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Physics - Fluid Dynamics, Astrophysics - High Energy Astrophysical Phenomena, Condensed Matter - Strongly Correlated Electrons, and Nuclear Theory

We investigate a relativistic adaptation of the Lattice Boltzmann Method that reproduces the equations of motion for a turbulent, two-dimensional, massless hydrodynamic system. The classical Lattice Boltzmann Method and its extension to relativistic fluid dynamics is described. The numeric formulation is evaluated using a zero-averaged stirring force introduced into the numerics to induce turbulence, and the flow characteristics produced are compared to properties of a classical turbulent hydrodynamic flow. The model can reasonably be expected to offer quantitative simulations of electron fluid flows in graphene or Kagome lattices.
Comment: 28 pages, 11 Figures, Comments Welcome

Physics - Fluid Dynamics

The Reynolds transport theorem occupies a central place in fluid dynamics, providing a generalized integral conservation equation for the transport of any conserved quantity within a fluid, and connected to its corresponding differential equation. Recently, a new generalized framework was presented for this theorem, enabling parametric transformations between positions on a manifold or in a generalized coordinate space, exploiting the underlying multivariate Lie symmetries associated with a conserved quantity. We examine the implications of this framework for fluid flow systems, within an Eulerian volume-velocity (phase space) description. The analysis invokes a hierarchy of five probability density functions, which by convolution are used to define five fluid densities and generalized densities appropriate for different spaces. We obtain 11 formulations of the generalized Reynolds transport theorem for different choices of the coordinate space, parameter space and density, only the first of which is known. These are used to generate 11 tables of integral and differential conservation laws applicable to these systems, for eight important conserved quantities (fluid mass, species mass, linear momentum, angular momentum, energy, charge, entropy and probability). These substantially expand the set of conservation laws for the analysis of fluid flow systems.
Comment: 4 figures

Astrophysics - Solar and Stellar Astrophysics and Physics - Fluid Dynamics

The use of the full potential of stellar seismology is made difficult by the improper modeling of the upper-most layers of solar-like stars and their influence on the modeled frequencies. Our knowledge on these \emph{surface effects} has improved thanks to the use of 3D hydrodynamical simulations but the calculation of eigenfrequencies relies on empirical models for the description of the Lagrangian perturbation of turbulent pressure: the reduced-$\Gamma_1$ model (RGM) and the gas-$\Gamma_1$ model (GGM). Starting from the fully compressible turbulence equations, we derive both the GGM and RGM models using a closure to model the flux of turbulent kinetic energy. It is found that both models originate from two terms: the source of turbulent pressure due to compression produced by the oscillations and the divergence of the flux of turbulent pressure. It is also demonstrated that they are both compatible with the adiabatic approximation but also imply a number of questionable assumptions mainly regarding mode physics. Among others hypothesis, one has to neglect the Lagrangian perturbation of the dissipation of turbulent kinetic energy into heat and the Lagrangian perturbation of buoyancy work.
Comment: 7 pages, 1 figure. Accepted as a Letter in Astronomy and Astrophysic

Physics - Computational Physics and Physics - Fluid Dynamics

The physics-based modeling has been the workhorse for many decades in many scientific and engineering applications ranging from wind power, weather forecasting, and aircraft design. Recently, data-driven models are increasingly becoming popular in many branches of science and engineering due to their non-intrusive nature and online learning capability. Despite the robust performance of data-driven models, they are faced with challenges of poor generalizability and difficulty in interpretation. These challenges have encouraged the integration of physics-based models with data-driven models, herein denoted hybrid analysis and modeling (HAM). We propose two different frameworks under the HAM paradigm for applications relevant to wind energy in order to bring the physical realism within emerging digital twin technologies. The physics-guided machine learning (PGML) framework reduces the uncertainty of neural network predictions by embedding physics-based features from a simplified model at intermediate layers and its performance is demonstrated for the aerodynamic force prediction task. Our results show that the proposed PGML framework achieves approximately 75\% reduction in uncertainty for smaller angle of attacks. The interface learning (IL) framework illustrates how different solvers can be coupled to produce a multi-fidelity model and is successfully applied for the Boussinesq equations that govern a broad class of transport processes. The IL approach paves the way for seamless integration of multi-scale, multi-physics and multi-fidelity models (M^3 models).
Comment: arXiv admin note: text overlap with arXiv:2012.13343

