Coupling effects and thin-shell corrections for surface instabilities of cylindrical fluid shells.

We show that when linear azimuthal perturbations on the surfaces of a fluid shell are regrouped according to α^{m}, they can be divided into Bell model terms, coupling terms, and the newly identified thin-shell correction terms, where α is the ratio of R_{out} to R_{in}, and m is the mode number of a given unstable mode on the surfaces. It is also revealed that α^{m} is a convenient index variable of coupling effects, with which we show that the evolution of instability is composed of three stages, i.e., strongly coupled stage, transition stage, and uncoupled stage. Roughly, when α^{m}<6, the fluid shell is in the strongly coupled stage, where both coupling effects and the newly identified thin-shell corrections play important roles. Strong feed through is expected to be observed. The uncoupled stage is reached at α^{m}∼36, where Bell's model of independent surface holds. In between is the transition stage, where mode competitions on the two surfaces are expected to be observed. These results afford an intuitive picture which is easy to use in guiding the design of experiments. They may also help to quickly grasp major features of instability experiments of this kind.

Scale-to-scale energy transfer in mixing flow induced by the Richtmyer-Meshkov instability.

The Richtmyer-Meshkov instability (RMI) mixing flow induced by a planar shock wave of Mach 1.6 is investigated using direct numerical simulation method. Interfacial perturbations of different scales between air and sulfur hexafluoride are introduced to study the effect of the initial conditions. Focus is placed on the analysis of the scale-to-scale transfer of kinetic energy in both Fourier and physical spaces. The kinetic energy injected from the perturbation scales is transferred to both larger and smaller scales in an average sense within the inner mixing zone (IMZ) at early times and is mainly passed down into smaller scales at the late stage. The physical-space energy flux due to the subgrid-scale (SGS) stress is studied using a filtering approach in order to shed light on the physical origin of the scale-to-scale kinetic energy transfer. It is found that the pointwise SGS energy flux is highly correlated with the local spike and bubble structures in the IMZ. Moreover, it turns out that the mean SGS energy flux is mainly ascribed to the component in the direction of shock wave propagation. An analysis using the method of conditional averaging manifests that the generation of local SGS energy flux is associated with the property of the surrounding flow induced by quadrupolar or dipolar vortex structures.

Joint-constraint model for large-eddy simulation of helical turbulence.

A three-term mixed subgrid-scale (SGS) stress model is proposed for large-eddy simulation (LES) of helical turbulence. The new model includes a Smagorinsky-Lilly term, a velocity gradient term, and a symmetric vorticity gradient term. The model coefficients are determined by minimizing the mean square error between the realistic and modeled Leonard stresses under a joint constraint of kinetic energy and helicity fluxes. The model formulated as such is referred to as joint-constraint dynamic three-term model (JCD3TM). First, the new model is evaluated a priori using the direct numerical simulation (DNS) data of homogeneous isotropic turbulence with helical forcing. It is shown that the SGS dissipation fractions from all three terms in JCD3TM have the properties of length-scale invariance in inertial subrange. JCD3TM can predict the SGS stresses, energy flux, and helicity flux more accurately than the dynamic Smagorinsky model (DSM) and dynamic mixed helical model (DMHM) in both pointwise and statistical senses. Then, the performance of JCD3TM is tested a posteriori in LESs of both forced and freely decaying helical isotropic turbulence. It is found that JCD3TM possesses certain features of superiority over the other two models in predicting the energy spectrum, helicity spectrum, high-order statistics, etc. It is also noteworthy that JCD3TM is capable of simulating the evolutions of both energy and helicity spectra more precisely than other models in decaying helical turbulence. We claim that the present SGS model can capture the main helical features of turbulent motions and may serve as a useful tool for LES of helical turbulent flows.

Cascade of kinetic energy in three-dimensional compressible turbulence.

The conservative cascade of kinetic energy is established using both Fourier analysis and a new exact physical-space flux relation in a simulated compressible turbulence. The subgrid scale (SGS) kinetic energy flux of the compressive mode is found to be significantly larger than that of the solenoidal mode in the inertial range, which is the main physical origin for the occurrence of Kolmogorov's -5/3 scaling of the energy spectrum in compressible turbulence. The perfect antiparallel alignment between the large-scale strain and the SGS stress leads to highly efficient kinetic energy transfer in shock regions, which is a distinctive feature of shock structures in comparison with vortex structures. The rescaled probability distribution functions of SGS kinetic energy flux collapse in the inertial range, indicating a statistical self-similarity of kinetic energy cascades.

Refined subgrid-scale model for large-eddy simulation of helical turbulence.

