# Fluid Dynamics

## New submissions

[ total of 13 entries: 1-13 ]
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### New submissions for Tue, 20 Mar 18

[1]
Title: Magnetic Prandtl number dependence of turbulence generated by chiral MHD dynamos
Comments: 18 pages, 10 figures, submitted to GAFD for the special issue "Recent Developments in Natural Dynamos"
Subjects: Fluid Dynamics (physics.flu-dyn); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Astrophysical Phenomena (astro-ph.HE); Plasma Physics (physics.plasm-ph)

An asymmetry in the number density of left- and right-handed fermions is known to give rise to a new term in the induction equation that can result in a small-scale instability. This is a microphysical effect characterised by a chiral chemical potential and is mathematically similar to the alpha effect, which is a turbulent or macrophysical effect. At high temperatures, when a chiral asymmetry can survive for long enough, these chiral MHD dynamos can amplify magnetic fields efficiently, which in turn drive turbulence via the Lorentz force. While it has been demonstrated in numerical simulations that chiral magnetically driven turbulence exists and modifies the evolution of the plasma, the details of this process remain unclear. The goal of this paper is to shed new light on the properties of chiral magnetically driven turbulence using numerical simulations with the Pencil Code. We explore the generation of turbulence for different initial conditions, including a variation of the initial chiral chemical potential and the magnetic Prandtl number, Pm. In particular, we determine the ratio of kinetic to magnetic energy, Upsilon^2, that can be reached in chiral magnetically driven turbulence. Within the parameter space explored in this study, Upsilon reaches a value of approximately 0.24-0.29 - independently of the initial chiral asymmetry and for Pm=1. Our simulations suggest, that Upsilon decreases as a power law when increasing Pm. While the exact scaling depends on the details of the fitting criteria and the Reynolds number regime, an approximate result of Upsilon(Pm)=0.3*Pm^{-0.2} is reported. Using the findings from our numerical simulations, we estimate the properties of chiral magnetically driven turbulence in the early Universe.

[2]
Title: Persistent incomplete mixing in reactive flows
Subjects: Fluid Dynamics (physics.flu-dyn)

We present an effective stochastic advection-diffusion-reaction (SADR) model that explains incomplete mixing typically observed in transport with bimolecular reactions. Unlike traditional advection-dispersion-reaction models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, mechanical mixing is driven by random advective velocity with the variance given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a Fickian diffusion with the effective diffusion coefficient. We demonstrate that the sum of the two coefficients is equal to the dispersion coefficients, but only the effective diffusion coefficient contributes to the mixing-controlled reactions, indicating that such systems do not get fully mixed at the Representative Elementary Volume scale where the deterministic equations and dispersion coefficient are defined. We use the experimental results of Gramling et al. \cite{Gramling} to show that for transport and bimolecular reactions in porous media, the SADR model is significantly more accurate than the traditional dispersion model, which overestimates the concentration of the reaction product by as much as 60\%.

[3]
Title: Universality in statistics of Stokes flow over no-slip wall with random roughness
Subjects: Fluid Dynamics (physics.flu-dyn)

Stochastic roughness is widespread feature of natural surfaces and is an inherent by-product of most fabrication techniques. In view of rapid development of microfluidics, the important question is how this inevitable evil affects the low-Reynolds flows which are common for micro-devices. Moreover, one could potentially turn the flaw into a virtue and control the flow properties by means of specially "tuned" random roughness. In this paper we investigate theoretically the statistics of fluctuations in fluid velocity produced by the waviness irregularities at the surface of a no-slip wall. Particular emphasis is laid on the issue of the universality of our findings.

[4]
Title: Scaling of energy amplification in viscoelastic channel and Couette flow
Comments: 40 pages, 10 figures, the material was partially presented at 2015 APS-DFD meeting, this manuscript was never submitted to a journal
Subjects: Fluid Dynamics (physics.flu-dyn); Computational Physics (physics.comp-ph)

The linear amplification of disturbances is critical in setting up transition scenarios in viscoelastic channel and Couette flow, and may also play an important role when such flows are fully turbulent. As such, it is of interest to assess how this amplification, defined as the steady-state variance maintained under Gaussian white noise forcing, scales with the main nondimensional parameters: the Reynolds ($Re$) and Weissenberg ($Wi$) numbers. This scaling is derived analytically in the two limits of strong and weak elasticity for when the forcing is streamwise-constant. The latter is the relevant forcing for capturing the overall behaviour because it was previously shown to have the dominant contribution to amplification. The final expressions show that for weak elasticity the scaling retains a form similar to the well-known O($Re^3$) relationship with an added elastic correction. For strong elasticity, however, the scaling is O($Wi^3$) with a viscous correction. The key factor leading to such a mirroring in the scaling is the introduction of forcing in the polymer stress. The results demonstrate that energy amplification in a viscoelastic flow can be very sensitive to the model parameters even at low $Re$. They also suggest that energy amplification can be significantly increased by forcing the polymer stress, thereby opening up possibilities such as flow control using systematically designed polymer stress perturbations.

[5]
Title: Slope limiting the velocity field in a discontinuous Galerkin divergence free two-phase flow solver
Subjects: Fluid Dynamics (physics.flu-dyn); Computational Physics (physics.comp-ph)

Solving the Navier-Stokes equations when the density field contains a large sharp discontinuity---such as a water/air free surface---is numerically challenging. Convective instabilities cause Gibbs oscillations which quickly destroy the solution. We investigate the use of slope limiters for the velocity field to overcome this problem in a way that does not compromise on the mass conservation properties. The equations are discretised using the interior penalty discontinuous Galerkin finite element method that is divergence free to machine precision.
A slope limiter made specifically for exactly divergence free (solenoidal) fields is presented and used to illustrated the difficulties in obtaining convectively stable fields that are also exactly solenoidal. The lessons learned from this are applied in constructing a simpler method based on the use of an existing scalar slope limiter applied to each velocity component.
We show by numerical examples how both presented slope limiting methods are vastly superior to the naive non-limited method. The methods can solve difficult two-phase problems with high density ratios and high Reynolds numbers---typical for marine and offshore water/air simulations---in a way that conserves mass and stops unbounded energy growth caused by the Gibbs phenomenon.