Physics - Fluid Dynamics and Mathematics - Dynamical Systems

We derive measures of local material stretching and rotation that are computable from individual trajectories without reliance on other trajectories or on an underlying velocity field. Both measures are quasi-objective: they approximate objective (i.e., observer-independent) coherence diagnostics in frames satisfying a certain condition. This condition requires the trajectory accelerations to dominate the angular acceleration induced by the spatial mean vorticity. We illustrate in examples how quasi-objective coherence diagnostics highlight elliptic and hyperbolic Lagrangian coherent structures even from very sparse trajectory data.

Physics - Biological Physics, Condensed Matter - Soft Condensed Matter, and Physics - Fluid Dynamics

Synchronisation is often observed in the swimming of flagellated cells, either for multiple appendages on the same organism or between the flagella of nearby cells. Beating cilia are also seen to synchronise their dynamics. In 1951, Taylor showed that the observed in-phase beating of the flagella of co-swimming spermatozoa was consistent with minimisation of the energy dissipated in the surrounding fluid. Here we revisit Taylor's hypothesis for three models of flagella and cilia: (1) Taylor's waving sheets with both longitudinal and transverse modes, as relevant for flexible flagella; (2) spheres orbiting above a no-slip surface to model interacting flexible cilia; and (3) whirling rods above a no-slip surface to address the interaction of nodal cilia. By calculating the flow fields explicitly, we show that the rate of working of the model flagella or cilia is minimised in our three models for (1) a phase difference depending on the separation of the sheets and precise waving kinematics; (2) in-phase or opposite-phase motion depending on the relative position and orientation of the spheres; and (3) in-phase whirling of the rods. These results will be useful in future models probing the dynamics of synchronisation in these setups.

Quantum Physics and Physics - Fluid Dynamics

We study phase contributions of wave functions that occur in the evolution of Gaussian surface gravity water wave packets with nonzero initial momenta propagating in the presence and absence of an effective external linear potential. Our approach takes advantage of the fact that in contrast to matter waves, water waves allow us to measure both their amplitudes and phases.
Comment: 6 pages, 1 table, 2 figures. Accepted to EPJ-ST, not published yet

Mathematics - Numerical Analysis and Physics - Fluid Dynamics

An understanding of the hydrodynamics of multiphase processes is essential for their design and operation. Multiphase computational fluid dynamics (CFD) simulations enable researchers to gain insight which is inaccessible experimentally. The model frequently used to simulate these processes is the two-fluid (Euler-Euler) model where fluids are treated as inter-penetrating continua. It is formulated for the multiphase flow regime where one phase is dispersed within another and enables simulation on experimentally relevant scales. Phase fractions are used to describe the composition of the mixture and are bounded quantities. Consequently, numerical solution methods used in simulations must preserve boundedness for accuracy and physical fidelity. In this work, a numerical method for the two-fluid model is developed in which phase fraction constraints are imposed through the use of an nonlinear variational inequality solver which implicitly imposes inequality constraints. The numerical method is verified and compared to an established explicit numerical method.

Physics - Fluid Dynamics and Mathematics - Analysis of PDEs

We introduce a simplified model of physiological coughing or sneezing, in the form of a thin liquid layer subject to a rapid (30 m/s) air stream. The setup is simulated using the Volume-Of-Fluid method with octree mesh adaptation, the latter allowing grid sizes small enough to capture the Kolmogorov length scale. The results confirm the trend to an intermediate distribution between a Log-Normal and a Pareto distribution $P(d) \propto d^{-3.3}$ for the distribution of droplet sizes in agreement with a previous re-analysis of experimental results by one of the authors. The mechanism of atomisation does not differ qualitatively from the multiphase mixing layer experiments and simulations. No mechanism for a bimodal distribution, also sometimes observed, is evidenced in these simulations.