A refined two-term helical subgrid-scale (SGS) stress model with respect to that suggested by Li et al. [Phys. Rev. E 74, 026310 (2006)] is designed for large-eddy simulation (LES) of helical turbulence. The model coefficients in the new model are verified a priori to be scale invariant in inertial range, which proves that our model is local in scale. A dynamic method based on minimizing the residual resolved energy and helicity dissipations is suggested to simultaneously evaluate the coefficients of the mixed SGS model as the simulation progresses. In addition, an SGS helicity dissipation (or helicity flux) constraint condition is proposed to optimize the mixed two-term model. Both techniques are first tested and validated in the LES of forced isotropic helical turbulence. The statistical results are analyzed and compared with those obtained from the dynamic Smagorinsky model, the traditional dynamic mixed model, and the direct numerical simulation. It is found that the introduction of this dynamic procedure can help overcome the drawback of the traditional dynamic method which can not capture the negative helicity fluxes and SGS dissipations. The probability density functions of the energy flux and the conditioned helicity flux and SGS stress demonstrate that the helicity flux constrained dynamic SGS model can effectively predict the real SGS helical effects on the resolved scales, such as backscatters of energy and helicity, accurate helicity dissipation rate, and so on. The present models are also applied to the simulation of freely decaying isotropic turbulence with no apparent improvement observed in comparison with the traditional SGS models. The underlying reasons for these issues are addressed in detail.

Acceleration of passive tracers in compressible turbulent flow.

In compressible turbulence at high Reynolds and Mach numbers, shocklets emerge as a new type of flow structure in addition to intense vortices as in incompressible turbulence. Using numerical simulation of compressible homogeneous isotropic turbulence, we conduct a Lagrangian study to explore the effects of shocklets on the dynamics of passive tracers. We show that shocklets cause very strong intermittency and short correlation time of tracer acceleration. The probability density function of acceleration magnitude exhibits a -2.5 power-law scaling in the high compression region. Through a heuristic model, we demonstrate that this scaling is directly related to the statistical behavior of strong negative velocity divergence, i.e., the local compression. Tracers experience intense acceleration near shocklets, and most of them are decelerated, usually with large curvatures in their trajectories.

Scaling and statistics in three-dimensional compressible turbulence.

The scaling and statistical properties of three-dimensional compressible turbulence are studied using high-resolution numerical simulations and a heuristic model. The two-point statistics of the solenoidal component of the velocity field are found to be not significantly different from those of incompressible turbulence, while the scaling exponents of the velocity structure function for the compressive component become saturated at high orders. Both the simulated flow and the heuristic model reveal the presence of a power-law tail in the probability density function of negative velocity divergence (high compression regime). The power-law exponent is different from that in Burgers turbulence, and this difference is shown to have a major contribution from the pressure effect, which is absent in the Burgers turbulence.

Is the Kelvin theorem valid for high Reynolds number turbulence?

The Kelvin-Helmholtz theorem on conservation of circulation is supposed to hold for ideal inviscid fluids and is believed to be play a crucial role in turbulent phenomena. However, this expectation does not take into account singularities in turbulent velocity fields at infinite Reynolds number. We present evidence from numerical simulations for the breakdown of the classical Kelvin theorem in the three-dimensional turbulent energy cascade. Although violated in individual realizations, we find that circulation is still conserved in some average sense. For comparison, we show that Kelvin's theorem holds for individual realizations in the two-dimensional enstrophy cascade, in agreement with theory. The turbulent "cascade of circulations" is shown to be a classical analogue of phase slip due to quantized vortices in superfluids, and various applications in geophysics and astrophysics are outlined.

Physical mechanism of the two-dimensional inverse energy cascade.

We study the physical mechanisms of the two-dimensional inverse energy cascade using theory, numerics, and experiment. Kraichnan's prediction of a -5/3 spectrum with constant, negative energy flux is verified in our simulations of 2D Navier-Stokes equations. We observe a similar but shorter range of inverse cascade in laboratory experiments. Our theory predicts, and the data confirm, that inverse cascade results mainly from turbulent stress proportional to small-scale strain rotated by 45 degrees. This "skew-Newtonian" stress is explained by the elongation and thinning of small-scale vortices by large-scale strain which weakens their velocity and transfers their energy upscale.

Physical mechanism of the two-dimensional enstrophy cascade.

In two-dimensional turbulence, irreversible forward transfer of enstrophy requires anticorrelation of the turbulent vorticity transport vector and the inertial-range vorticity gradient. We investigate the basic mechanism by numerical simulation of the forced Navier-Stokes equation. In particular, we obtain the probability distributions of the local enstrophy flux and of the alignment angle between vorticity gradient and transport vector. These are surprisingly symmetric and cannot be explained by a local eddy-viscosity approximation. The vorticity transport tends to be directed along streamlines of the flow and only weakly aligned down the fluctuating vorticity gradient. All these features are well explained by a local nonlinear model. The physical origin of the cascade lies in steepening of inertial-range vorticity gradients due to compression of vorticity level sets by the large-scale strain field.