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arXiv2007

Coupling Lattice Boltzmann with Atomistic Dynamics for the multiscale simulation of nano-biological flows

We describe a recent multiscale approach based on the concurrent coupling of constrained molecular dynamics for long biomolecules with a mesoscopic lattice Boltzmann treatment of solvent hydrodynamics. The multiscale approach is based on a simple scheme of exchange of space-time information between the atomistic and mesoscopic scales and is capable of describing self-consistent hydrodynamic effects on molecular motion at a computational cost which scales linearly with both solute size and solvent volume. For an application of our multiscale method, we consider the much studied problem of biopolymer translocation through nanopores: we find that the method reproduces with remarkable accuracy the statistical scaling behavior of the translocation process and provides valuable insight into the cooperative aspects of biopolymer and hydrodynamic motion.

physics.bio-ph↗

arXiv2009

Parametric internal waves in a compressible fluid

We describe the effect of vibration on a confined volume of fluid which is density stratified due to its compressibility. We show that internal gravity-acoustic waves can be parametrically destabilized by the vibration. The resulting instability is similar to the classic Faraday instability of surface waves, albeit modified by the compressible nature of the fluid. It may be possible to observe experimentally near a gas-liquid critical point.

physics.flu-dyn↗

arXiv2008

Condensation of cloud microdroplets in homogeneous isotropic turbulence

The growth by condensation of small water droplets in a three-dimensional homogeneous isotropic turbulent flow is considered. Within a simple model of advection and condensation, the dynamics and growth of millions of droplets are integrated. A droplet-size spectra broadening is obtained and it is shown to increase with the Reynolds number of turbulence, by means of two series of direct numerical simulations at increasing resolution. This is a key point towards a proper evaluation of the effects of turbulence for condensation in warm clouds, where the Reynolds numbers typically achieve huge values. The obtained droplet-size spectra broadening as a function of the Reynolds number is shown to be consistent with dimensional arguments. A generalization of this expectation to Reynolds numbers not accessible by DNS is proposed, yielding upper and lower bounds to the actual size-spectra broadening. A further DNS matching the large scales of the system suggests consistency of the picture drawn, while additional effort is needed to evaluate the impact of this effect for condensation in more realistic cloud conditions.

nlin.CD↗

arXiv2008

Investigations of the NS-alpha model using a lid-driven cavity flow

In this paper we investigate a subgrid model based on an anisotropic version of the NS-$α$ model using a lid-driven cavity flow at a Reynolds number of 10,000. Previously the NS-$α$ model has only been used numerically in the isotropic form. The subgrid model is developed from the Eulerian-averaged anisotropic equations [Holm, \textit{Physica D}, v.133, pp 215-269, 1999]. It was found that when $α^{2}$ was based on the mesh numerical oscillations developed which manifested themselves in the appearance of streamwise vortices and a `mixing out' of the velocity profile. This is analogous to the Craik-Leibovich mechanism, with the difference being that the oscillations here are not physical but numerical. The problem could be traced back to the discontinuity in $α^{2}$ encountered when $α^{2}=0$ on the endwalls. An alternative definition of $α^{2}$ based on velocity gradients, rather than mesh spacing, is proposed and tested. Using this definition the results with the model shown a significant improvement. The splitting of the downstream wall jet, rms and shear stress profiles are correctly captured a coarse mesh. The model is shown to predict both positive and negative energy transfer in the jet impingement region, in qualitative agreement with DNS results.

physics.flu-dyn↗

arXiv2007

Theoretical Criteria for the Occurrence of Turbulence in Burger's Equation

Throughout the history of the study of turbulence in fluid dynamics, there has yet to arise a unique definition or theoretical criterion for this important phenomenon. There have been interesting conjectures made by Ruelle [2], Muriel [3], and Getreuer, Albano and Muriel [6], however, attempting to provide the sufficient criteria for the onset of turbulence. In this paper, a classic equation in fluid dynamics, Burger's equation, is solved in one and two dimensions, and these conjectures are illustrated. This illustration supports these conjectures by showing that the proposed criteria do arise mathematically from the solutions of an equation modelling fluid flows.

physics.flu-dyn↗

arXiv2008

Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarisation and localised `edge' states

Fully 3-dimensional computations of flow through a long pipe demand a huge number of degrees of freedom, making it very expensive to explore parameter space and difficult to isolate the structure of the underlying dynamics. We therefore introduce a `2+epsilon' dimensional model of pipe flow which is a minimal 3-dimensionalisation of the axisymmetric case: only sinusoidal variation in azimuth plus azimuthal shifts are retained, yet the same dynamics familiar from experiments are found. In particular the model retains the subcritical dynamics of fully resolved pipe flow, capturing realistic localised `puff'-like structures which can decay abruptly after long times, as well as global `slug' turbulence. Relaminarisation statistics of puffs reproduce the memoryless feature of pipe flow and indicate the existence of a Reynolds number about which lifetimes diverge rapidly, provided that the pipe is sufficiently long. Exponential divergence of the lifetime is prevalent in shorter periodic domains. In a short pipe, exact travelling-wave solutions are found nearby to flow trajectories on the boundary between laminar and turbulent flow. In a long pipe, the attracting state on the laminar-turbulent boundary is a localised structure which resembles a smoothened puff. This `edge' state remains localised even for Reynolds numbers where the turbulent state is global.