Physics - Fluid Dynamics, Condensed Matter - Soft Condensed Matter, and Physics - Geophysics

We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion, namely, the smoothing of intra-pore velocity contrasts, the increase of the tortuosity of particle paths, and the setting of a maximum time for particle transitions. Based on these mechanisms, we derive a theory that predicts anomalous and normal hydrodynamic dispersion based on the characteristic pore length, Eulerian velocity distribution and P\'eclet number.

Physics - Chemical Physics, Condensed Matter - Materials Science, Condensed Matter - Soft Condensed Matter, and Physics - Fluid Dynamics

This study focuses on comparing the individual polymer chain dynamics in an entangled polymeric liquid under different shear and extension rates. Polymer chains under various shear rates and extension rates were simulated using a stochastic-tube model [J. Rheol. 56: 1057 (2012)]. We developed a Matlab code to visualize and analyze the simulated configurations from the stochastic-tube model. We introduced new variables to determine how the extent of linearity changes with time for different shear rates, which is more useful than a typical end-to-end distance analysis. We identified whether the polymer chains undergo a tumbling rotation (slight elongation not accompanying contraction) or flipping rotation (elongation accompanying contraction). The simulation results indicate that the polymer chains exhibit a significant tendency to elongate at higher shear rates and occasionally experience flipping, while lower shear rates tend to exhibit very frequent tumbling. Furthermore, no rotations were observed under extensional flows. These results help clarifying uncertainty of previously proposed polymer deformation mechanisms of the convective constraint release and the configuration-dependent friction coefficient.
Comment: 18 pages, 15 figures

Physics - Fluid Dynamics

Negative viscosity seems to be an impossible parameter for any thermodynamic system. But for some special boundary conditions the viscosity of a fluid has apparently become negative, like for secondary flow of a fluid or in a plasma flow interacting with a dominant magnetic field. This work focuses on the effect of apparent negative viscosity for a fluid flow over a cylinder. Five different viscosities are applied, which consist of zero viscosity and two negative and positive viscosities. The results show a vast difference in the vortex formation, pattern and their sustainability. General incompressible Navier Stokes equation has been employed for the analysis. The stability of the Navier Stokes equation with negative viscosity has been studied using CFL criterion. The vortex formation and the subsequent analysis of their kinetic energies has been performed using the spatially averaged and time averaged vorticity magnitude and the magnitude of Enstrophy. The sustainability of the vortices with respect to the overall flow kinetic energy has been studied by using the Vorticity Sustainability Number (VSN), which has been also defined in the same work. This parameter provides a parameterization of the sustainability of the vorticities in a flow.
Comment: 14 pages, 17 figures, https://orcid.org/0000-0002-5201-3976

Physics - Fluid Dynamics

Wall-bounded turbulent flows can be challenging to measure within experiments due to the breadth of spatial and temporal scales inherent in such flows. Instrumentation capable of obtaining time-resolved data (e.g., Hot-Wire Anemometers) tends to be restricted to spatially-localized point measurements; likewise, instrumentation capable of achieving spatially-resolved field measurements (e.g., Particle Image Velocimetry) tends to lack the sampling rates needed to attain time-resolution in many such flows. In this study, we propose to fuse measurements from multi-rate and multi-fidelity sensors with predictions from a physics-based model to reconstruct the spatiotemporal evolution of a wall-bounded turbulent flow. A "fast" filter is formulated to assimilate high-rate point measurements with estimates from a linear model derived from the Navier-Stokes equations. Additionally, a "slow" filter is used to update the reconstruction every time a new field measurement becomes available. By marching through the data both forward and backward in time, we are able to reconstruct the turbulent flow with greater spatiotemporal resolution than either sensing modality alone. We demonstrate the approach using direct numerical simulations of a turbulent channel flow from the Johns Hopkins Turbulence Database. A statistical analysis of the model-based multi-sensor fusion approach is also conducted.

