Vorticity intensification and transition to turbulence in three-dimensional euler equations

The evolution of a perturbed vortex tube is studied by means of a second-order projection method for the incompressible Euler equations. We observe, to the limits of grid resolution, a nonintegrable blowup in vorticity. The onset of the intensification is accompanied by a decay in the mean kinetic energy. Locally, the intensification is characterized by tightly curved regions of alternating-sign vorticity in a 2n-pole structure. After the firstL peak, the enstrophy and entropy continue to increase, and we observe reconnection events, continued decay of the mean kinetic energy, and the emergence of a Kolmogorov (k ^–5/3) range in the energy spectrum.     

Thermal dissipation in quantum turbulence

The microscopic mechanism of thermal dissipation in quantum turbulence is numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the obtained dissipation does not work at scales greater than the vortex core size. However, as the temperature increases, dissipation works at large scales and it affects the vortex dynamics. We successfully obtain the mutual friction coefficients of the vortex in dilute Bose-Einstein condensates dynamics as functions of temperature.     

External dissipation in driven two-dimensional turbulence

Turbulence in a freely suspended soap film is created by electromagnetic forcing and measured by particle tracking. The velocity fluctuations are shown to be adequately described by the forced Navier-Stokes equation for an incompressible two-dimensional fluid with a linear drag term to model the frictional coupling to the surrounding air. Using this equation, the energy dissipation rates due to air friction and the film's internal viscosity are measured, as is the rate of energy injection from the electromagnetic forcing. Comparison of these rates demonstrates that the air friction is a significant energy dissipation mechanism in the system.     

Weak turbulence in periodic flows

We consider the stability of a two-dimensional plane-parallel flow of viscous liquid in an external force field which is a periodic function of one of the coordinates. At sufficiently high Reynolds numbers the plane-parallel flow becomes unstable and a two-dimensional secondary flow ensues. Near the stability threshold, the secondary flow turns out to be large-scale and chaotically self-fluctuating in time.     

Large scale dissipation and filament instability in two-dimensional turbulence

Coherent vortices in two-dimensional turbulence induce far-field effects that stabilize vorticity filaments and inhibit the generation of new vortices. We show that the large-scale energy sink often included in numerical simulations of statistically stationary two-dimensional turbulence reduces the stabilizing role of the vortices, leading to filament instability and to continuous formation of new coherent vortices. This counterintuitive effect sheds new light on the mechanisms responsible for vortex formation in forced-dissipated two-dimensional turbulence, and it has significant impact on the temporal evolution of the vortex population in freely decaying turbulence. The time dependence of vortex statistics in the presence of a large-scale energy sink can be approximately described by a modified version of the scaling theory developed for small-scale dissipation.     

Geometry of intensive scalar dissipation events in turbulence

The maxima of the scalar dissipation rate in turbulence appear in the form of sheets and correspond to the potentially most intensive scalar mixing events. Their cross section extension determines a locally varying diffusion scale of the mixing process and extends the classical Batchelor picture of one mean diffusion scale. The distribution of the local diffusion scales is analyzed for different Reynolds and Schmidt numbers with a fast multiscale technique applied to very high-resolution simulation data. The scales always take values across the whole Batchelor range and beyond. Furthermore, their distribution is traced back to the distribution of the contractive short-time Lyapunov exponent of the flow.     

A spectrally refined interface approach for simulating multiphase flows

This paper presents a novel approach to phase-interface transport based on pseudo-spectral sub-grid refinement of a level set function. In each flow solver grid cell, a set of quadrature points is introduced on which the value of the level set function is known. This methodology allows to define a polynomial reconstruction of the level set function in each cell. The transport is performed using a semi-Lagrangian technique, removing all constraints on the time step size. Such an approach provides sub-cell resolution of the phase-interface and leads to excellent accuracy in the transport, while a reasonable cost is obtained by pre-computing some of the metrics associated with the polynomials. To couple this approach with a flow solver, an converging curvature computation is introduced. First, a second order explicit distance to the sub-grid interface is reconstructed on the flow solver mesh. Then, a least squares approach is employed to extract the curvature from this distance function. This technique is found to combine the high accuracy and good conservation found in the particle level set method with the converging curvature usually obtained with classical high order PDE transport of the level set function. Tests are presented for both transport as well as two-phase flows, that suggest that this technique is capable of retaining the thin liquid structures that are expected in turbulent atomization of liquids.     

Beam spreading of truncated Gaussian beams in Kolmogorov turbulence

Based on the extended Huygens-Fresnel principle and the hard-edge aperture function expanded as the sum of finite-term complex Gaussian function, analytical expression for average intensity of truncated Gaussian beam in Kolmogorov turbulence is derived, and some limiting cases are discussed. The influences of many factors, such as Fresnel number, wavelength, truncation parameter and structure constant on beam spreading are studied with the help of the average intensity formula. We found that the peak value of average intensity decreases and the beam spot spreads with the decrease of Fresnel number. The change of peak intensity against Fresnel number is slower with large aperture than that with small aperture. When Fresnel number is not small enough the influence of turbulence on intensity profiles is so small that can be neglected if structure constant is small.     

