The Hamiltonian formulation of hydrodynamics in Clebsch variables is used for construction of a statistical theory of turbulence. It is shown that the interaction of the random and large-scale coherent components of t...
The Hamiltonian formulation of hydrodynamics in Clebsch variables is used for construction of a statistical theory of turbulence. It is shown that the interaction of the random and large-scale coherent components of the Clebsch fields is responsible for generation of two energy spectra E(k)∝k−7/3 and E(k)∝k−2 at scales somewhat larger than those corresponding to the -5/3 inertial range. This interaction is also responsible for the experimentally observed Gaussian statistics of the velocity differences at large scales, and the nontrivial scaling behavior of their high-order moments for inertial-range values of the displacement r. The ‘‘anomalous scaling exponents’’ are derived and compared with experimental data.
We consider a family of three-dimensional, volume preserving maps depending on a small parameter epsilon. As epsilon --> 0+ these maps asymptote to flows which attain a heteroclinic connection. We show that for sma...
We consider a family of three-dimensional, volume preserving maps depending on a small parameter epsilon. As epsilon --> 0+ these maps asymptote to flows which attain a heteroclinic connection. We show that for small epsilon the heteroclinic connection breaks up and that the splitting between its components scales with epsilon like epsilon(gamma) exp(-beta/epsilon). We estimate beta using the singularities of the epsilon --> 0+ heteroclinic orbit in the complex plane. We then estimate gamma using linearization about orbits in the complex plane. While these estimates are not proven, they are well supported by our numerical calculations. The work described here is a special case of the theory derived by Amick et al. which applies to q-dimensional volume preserving mappings.
A new rotation symmetry for steady Hele-Shaw flows is reported. In the case when surface tension is neglected, it is shown that if a curve L moving with constant velocity U is a solution to the Hele-Shaw problem, then...
A new rotation symmetry for steady Hele-Shaw flows is reported. In the case when surface tension is neglected, it is shown that if a curve L moving with constant velocity U is a solution to the Hele-Shaw problem, then the curve L obtained from a rotation of L about its center by an arbitrary angle is also a solution with the same velocity U. Similar results hold for the case with surface tension if and only if the Schwarz function of the curve L is regular in the fluid region and at most a linear function at infinity. Several examples in which this principle is used to generate new solutions to the problem are also discussed.
In this letter, a nonlinear deviation from the Navier-Stokes equation is obtained from the recently proposed LBGK models, which are designed as an alternative to lattice gas or lattice Boltzmann equation. The classica...
In this letter, a nonlinear deviation from the Navier-Stokes equation is obtained from the recently proposed LBGK models, which are designed as an alternative to lattice gas or lattice Boltzmann equation. The classical Chapman-Enskog method is extended to derive the nonlinear-deviation term as well as its coefficient. Their analytical expression is derived for the first time, thanks to the simplicity of the LBGK models. A numerical simulation of a shock profile is presented. The influence of the correction on the kinetics of compressible flow is discussed. A complete analysis of the thermodynamics including the temperature will be presented elsewhere.
A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell avera...
A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell averaging and reconstruction procedures, that employs a staggered grid of Gauss-Chebyshev and Gauss-Lobatto Chebyshev discretizations. The non-oscillatory reconstruction procedure is based on ideas similar to those proposed by Cai et al. (Math. Comput. 52, 389 (1989)) but employs a modified technique which is more robust and simpler in terms of determining the location and strength of a discontinuity. It is demonstrated through model problems of linear advection, inviscid Burgers equation, and one-dimensional Euler system that the proposed algorithm leads to stable, non-oscillatory accurate results. Exponential accuracy away from the discontinuity is realized for the inviscid Burgers equation example.
The short-time behavior of the turbulent viscosity is inferred from the immediate response of the Reynolds stress deduced by Crow [1] for the problem of isotropic turbulence subjected to a mean strain at time t=0. The...
Direct numerical simulations with up to 40962 resolution are performed to address the question of universality of statistical properties of the enstrophy cascade in homogeneous two-dimensional turbulence driven by lar...
Direct numerical simulations with up to 40962 resolution are performed to address the question of universality of statistical properties of the enstrophy cascade in homogeneous two-dimensional turbulence driven by large-scale Gaussian white-in-time noise. Data with different Reynolds numbers are compared with each other. The energy spectrum is found to be very close to 1/k3. It is shown that the primary contribution to the enstrophy transfer function comes from wave-number triads with one small leg and two long ones, corresponding to wave numbers in the inertial range.
Thin films can be effectively described by the lubrication approximation, in which the equation of motion is ht+(hnhxxx)x=0. Here h is a necessarily positive quantity which represents the height or thickness of the fi...
Thin films can be effectively described by the lubrication approximation, in which the equation of motion is ht+(hnhxxx)x=0. Here h is a necessarily positive quantity which represents the height or thickness of the film. Different values of n, especially 1, 2, and 3 correspond to different physical situations. This equation permits solutions in the form of traveling disturbances with a fixed form. If u is the propagation velocity, the resulting equation for the disturbance is uhx=(hnhxxx)x. Here, quantitative and qualitative solutions to the equation are presented. The study has been limited to the intervals in x where the solutions are positive. It is found that transitions between different qualitative behaviors occur at n=3, 2, 3/2, and 1/2. For example, if u is not zero, solitonlike solutions defined on a finite interval are only possible for n<3. More specific results can be obtained. In the case in which the velocity is zero, solitons occur for n<2. For n=1, the region 3/21/2, single-minimum solutions diverging at ±∞ are possible. The generic solution, present for all positive values of n, is a receding front, which diverges at finite x for n<0.
Results of a numerical study of the dynamics of a collection of disks colliding inelastically in a periodic two-dimensional enclosure are presented. The properties of this system, which is perhaps the simplest model f...
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As the depth of focus of optical steppers grows smaller, it becomesmore important to determine the position of best focus accurately andquickly. This paper describes the use of phase-shifted mask technologyto form a f...
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