Physics - Fluid Dynamics

The dispersion of a tracer in a fluid flow is influenced by the Lagrangian motion of fluid elements. Even in laminar regimes, the irregular chaotic behavior of a fluid flow can lead to effective stirring that rapidly redistributes a tracer throughout the domain. When the advected particles possess a finite size and nontrivial shape, however, their dynamics can differ markedly from passive tracers, thus affecting the dispersion phenomena. Here we investigate the behavior of neutrally buoyant particles in 2-dimensional chaotic flows, combining numerical simulations and laboratory experiments. We show that depending on the particles shape and size, the underlying Lagrangian coherent structures can be altered, resulting in distinct dispersion phenomena within the same flow field. Experiments performed in a two-dimensional cellular flow, exhibited a focusing effect in vortex cores of particles with anisotropic shape. In agreement with our numerical model, neutrally buoyant ellipsoidal particles display markedly different trajectories and overall organization than spherical particles, with a clustering in vortices that changes accordingly with the aspect ratio of the particles.

Mathematics - Numerical Analysis, Physics - Computational Physics, and Physics - Fluid Dynamics

In this paper, we develop a new free-stream preserving (FP) method for high-order upwind conservative finite-difference (FD) schemes on the curvilinear grids. This FP method is constrcuted by subtracting a reference cell-face flow state from each cell-center value in the local stencil of the original upwind conservative FD schemes, which effectively leads to a reformulated dissipation. It is convenient to implement this method, as it does not require to modify the original forms of the upwind schemes. In addition, the proposed method removes the constraint in the traditional FP conservative FD schemes that require a consistent discretization of the mesh metrics and the fluxes. With this, the proposed method is more flexible in simulating the engineering problems which usually require a low-order scheme for their low-quality mesh, while the high-order schemes can be applied to approximate the flow states to improve the resolution. After demonstrating the strict FP property and the order of accuracy by two simple test cases, we consider various validation cases, including the supersonic flow around the cylinder, the subsonic flow past the three-element airfoil, and the transonic flow around the ONERA M6 wing, etc., to show that the method is suitable for a wide range of fluid dynamic problems containing complex geometries. Moreover, these test cases also indicate that the discretization order of the metrics have no significant influences on the numerical results if the mesh resolution is not sufficiently large.

Physics - Fluid Dynamics

We present an exact analytical solution to the problem of shear dispersion given a general initial condition. The solution is expressed as an infinite series expansion involving Mathieu functions and their eigenvalues. The eigenvalue system depends on the imaginary parameter $q=2ik$Pe, with $k$ the wavenumber that determines the tracer scale in the initial condition and Pe the P\'{e}clet number. Solutions are valid for all Pe, $t>0$, and $k>0$ except at specific values of $q=q_{\ell}^{EP}$ called Exceptional Points (EPs), the first occurring at $q_{0}^{EP}\approx1.468i$. For values of $q \lessapprox 1.468i$, all the eigenvalues are real, different and eigenfunctions decay with time, thus shear dispersion can be represented as a diffusive process. For values of $q \gtrapprox 1.468i$, pairs of eigenvalues coalesce at EPs becoming complex conjugates, the eigenfunctions propagate and decay with time, and so shear dispersion is no longer a purely diffusive process. The limit $q\rightarrow0$ is approached by the small P\'{e}clet number limit for all finite $k>0$, or equally by the large P\'{e}clet number limit as long as $2k \ll 1/$Pe. The latter implies $k\rightarrow0$, strong separation of scales between the tracer and flow. The limit $q\rightarrow\infty$ results from large P\'{e}clet number for any $k>0$, or from large $k$ and non-vanishing Pe. We derive an exact closure that is continuous in wavenumber space. At small $q$, the closure approaches a diffusion operator with an effective diffusivity proportional to $U_0^2/\kappa$, for flow speed $U_0$ and diffusivity $\kappa$. At large $q$, the closure approaches the sum of an advection operator plus a half-derivative operator (differential operator of fractional order), the latter with coefficient proportional to $\sqrt{\kappa U_0}$.

Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics, and Physics - Fluid Dynamics

Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions provide us with the solutions of various hydrodynamic type equations. Integrable one dimensional systems in terms of Riemann invariants and its extensions, multidimensional equations describing isoenthalpic and polytropic motions and shallow water type equations are among them.
Comment: 20 pages, no figures

Physics - Fluid Dynamics, Physics - Computational Physics, and physics.flu-dyn

We study the three-dimensional turbulent Kolmogorov flow, i.e. the Navier-Stokes equations forced by a low-single-wave-number sinusoidal force in a periodic domain, by means of direct numerical simulations. This classical model system is a realization of anisotropic and non-homogeneous hydrodynamic turbulence. Boussinesq's eddy viscosity linear relation is checked and found to be approximately valid over half of the system volume. A more general nonlinear quadratic constitutive equation is proposed and its parameters estimated at varying the Taylor scale-based Reynolds number in the flow up to the value 200. This provides a Reynolds number-dependent quadratic closure for the Kolmogorov flow. The case of a forcing with a different shape, here chosen Gaussian, is considered and the differences with the sinusoidal forcing are emphasized.
Comment: 10 pages

Physics - Fluid Dynamics

When a droplet hits a surface fast enough, droplet splashing can occur: smaller secondary droplets detach from the main droplet during impact. While droplet splashing on smooth surfaces is by now well understood, the surface roughness also affects at which impact velocity a droplet splashes. In this study, the influence of the surface roughness on droplet splashing is investigated. By changing the root mean square roughness of the impacted surface, we show that the droplet splashing velocity is only affected when the droplet roughness is large enough to disrupt the spreading droplet lamella and change the droplet splashing mechanism from corona to prompt splashing. Finally, using Weber and Ohnesorge number scaling models, we also show that the measured splashing velocity for both water and ethanol on surfaces with different roughness and water-ethanol mixtures collapse onto a single curve, showing that the droplet splashing velocity on rough surfaces scales with the Ohnesorge number defined with the surface roughness length scale.

Physics - Fluid Dynamics and Physics - Biological Physics

There is overwhelming evidence on SARS-CoV-2 Airborne Transmission (AT) in the ongoing COVID-19 outbreak. It is extraordinarily difficult, however, to deduce a generalized framework to assess the relative airborne transmission risk with respect to other modes. This is due to the complex biophysics entailed in such phenomena. Since the SARS outbreak in 2002, Computational Fluid Dynamics (CFD) has been one of the main tools scientists used to investigate AT of respiratory viruses. Now, CFD simulations produce intuitive and physically plausible colour-coded results that help scientists understand SARS-CoV-2 airborne transmission patterns. In addition to validation requirements, for any CFD model to be of epistemic value to the scientific community; it must be reproducible. In 2020, more than 45 published studies investigated SARS-CoV-2 airborne transmission in different scenarios using CFD. Here, I systematically review the published CFD studies of COVID-19 and discuss their reproducibility criteria with respect to the CFD modeling process. Using a Weighted Scoring Model (WSM), I propose a novel reproducibility index for CFD simulations of SARS-CoV-2 AT. The proposed index $(0 \leq R^{CFD}_j \leq 1)$ relies on three reproducibility criteria comprising 10 elements that represent the possibility of a CFD study (j) to be reproduced. Frustratingly, only 3 of 23 studies (13%) achieved full reproducibility index $(R^{CFD}_j\geq 0.9)$ while the remaining 87% were found generally irreproducible $(R^{CFD}_j<0.9)$. Without reproducible models, the scientific benefit of CFD simulations will remain hindered, fragmented and limited. In conclusion, I call the scientific community to apply more rigorous measures on reporting and publishing CFD simulations in COVID-19 research.
Comment: 14 pages, 4 figures, 2 tables