Lagrangian turbulence in nonstationary 2-D flows

Lagrangian particle transport in nonstationary 2-D flows is studied both analytically and numerically. Analytic expressions for the diffusion coefficients are obtained for the adiabatic regime. Numerical estimates of the diffusion coefficients are found to agree with the theoretical results.     

Effective eddy viscosity in stratified turbulence

This paper investigates the effective eddy viscosity inferred from direct numerical simulations of decaying stratified and non-stratified turbulence. It is shown that stratification affects the horizontal eddy viscosity dramatically, by increasing non-local energy transfer between large and small horizontal scales. This non-local horizontal energy transfer is around 20% of the local horizontal energy transfer at the cutoff wavenumber k_c = 40. The non-local horizontal energy transfer occurs at large vertical wavenumbers, which may be larger than the buoyancy wavenumber k_b = N/u_rms, where N is the buoyancy frequency and u_rms is the root-mean-square velocity. By increasing the value of the test cutoff wavenumber k_c from large scales to the dissipation range, the non-local horizontal eddy viscosity decreases and the local eddy viscosity is dominant. Overall, the presence of stratification can significantly change the features of subgrid-scale (SGS) motions. Current SGS models should, therefore, be modified for use in large-eddy simulation of stratified turbulence.     

Extended self-similarity and dissipation range dynamics of three-dimensional turbulence

We carry out a self-consistent calculation of the structure functions in the dissipation range using the Navier-Stokes equation. Combining these results with the known structures in the inertial range, we actually propose crossover functions for the structure functions that take one smoothly from the inertial to the dissipation regime. These crossover functions are shown to exhibit extended self-similarity properties consistent with experimental findings.     

Imprint of large-scale flows on turbulence

We investigate the locality of interactions in hydrodynamic turbulence using data from a direct numerical simulation on a grid of 1024(3) points; the flow is forced with the Taylor-Green vortex. An inertial range for the energy is obtained in which the flux is constant and the spectrum follows an approximate Kolmogorov law. Nonlinear triadic interactions are dominated by their nonlocal components, involving widely separated scales. The resulting nonlinear transfer itself is local at each scale but the step in the energy cascade is independent of that scale and directly related to the integral scale of the flow. Interactions with large scales represent 20% of the total energy flux. Possible explanations for the deviation from self-similar models, the link between these findings and intermittency, and their consequences for modeling of turbulent flows are briefly discussed.     

A turbulence model in unbounded smooth shear flows: The weak turbulence approach

We discuss a new concept of the subcritical transition to turbulence in unbounded smooth (noninflectional) spectrally stable shear flows. This concept (the so-called bypass transition) follows from considering the nonnormality of the linear dynamics of vortex disturbances in shear flows and is most easily interpreted by tracing the evolution of spatial Fourier harmonics (SFHs) of the disturbances. The key features of the concept are as follows: the transition of the flow by only finite-amplitude vortex disturbances despite the fact that the phenomenon is energetically supported by a linear process (the transient growth of SFHs); the anisotropy of processes in the k space; the onset of chaos due to the dynamical (not stochastic) process—nonlinear processes that close the transition feedback loop by the angular redistribution of SFHs in the k space. The evolution of two-dimensional small-scale vortex disturbances in a parallel flow with a uniform shear is analyzed within the weak turbulence approach. This numerical test analysis is carried out to prove the most problematic statement of the concept, the existence of a positive feedback caused by the nonlinear process. Numerical calculations also show the existence of a threshold: if the amplitude of the initial disturbance exceeds the threshold value, the self-maintenance of disturbances becomes realistic. The latter is a characteristic feature of the flow transition to the turbulent state and its maintenance.     

Towards lowering dissipation bounds for turbulent flows

We examine the background flow variational principle for calculating bounds on the energy dissipation rate in turbulent shear flow, and suggest to select this principle's test functions such that they comply with the small-scale smoothness of real turbulent velocity fields. A self-consistent algorithm implementing this requirement then yields an upper bound on the dimensionless dissipation coefficient which shows a weak power-law decrease at high Reynolds numbers, instead of approaching a nonzero constant, as it did in previous estimates. Received 26 October 1998     

Transition to turbulence for doubly periodic flows

We construct a typical model for the Poincaré map of doubly periodic flows, which presents numerically a transition to chaotic behavior. After the frequency locking phenomenon, we observe two types of transitions to turbulence. The first one involves successive subharmonic instabilities of a periodic solution. The second one occurs after the disappearance of a periodic solution and can be either intermittent or discontinuous with hysteresis.