Daniel I. Meiron

Small-scale structure of the Taylor–Green vortex

The dynamics of both the inviscid and viscous Taylor–Green (TG) three-dimensional vortex flows are investigated. This flow is perhaps the simplest system in which one can study the generation of small scales by three-dimensional vortex stretching and the resulting turbulence. The problem is studied by both direct spectral numerical solution of the Navier–Stokes equations (with up to 256 3 modes) and by power-series analysis in time. The inviscid dynamics are strongly influenced by symmetries which confine the flow to an impermeable box with stress-free boundaries. There is an early stage during which the flow is strongly anisotropic with well-organized (laminar) small-scale excitation in the form of vortex sheets located near the walls of this box. The flow is smooth but has complex-space singularities within a distance

Generalized vortex methods for free-surface flow problems

\hat{\delta}(t)

Vortex simulations of the Rayleigh--Taylor instability

of real (physical) space which give rise to an exponential tail in the energy spectrum. It is found that

Nonlinear effects of multifrequency hydrodynamic instabilities on ablatively accelerated thin shells

\hat{\delta}(t)

Applications of Numerical Conformal Mapping.

decreases exponentially in time to the limit of our resolution. Indirect evidence is presented that more violent vortex stretching takes place at later times, possibly leading to a real singularity (

Physical Review Letters: Ising-Model Critical Indices in Three Dimensions from the Callan-Symanzik Equation*

\hat{\delta}(t) = 0

Partial color screening by classical Yang-Mills fields

) at a finite time. These direct integration results are consistent with new temporal power-series results that extend the Morf, Orszag & Frisch (1980) analysis from order t 44 to order t 80 . Still, convincing evidence for or against the existence of a real singularity will require even more sophisticated analysis. The viscous dynamics (decay) have been studied for Reynolds numbers R (based on an integral scale) up to 3000 and beyond the time t max at which the maximum energy dissipation is achieved. Early-time, high- R dynamics are essentially inviscid and laminar. The inviscidly formed vortex sheets are observed to roll up and are then subject to instabilities accompanied by reconnection processes which make the flow increasingly chaotic (turbulent) with extended high-vorticity patches appearing away from the impermeable walls. Near t max the small scales of the flow are nearly isotropic provided that R [gsim ] 1000. Various features characteristic of fully developed turbulence are observed near t max when R = 3000 and R λ = 110: a k − n inertial range in the energy spectrum is obtained with n ≈ 1.6–2.2 (in contrast with a much steeper spectrum at earlier times); th energy dissipation has considerable spatial intermittency; its spectrum has a k −1+μ inertial range with the codimension μ ≈ 0.3−0.7. Skewness and flatness results are also presented.

Critical Indices from Perturbation Analysis of the Callan-Symanzik Equation

The motion of free surfaces in incompressible, irrotational, inviscid layered flows is studied by evolution equations for the position of the free surfaces and appropriate dipole (vortex) and source strengths. The resulting Fredholm integral equations of the second kind may be solved efficiently in both storage and work by iteration in both two and three dimensions. Applications to breaking water waves over finite-bottom topography and interacting triads of surface and interfacial waves are given.

Ising Model Critical Indices in Three-Dimensions from the Callan-Symanzik Equation

A vortex technique capable of calculating the Rayleigh–Taylor instability to large amplitudes in inviscid, incompressible, layered flows is introduced. The results show the formation of a steady‐state bubble at large times, whose velocity is in agreement with the theory of Birkhoff and Carter. It is shown that the spike acceleration can exceed free fall, as suggested recently by Menikoff and Zemach. Results are also presented for instability at various Atwood ratios and for fluids having several layers.

Analytic structure of vortex sheet dynamics. Part 1. Kelvin–Helmholtz instability

Two‐dimensional numerical simulations of ablatively accelerated thin‐shell fusion targets, susceptible to rupture and failure by Rayleigh–Taylor instability, are presented. The results show that nonlinear effects of Rayleigh–Taylor instability are manifested in the dynamics of the ’’bubble’’ (head of the nonlinear fluid perturbation) rather than in the dynamics of the spike (tail of the perturbation). The role of multiwavelength perturbations on the shell is clarified, and rules are presented to predict the dominant nonlinear mode‐mode interactions which limit shell performance. It is also shown that the essential dynamics of strongly driven flows are governed by the classical Rayleigh–Taylor instability of an ideal, incompressible, thin fluid layer.