### Cross-lists for Tue, 20 Mar 18

[6]  arXiv:1803.06893 (cross-list from math.NA) [pdf, other]
Title: On reference solutions and the sensitivity of the 2d Kelvin-Helmholtz instability problem
Comments: 20 pages, 11 figures, 1 table
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph); Fluid Dynamics (physics.flu-dyn)

Two-dimensional Kelvin-Helmholtz instability problems are popular examples for assessing discretizations or turbulence models for incompressible flows. Unfortunately, the results in the literature differ considerably. This paper presents computational studies of a Kelvin-Helmholtz instability problem with high order divergence-free finite element methods. Reference results in several quantities of interest are obtained for three different Reynolds numbers up to the beginning of the final vortex pairing. A mesh-independent prediction of the final pairing is not achieved due to the sensitivity of the considered problem with respect to small perturbations. A theoretical explanation of this sensitivity to small perturbations is provided based on the theory of self-organization of 2d turbulence. Possible sources of perturbations that arise in almost any numerical simulation are discussed.

[7]  arXiv:1803.07035 (cross-list from astro-ph.SR) [pdf, other]
Title: Prandtl-Number Effects in High-Rayleigh-Number Spherical Convection
Subjects: Solar and Stellar Astrophysics (astro-ph.SR); Fluid Dynamics (physics.flu-dyn)

Convection is the predominant mechanism by which energy and angular momentum are transported in the outer portion of the Sun. The resulting overturning motions are also the primary energy source for the solar magnetic field. An accurate solar dynamo model therefore requires a complete description of the convective motions, but these motions remain poorly understood. Studying stellar convection numerically remains challenging; it occurs within a parameter regime that is extreme by computational standards. The fluid properties of the convection zone are characterized in part by the Prandtl number $\mathrm{Pr}=\nu/\kappa$, where $\nu$ is the kinematic viscosity and $\kappa$ is the thermal diffusion; in stars, $\mathrm{Pr}$ is extremely low, $\mathrm{Pr}\approx 10^{-7}$. The influence of $\mathrm{Pr}$ on the convective motions at the heart of the dynamo is not well understood since most numerical studies are limited to using $\mathrm{Pr}\approx1$. We systematically vary $\mathrm{Pr}$ and the degree of thermal forcing, characterized through a Rayleigh number, to explore its influence on the convective dynamics. For sufficiently large thermal driving, the simulations reach a so-called convective free-fall state where diffusion no longer plays an important role in the interior dynamics. Simulations with a lower $\mathrm{Pr}$ generate faster convective flows and broader ranges of scales for equivalent levels of thermal forcing. Characteristics of the spectral distribution of the velocity remain largely insensitive to changes in $\mathrm{Pr}$. Importantly, we find that $\mathrm{Pr}$ plays a key role in determining when the free-fall regime is reached by controlling the thickness of the thermal boundary layer.

### Replacements for Tue, 20 Mar 18

[8]  arXiv:1706.04629 (replaced) [pdf, other]
Title: Verification Studies for the Noh Problem using Non-ideal Equations of State and Finite Strength Shocks
Comments: 14 pages, 7 figures, 19 images
Subjects: Fluid Dynamics (physics.flu-dyn); Computational Engineering, Finance, and Science (cs.CE); Mathematical Physics (math-ph)
[9]  arXiv:1801.04588 (replaced) [pdf, ps, other]
Title: Maximal heat transfer between two parallel plates
Subjects: Fluid Dynamics (physics.flu-dyn)
[10]  arXiv:1801.10150 (replaced) [pdf, other]
Title: Odd surface waves in two-dimensional incompressible fluids
Comments: 34 pages, 7 figures, revised version: added discussion on the Hamiltonian structure and conservation laws, new references added, minor typos corrected
Subjects: Fluid Dynamics (physics.flu-dyn); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
[11]  arXiv:1609.04803 (replaced) [pdf, other]
Title: Hydrodynamic series and hydrodynamization of expanding plasma in kinetic theory
Comments: 6 pages, 2 figures, v2: author added, major rewrite, mysterious off real axis singularities in the Borel plane explained (!), see also arXiv:1802.08225 [nucl-th] by Heller and Svensson; v3: references added, minor improvements in the text, first 426 terms from Eq. (8) included in the submission
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Fluid Dynamics (physics.flu-dyn)
[12]  arXiv:1709.05198 (replaced) [pdf]
Title: Tunable viscosity modification with diluted particles: When particles decrease the viscosity of complex fluids
Subjects: Soft Condensed Matter (cond-mat.soft); Fluid Dynamics (physics.flu-dyn)
[13]  arXiv:1710.01954 (replaced) [pdf, ps, other]
Title: Actuated rheology of magnetic micro-swimmers suspensions : emergence of motor and brake states
Comments: 10 pages, 6 figures, accepted in PRFluids
Subjects: Biological Physics (physics.bio-ph); Soft Condensed Matter (cond-mat.soft); Fluid Dynamics (physics.flu-dyn)
[ total of 13 entries: 1-13 ]
[ showing up to 2000 entries per page: fewer | more ]

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