physics.flu-dyn↗

arXiv2007

The minimum entropy principle for fluid flows in a nozzle with discontinuous cross-section

We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in the sense of Dal Maso, LeFloch, and Murat. Observing that the entropy equality has a fully conservative form, we derive a minimum entropy principle satisfied by entropy solutions. We then establish the stability of a class of numerical approximations for this system.

math.NA↗

arXiv2007

The Riemann problem for the shallow water equations with discontinuous topography

We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the existence of two-parameter wave sets, rather than wave curves. The selection of admissible waves is particularly challenging. Our construction is fully explicit, and leads to formulas that can be implemented numerically for the approximation of the general initial-value problem.

math.AP↗

arXiv2008

Supercritical transition to turbulence in an inertially-driven von Karman closed flow

We study the transition from laminar flow to fully developed turbulence for an inertially-driven von Karman flow between two counter-rotating large impellers fitted with curved blades over a wide range of Reynolds number (100 - 1 000 000). The transition is driven by the destabilisation of the azimuthal shear-layer, i.e., Kelvin-Helmholtz instability which exhibits travelling/drifting waves, modulated travelling waves and chaos below the emergence of a turbulent spectrum. A local quantity -the energy of the velocity fluctuations at a given point- and a global quantity -the applied torque- are used to monitor the dynamics. The local quantity defines a critical Reynolds number Rec for the onset of time-dependence in the flow, and an upper threshold/crossover Ret for the saturation of the energy cascade. The dimensionless drag coefficient, i.e., the turbulent dissipation, reaches a plateau above this finite Ret, as expected for a "Kolmogorov"-like turbulence for Re -> infinity. Our observations suggest that the transition to turbulence in this closed flow is globally supercritical: the energy of the velocity fluctuations can be considered as an order parameter characterizing the dynamics from the first laminar time-dependence up to the fully developed turbulence. Spectral analysis in temporal domain moreover reveals that almost all of the fluctuations energy is stored in time-scales one or two orders of magnitude slower than the time-scale based on impeller frequency.

physics.flu-dyn↗

arXiv2013

Exact solution of the 1D Riemann problem in Newtonian and relativistic hydrodynamics

Some of the most interesting scenarios that can be studied in astrophysics, contain fluids and plasma moving under the influence of strong gravitational fields. To study these problems it is required to implement numerical algorithms robust enough to deal with the equations describing such scenarios, which usually involve hydrodynamical shocks. It is traditional that the first problem a student willing to develop research in this area is to numerically solve the one dimensional Riemann problem, both Newtonian and relativistic. Even a more basic requirement is the construction of the exact solution to this problem in order to verify that the numerical implementations are correct. We describe in this paper the construction of the exact solution and a detailed procedure of its implementation.

astro-ph.HE↗

arXiv2013

On the Self-Recovery Phenomenon in the Process of Diffusion

We report a new phenomenon, called self-recovery, in the process of diffusion in a region with boundary. Suppose that a diffusing quantity is uniformly distributed initially and then gets excited by the change in the boundary values over a time interval. When the boundary values return to their initial values and stop varying afterwards, the value of a physical quantity related to the diffusion automatically comes back to its original value. This self-recovery phenomenon has been discovered and fairly well understood for finite-dimensional mechanical systems with viscous damping. In this paper, we show that it also occurs in the process of diffusion. Several examples are provided from fluid flows, quasi-static electromagnetic fields and heat conduction. In particular, our result in fluid flows provides a dynamic explanation for the famous experiment by Sir G.I. Taylor with glycerine in an annulus on kinematic reversibility of low-Reynolds-number flows.

physics.flu-dyn↗

arXiv2013

Large eddy simulation of a muffler with the high-order spectral difference method

The combination of the high-order accurate spectral difference discretization on unstructured grids with subgrid-scale modelling is investigated for large eddy simulation of a muffler at Re = 4.64 10^4 and low Mach number. The subgrid-scale stress tensor is modelled by the wall-adapting local eddy-viscosity model with a cut-off length which is a decreasing function of the order of accuracy of the scheme. Numerical results indicate that although the high-order solver without subgrid-scale modelling is already able to capture well the features of the flow, the coupling with the wall-adapting local eddy-viscosity model improves the quality of the solution.

