Uriel Frisch - Academia.edu (original) (raw)
Papers by Uriel Frisch
Journal of Fluid Mechanics, 2014
It is known that the Eulerian and Lagrangian structures of fluid flow can be drastically differen... more It is known that the Eulerian and Lagrangian structures of fluid flow can be drastically different; for example, ideal fluid flow can have a trivial (static) Eulerian structure, while displaying chaotic streamlines. Here, we show that ideal flow with limited spatial smoothness (an initial vorticity that is just a little better than continuous) nevertheless has time-analytic Lagrangian trajectories before the initial limited smoothness is lost. To prove these results we use a little-known Lagrangian formulation of ideal fluid flow derived by Cauchy in 1815 in a manuscript submitted for a prize of the French Academy. This formulation leads to simple recurrence relations among the time-Taylor coefficients of the Lagrangian map from initial to current fluid particle positions; the coefficients can then be bounded using elementary methods. We first consider various classes of incompressible fluid flow, governed by the Euler equations, and then turn to highly compressible flow, governed b...
This textbook presents a modern account of turbulence. The state-of-the-art is put into historica... more This textbook presents a modern account of turbulence. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such "fully developed turbulence" is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life.
Physics of Fluids, 1973
ABSTRACT Based on total helicity conservation in inviscid incompressible flows, the existence of ... more ABSTRACT Based on total helicity conservation in inviscid incompressible flows, the existence of simultaneous energy and helicity cascades is envisaged.
Journal of Fluid Mechanics, 1974
The Markovian random coupling (MRC) model is a modified form of the stochastic model of the Navie... more The Markovian random coupling (MRC) model is a modified form of the stochastic model of the Navier-Stokes equations introduced by Kraichnan (1958, 1961). Instead of constant random coupling coefficients, white-noise time dependence is assumed for the MRC model. Like the Kraichnan model, the MRC model preserves many structural properties of the original Navier-Stokes equations and should be useful for investigating qualitative features of turbulent flows, in particular in the limit of vanishing viscosity. The closure problem is solved exactly for the MRC model by a technique which, contrary to the original Kraichnan derivation, is not based on diagrammatic expansions. A closed equation is obtained for the functional probability distribution of the velocity field which is a special case of Edwards' (1964) Fokker-Planck equation; this equation is an exact consequence of the stochastic model whereas Edwards' equation constitutes only the first step in a formal expansion based directly on the Navier-Stokes equations. From the functional equation an exact master equation is derived for simultaneous second-order moments which happens t o be essentially a Markovianized version of the single-time quasi-normal approximation characterized by a constant triad-interaction time.
Communications in Mathematical Physics, 1981
The well-posed property for the finite time vortex sheet problem with analytic initial data was f... more The well-posed property for the finite time vortex sheet problem with analytic initial data was first conjectured by Birkhoff in two dimensions and is shown here to hold both in two and three dimensions. Incompressible, inviscid and irrotational flow with a velocity jump across an interface is assumed. In two dimensions, global existence of a weak solution to the Euler equation with such initial conditions is established. In three dimensions, a Lagrangian representation of the vortex sheet analogous to the Birkhoff equation in two dimensions is presented.
Europhysics Letters (epl), 1986
Page 1. Lattice Gas Models for 3D Hydrodynamics This article has been downloaded from IOPscience.... more Page 1. Lattice Gas Models for 3D Hydrodynamics This article has been downloaded from IOPscience. Please scroll down to see the full text article. 1986 Europhys. Lett. 2 291 (http://iopscience.iop.org/0295-5075/2/4/006) Download ...
Physical Review Letters, 1986
Physics Today, 1990
ABSTRACT Key ideas about turbulent flows that have evolved over the last century are surveyed. Th... more ABSTRACT Key ideas about turbulent flows that have evolved over the last century are surveyed. The basic concepts of randomness, eddy viscosity, cascade, and scaling that are at the root of early attempts to understand turbulence are reviewed. The influence of statistical theories, intermittency and fractals, and vortex dynamics on the understanding of turbulence is addressed. The present and future theoretical and experimental challenges in the field are considered.
Physical Review Letters, 1980
In the present paper, evidence in support of the conjecture that vortex lines may be stretched an... more In the present paper, evidence in support of the conjecture that vortex lines may be stretched an infinite amount in a finite time is obtained by applying series-analysis techniques to the time evolution of the inviscid Taylor-Green vortex (1937). The resulting power-series expansions are analyzed, using techniques developed for studying singularities in critical phenomena. The flow is the solution of the incompressible Euler equations, in Fourier representation.
Journal of Fluid Mechanics, 1983
& Frisch (1980), by a shift of origin. It offers the advantage of the symmetric Fourier represent... more & Frisch (1980), by a shift of origin. It offers the advantage of the symmetric Fourier representation (1 2 ) .
Physical Review A, 1981
... dependence of intermittency. We note that (i) the temporal structure of signals measured at a... more ... dependence of intermittency. We note that (i) the temporal structure of signals measured at a given point reflects mostly, the spatial structure of the velocity field in the frame of the mean velocity ("Taylor hypothesis" ); (ii) spectral analysis of high-Reynolds number flows reveals ...
