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Roberto Benzi

Publications and source records attributed to Roberto Benzi.

10 recordsLinked to original sources
PubMed2005

Identification and calculation of the universal asymptote for drag reduction by polymers in wall bounded turbulence.

Drag reduction by polymers in wall turbulence is bounded from above by a universal maximal drag reduction (MDR) velocity profile that is a log law, estimated experimentally by Virk as V+(y+) approximately 11.7logy+ - 17. Here V+(y+) and y+ are the mean streamwise velocity and the distance from the wall in "wall" units. In this Letter we propose that this MDR profile is an edge solution of the Navier-Stokes equations (with an effective viscosity profile) beyond which no turbulent solutions exist. This insight rationalizes the universality of the MDR and provides a maximum principle which allows an ab initio calculation of the parameters in this law without any viscoelastic experimental input.

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PubMed2005

Additive equivalence in turbulent drag reduction by flexible and rodlike polymers.

We address the additive equivalence discovered by Virk and co-workers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wall-bounded flows is limited from above by a very similar maximum drag reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wall-bounded turbulent ensembles, we show that although the microscopic mechanism of attaining the MDR is very different, the macroscopic theory is isomorphic, rationalizing the interesting experimental observations.

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PubMed2005

Flow reversal in a simple dynamical model of turbulence.

In this Letter, we study a simple hydrodynamical model showing abrupt flow reversals at random times. For a suitable range of parameters, we show that the dynamics of flow reversal is accurately described by stochastic differential equations, where the noise represents the effect of turbulence.

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PubMed2005

Dynamical scaling and intermittency in shell models of turbulence.

We introduce a model for the turbulent energy cascade aimed at studying the effect of dynamical scaling on intermittency. In particular, we show that by slowing down the energy-transfer mechanism for fixed energy flux, intermittency decreases and eventually disappears. This result supports the conjecture that intermittency can be observed only if energy is flowing towards faster and faster scales of motion.

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PubMed2004

Drag reduction in homogeneous turbulence by scale-dependent effective viscosity.

We demonstrate, by using suitable shell models, that drag reduction in homogeneous turbulence is usefully discussed in terms of a scale-dependent effective viscosity. The essence of the phenomenon of drag reduction found in models that couple the velocity field to the polymers can be recaptured by an "equivalent" equation of motion for the velocity field alone, with a judiciously chosen scale-dependent effective viscosity that succinctly summarizes the important aspects of the interaction between the velocity and the polymer fields. Finally, we clarify the differences between drag reduction in homogeneous and in wall bounded flows.

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PubMed2004

Theory of concentration dependence in drag reduction by polymers and of the maximum drag reduction asymptote.

A simple model of the effect of polymer concentration on the amount of drag reduction in turbulence is presented, simulated, and analyzed. The qualitative phase diagram of drag coefficient versus Reynolds number (Re) is recaptured in this model, including the theoretically elusive onset of drag reduction and the maximum drag reduction (MDR) asymptote. The Re-dependent drag and the MDR are analytically explained, and the dependence of the amount of drag on material parameters is rationalized.

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PubMed2003

Intermittency in turbulence: computing the scaling exponents in shell models.

We discuss a stochastic closure for the equation of motion satisfied by multiscale correlation functions in the framework of shell models of turbulence. We present a plausible closure scheme to calculate the anomalous scaling exponents of structure functions by using the exact constraints imposed by the equation of motion. We present an explicit calculation for fifth-order scaling exponent by varying the free parameter entering in the nonlinear term of the model. The same method applied to the case of shell models for Kraichnan passive scalar provides a connection between the concept of zero-modes and time-dependent cascade processes.

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PubMed2003

Simple model for drag reduction.

Direct numerical simulations established that the finite-extension nonlinear-elasticity-Peterlin (FENE-P) model of viscoelastic flows exhibits the phenomenon of turbulent drag reduction which is caused in experiments by dilute polymeric additives. To gain analytic understanding of the phenomenon, we introduce in this paper a simple one-dimensional model of the FENE-P equations. We demonstrate drag reduction in the simple model, and explain analytically the main observations which include (i) reduction of velocity gradients for fixed throughput and (ii) increase of throughput for fixed dissipation.

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PubMed2003

Shell model for drag reduction with polymer additives in homogeneous turbulence.

Recent direct numerical simulations of the finite-extensibility nonlinear elastic dumbbell model with the Peterlin approximation of non-Newtonian hydrodynamics revealed that the phenomenon of drag reduction by polymer additives exists (albeit in reduced form) also in homogeneous turbulence. We use here a simple shell model for homogeneous viscoelastic flows, which recaptures the essential observations of the full simulations. The simplicity of the shell model allows us to offer a transparent explanation of the main observations. It is shown that the mechanism for drag reduction operates mainly on large scales. Understanding the mechanism allows us to predict how the amount of drag reduction depends on the various parameters in the model. The main conclusion is that drag reduction is not a universal phenomenon; it peaks in a window of parameters such as the Reynolds number and the relaxation rate of the polymer.

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