133 research outputs found
Problems with the definition of renormalized Hamiltonians for momentum-space renormalization transformations
For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the phase diagram
Shell Model for Drag Reduction with Polymer Additive in Homogeneous Turbulence
Recent direct numerical simulations of the FENE-P model of non-Newtonian
hydrodynamics revealed that the phenomenon of drag reduction by polymer
additives exists (albeit in reduced form) also in homogeneous turbulence. We
introduce here a simple shell model for homogeneous viscoelastic flows that
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 the large scales. Understanding the mechanism allows us to predict how the
amount of drag reduction depends of 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 like Reynolds number and the relaxation rate of the
polymer
A simple model for drag reduction
Direct Numerical Simulations established that the 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 Letter a simple
1-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.Comment: submitted to PR
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