Journal of Fluid Mechanics, 2014
It is known that the Eulerian and Lagrangian structures of fluid flow can be drastically differen... more It is known that the Eulerian and Lagrangian structures of fluid flow can be drastically different; for example, ideal fluid flow can have a trivial (static) Eulerian structure, while displaying chaotic streamlines. Here, we show that ideal flow with limited spatial smoothness (an initial vorticity that is just a little better than continuous) nevertheless has time-analytic Lagrangian trajectories before the initial limited smoothness is lost. To prove these results we use a little-known Lagrangian formulation of ideal fluid flow derived by Cauchy in 1815 in a manuscript submitted for a prize of the French Academy. This formulation leads to simple recurrence relations among the time-Taylor coefficients of the Lagrangian map from initial to current fluid particle positions; the coefficients can then be bounded using elementary methods. We first consider various classes of incompressible fluid flow, governed by the Euler equations, and then turn to highly compressible flow, governed b...
This textbook presents a modern account of turbulence. The state-of-the-art is put into historica... more This textbook presents a modern account of turbulence. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such "fully developed turbulence" is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life.
Physics of Fluids, 1973
ABSTRACT Based on total helicity conservation in inviscid incompressible flows, the existence of ... more ABSTRACT Based on total helicity conservation in inviscid incompressible flows, the existence of simultaneous energy and helicity cascades is envisaged.
Journal of Fluid Mechanics, 1974
The Markovian random coupling (MRC) model is a modified form of the stochastic model of the Navie... more The Markovian random coupling (MRC) model is a modified form of the stochastic model of the Navier-Stokes equations introduced by Kraichnan (1958, 1961). Instead of constant random coupling coefficients, white-noise time dependence is assumed for the MRC model. Like the Kraichnan model, the MRC model preserves many structural properties of the original Navier-Stokes equations and should be useful for investigating qualitative features of turbulent flows, in particular in the limit of vanishing viscosity. The closure problem is solved exactly for the MRC model by a technique which, contrary to the original Kraichnan derivation, is not based on diagrammatic expansions. A closed equation is obtained for the functional probability distribution of the velocity field which is a special case of Edwards' (1964) Fokker-Planck equation; this equation is an exact consequence of the stochastic model whereas Edwards' equation constitutes only the first step in a formal expansion based directly on the Navier-Stokes equations. From the functional equation an exact master equation is derived for simultaneous second-order moments which happens t o be essentially a Markovianized version of the single-time quasi-normal approximation characterized by a constant triad-interaction time.
Communications in Mathematical Physics, 1981
The well-posed property for the finite time vortex sheet problem with analytic initial data was f... more The well-posed property for the finite time vortex sheet problem with analytic initial data was first conjectured by Birkhoff in two dimensions and is shown here to hold both in two and three dimensions. Incompressible, inviscid and irrotational flow with a velocity jump across an interface is assumed. In two dimensions, global existence of a weak solution to the Euler equation with such initial conditions is established. In three dimensions, a Lagrangian representation of the vortex sheet analogous to the Birkhoff equation in two dimensions is presented.
Europhysics Letters (epl), 1986
Page 1. Lattice Gas Models for 3D Hydrodynamics This article has been downloaded from IOPscience.... more Page 1. Lattice Gas Models for 3D Hydrodynamics This article has been downloaded from IOPscience. Please scroll down to see the full text article. 1986 Europhys. Lett. 2 291 (http://iopscience.iop.org/0295-5075/2/4/006) Download ...
Physical Review Letters, 1986
Physics Today, 1990
ABSTRACT Key ideas about turbulent flows that have evolved over the last century are surveyed. Th... more ABSTRACT Key ideas about turbulent flows that have evolved over the last century are surveyed. The basic concepts of randomness, eddy viscosity, cascade, and scaling that are at the root of early attempts to understand turbulence are reviewed. The influence of statistical theories, intermittency and fractals, and vortex dynamics on the understanding of turbulence is addressed. The present and future theoretical and experimental challenges in the field are considered.
Physical Review Letters, 1980
In the present paper, evidence in support of the conjecture that vortex lines may be stretched an... more In the present paper, evidence in support of the conjecture that vortex lines may be stretched an infinite amount in a finite time is obtained by applying series-analysis techniques to the time evolution of the inviscid Taylor-Green vortex (1937). The resulting power-series expansions are analyzed, using techniques developed for studying singularities in critical phenomena. The flow is the solution of the incompressible Euler equations, in Fourier representation.
Journal of Fluid Mechanics, 1983
& Frisch (1980), by a shift of origin. It offers the advantage of the symmetric Fourier represent... more & Frisch (1980), by a shift of origin. It offers the advantage of the symmetric Fourier representation (1 2 ) .
Physical Review A, 1981
... dependence of intermittency. We note that (i) the temporal structure of signals measured at a... more ... dependence of intermittency. We note that (i) the temporal structure of signals measured at a given point reflects mostly, the spatial structure of the velocity field in the frame of the mean velocity ("Taylor hypothesis" ); (ii) spectral analysis of high-Reynolds number flows reveals ...