Flow Through Randomly Curved Manifolds

We present a computational study of the transport properties of campylotic (intrinsically curved) media. It is found that the relation between the flow through a campylotic media, consisting of randomly located curvature perturbations, and the average Ricci scalar of the system, exhibits two distinct functional expressions, depending on whether the typical spatial extent of the curvature perturbation lies above or below the critical value maximizing the overall scalar of curvature. Furthermore, the flow through such systems as a function of the number of curvature perturbations is found to present a sublinear behavior for large concentrations, due to the interference between curvature perturbations leading to an overall less curved space. We have also characterized the flux through such media as a function of the local Reynolds number and the scale of interaction between impurities. For the purpose of this study, we have also developed and validated a new lattice Boltzmann model.

[1]  Roberto Benzi,et al.  Numerical simulations of ion temperature gradient‐driven turbulence , 1990 .

[2]  S. Shapiro,et al.  On the numerical integration of Einstein's field equations , 1998, gr-qc/9810065.

[3]  Scott H. Hawley,et al.  Evolutions in 3D numerical relativity using fixed mesh refinement , 2003, gr-qc/0310042.

[4]  P. Love,et al.  From the Boltzmann equation to fluid mechanics on a manifold , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[5]  Y Amarouchene,et al.  Thermal convection and emergence of isolated vortices in soap bubbles. , 2008, Physical review letters.

[6]  X. He,et al.  Discretization of the Velocity Space in the Solution of the Boltzmann Equation , 1997, comp-gas/9712001.

[7]  Tom Mullin,et al.  Bifurcation phenomena in a Taylor–Couette flow with asymmetric boundary conditions , 2001 .

[8]  S. Orszag,et al.  Extended Boltzmann Kinetic Equation for Turbulent Flows , 2003, Science.

[9]  F. Bartels.  Taylor vortices between two concentric rotating spheres , 1982, Journal of Fluid Mechanics.

[10]  S. Succi,et al.  Radiation pressure vs. friction effects in the description of the Poynting-Robertson scattering process , 2012 .

[11]  E. M. Lifshitz,et al.  Classical theory of fields , 1952 .

[12]  Nicos Martys,et al.  Evaluation of the external force term in the discrete Boltzmann equation , 1998 .

[13]  Ch. Hirsch,et al.  Fundamentals Of Computational Fluid Dynamics , 2016 .

[14]  G. Schrauf.  The first instability in spherical Taylor-Couette flow , 1986, Journal of Fluid Mechanics.

[15]  H S Borovetz,et al.  A model of pulsatile flow in a uniform deformable vessel. , 1992, Journal of biomechanics.

[16]  M. Wimmer.  Experiments on a viscous fluid flow between concentric rotating spheres , 1976, Journal of Fluid Mechanics.

[17]  I. Karlin,et al.  Lattices for the lattice Boltzmann method. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[19]  L. Richardson,et al.  The Deferred Approach to the Limit. Part I. Single Lattice. Part II. Interpenetrating Lattices , 1927 .

[20]  H. Grad.  Note on N‐dimensional hermite polynomials , 1949 .

[21]  H. Swinney,et al.  Instabilities and transition in flow between concentric rotating cylinders , 1981 .

[22]  Alexander N Gorban,et al.  Maximum Entropy Principle for Lattice Kinetic Equations , 1998 .

[23]  S Succi,et al.  Preturbulent regimes in graphene flow. , 2011, Physical review letters.

[24]  Laurette S. Tuckerman,et al.  Simulation of flow between concentric rotating spheres. Part 1. Steady states , 1987, Journal of Fluid Mechanics.

[25]  L. Richardson.  The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam , 1911 .

[26]  L. Stella,et al.  The general relativistic Poynting–Robertson effect , 2008, 0808.1083.

[27]  S Succi,et al.  Fast lattice Boltzmann solver for relativistic hydrodynamics. , 2010, Physical review letters.