2003;Kalelkar 2005;van Bokhoven et al 2007).…”

Coherent structures and turbulence evolution in magnetized non-neutral plasmas

“…On the other hand, a well estabilished (both numerically and experimentally) feature of 2D turbulent flows is the formation of large-scale, long-lived coherent structures or vortices arising from smaller-scale structures [38,39]. In general, the vortex interactions depend on vortex size and circulation, distance between the vortex centers, background shear induced by the surrounding vortices [40,41,42,22,43], and all these features of the flow may strongly depend on the initial vorticity distribution [44,39,45,46,47]. The influence of the initial conditions in a pure electron plasma has been demonstrated computing the scaling properties of the freely relaxing 2D turbulence [48,10,49] from the analysis of experimental results obtained in different Penning-Malmberg traps [50,25].…”