physics.flu-dyn↗

arXiv2013

Extraterrestrial sink dynamics in granular matter

A loosely packed bed of sand sits precariously on the fence between mechanically stable and flowing states. This has especially strong implications for animals or vehicles needing to navigate sandy environments, which can sink and become stuck in a "dry quicksand" if their weight exceeds the yield stress of this fragile matter. While it is known that the contact stresses in these systems are loaded by gravity, very little is known about the sinking dynamics of objects into loose granular systems under gravitational accelerations different from the Earth's (g). A fundamental understanding of how objects sink in different gravitational environments is not only necessary for successful planetary navigation and engineering, but it can also improve our understanding of celestial impact dynamics and crater geomorphology. Here we perform and explain the first systematic experiments of the sink dynamics of objects into granular media in different gravitational accelerations. By using an accelerating experimental apparatus, we explore gravitational conditions ranging from 0.4g to 1.2g. With the aid of discrete element modeling simulations, we reproduce these results and extend this range to include objects as small as asteroids and as large as Jupiter. Surprisingly, we find that the final sink depth is independent of the gravitational acceleration, an observation with immediate relevance to the design of future extraterrestrial structures land-roving spacecraft. Using a phenomenological equation of motion that includes a gravity-loaded frictional term, we are able to quantitatively explain the experimental and simulation results.

cond-mat.soft↗

arXiv2013

Exact Solutions for an MHD Generalized Burgers fluid: Stokes' Second Problem

This paper offers the exact analytical solutions for the magnetohydrodynamic (MHD) flow of an incompressible generalized Burgers fluid corresponding to the second problem of Stokes in the presence of the transverse magnetic field. Modified Darcy's law has been taken into account. The expression for the velocity field and associated tangential stress, presented as a sum of the steady-state and transient solutions, are obtained by means of the integral transforms. Moreover, several figures are plotted to investigate the effects of various emerging parameters on the velocity field. The obtained results show that the magnitude of the velocity and boundary layer thickness significantly reduce in the presence of magnetic field.

physics.flu-dyn↗

arXiv2013

Proceedings of the 2013 UK National Conference on Geophysical, Astrophysical and Industrial Magnetohydrodynamics at Glasgow

This document presents an accurate record of the scientific programme of the 2013 UK National Conference on Geophysical, Astrophysical and Industrial Magnetohydrodynamics held on 23rd and 24th of May 2013 at the School of Mathematics and Statistics of the University of Glasgow. The abstracts of presented contributions are listed in chronological order and a full list of participants and their affiliations is included.

physics.flu-dyn↗

arXiv2013

Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence

We study sign changes and scaling laws in the Cartesian components of the velocity and vorticity of rotating turbulence, in the helicity, and in the components of vertically-averaged fields. Data for the analysis is provided by high-resolution direct numerical simulations of rotating turbulence with different forcing functions, with up to 1536^3 grid points, with Reynolds numbers between ~1100 and ~5100, and with moderate Rossby numbers between ~0.06 and ~8. When rotation is negligible, all Cartesian components of the velocity show similar scaling, in agreement with the expected isotropy of the flow. However, in the presence of rotation only the vertical components of the fields show clear scaling laws, with evidence of possible sign singularity in the limit of infinite Reynolds number. Horizontal components of the velocity are smooth and do not display rapid fluctuations for arbitrarily small scales. The vertical velocity and vorticity, as well as the vertically-averaged vertical velocity and vorticity, show the same scaling within error bars, in agreement with theories that predict that these quantities have the same dynamical equation for very strong rotation.

physics.flu-dyn↗

arXiv2013

Speed of sound in liquids at high pressure

In this paper, a new general formula for the sound speed in adiabatic conditions ( S = const ) has been established. The sound speed depends on the mass density ρ (p,T ) and the internal energy per unit mass E(p,T ), both expressed as functions of the pressure p and the temperature T . This formula has been compared with experimental data on the example of triolein over the pressure range up to 450 MPa. For experimental data, phenomenological approximate formulas have been proposed. Those formulas have two versions, depending on the 2 and 3 parameters. Both versions have been developed with the help of the new expression (Eq.8) for the sound speed. The explicit form of both approximate curves can be regarded as the result of purely phenomenological modeling. However, in this paper, these new analytical expressions have been obtained by applying the heuristic procedure described in Appendix.

physics.flu-dyn↗

arXiv2013

A critique of recent theories of spin half quantum plasmas

In this Letter certain fundamental physics issues relating to recent theories of so-called `spin quantum plasmas' are examined. It is shown that the derivations and some of the results obtained in these theories contradict well-established principles of quantum mechanics, especially in their treatment of fermions and spin. The analysis presented suggests that the aforementioned theories do not apply for any range of temperatures at the stated densities and furthermore fail to make any experimentally accessible and testable predictions.

physics.plasm-ph↗