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arXiv2013

Asymptotic Multi-Layer Analysis of Wind Over Unsteady Monochromatic Surface Waves

Asymptotic multi-layer analyses and computation of solutions for turbulent flows over steady and unsteady monochromatic surface wave are reviewed, in the limits of low turbulent stresses and small wave amplitude. The structure of the flow is defined in terms of asymptotically-matched thin-layers, namely the surface layer and a critical layer, whether it is elevated or immersed, corresponding to its location above or within the surface layer. The results particularly demonstrate the physical importance of the singular flow features and physical implications of the elevated critical layer in the limit of the unsteadiness tending to zero. These agree with the variational mathematical solution of Miles (1957) for small but finite growth rate, but they are not consistent physically or mathematically with his analysis in the limit of growth rate tending to zero. As this and other studies conclude, in the limit of zero growth rate the effect of the elevated critical layer is eliminated by finite turbulent diffusivity, so that the perturbed flow and the drag force are determined by the asymmetric or sheltering flow in the surface shear layer and its matched interaction with the upper region. But for groups of waves, in which the individual waves grow and decay, there is a net contribution of the elevated critical layer to the wave growth. Critical layers, whether elevated or immersed, affect this asymmetric sheltering mechanism, but in quite a different way to their effect on growing waves. These asymptotic multi-layer methods lead to physical insight and suggest approximate methods for analyzing higher amplitude and more complex flows, such as flow over wave groups.

physics.flu-dyn↗
arXiv2013

Modulational Instability in Basic Plasma and Geophysical Models

This is a review of the theory of the modulational instability in idealised fluid models of strongly magnetised plasmas and reduced models of geophysical fluid dynamics, particularly the role it plays in the formation of zonal flows. The discussion focusses on the Charney-Hasegawa-Mima and Hasegawa-Wakatani models. Particular attention is paid to the wave turbulence - zonal flow feedback loop whereby large scale zonal flows which are initially generated by modulational instability of small-scale drift/Rossby waves tend to subsequently suppress these small scale waves by their shearing action. This negative feedback can result in a dynamic equilibrium in which large scale zonal flows grow by drawing energy from small scale turbulence but suppress the small scale turbulence in the process until a balance is reached. In this regime, the level of small scale turbulence is greatly reduced compared to the level one would observe in the absence of the zonal flows.

nlin.CD↗
arXiv2013

Study of the Kelvin-Helmholtz instability through simulation with the code Athena

Kelvin-Helmholtz instabilities are common in astrophysical systems, ranging from jet black holes up to protoplanetary accretion disk. An astrophysical object with strong characteristics of the Kelvin-Helmholtz instability is Caraguejo Nebula, in which the material expansion was caused by the explosion of a supernova about 1000 years ago. This instability occurs at the boundary between two fluids of different densities when one of the fluids accelerated with respect to the other. In order to study this instability, we performed a simulation with the code ATHENA Eulerian mesh. For this simulation, we consider a square domain with periodic boundaries on the sides, and reflecting on the boundary of the top and bottom. The upper box is filled with a gas density ρ=1.0, pressure P1 = 1.0, adiabatic index γ=5/3, and velocity u1=0.03 in the x direction (to the right). The lower portion has a density ρ=2.0, the same pressure, velocity, and adiabatic index, only in the opposite direction to the left. Speed is defined as a sinusoidal function, which creates the initial disturbance. As a result, we observe the principle of instability and the formation of vortices, with well-defined ridges. The distinctness of the boundary between the material of high and low density is well preserved due to the relatively low diffusion algorithm. We also note that the simulation evolving vortices formed from the turmoil merge.

physics.flu-dyn↗
arXiv2014

The energy conservation law in hydrodynamics vs the pseudo-law of alternative energy. Comment on 'Alternative energy vs pseudoscience' and the papers cited and not cited therein

A series of papers in the ISJAEE Journal on 'dam-free hydroelectric power station' concluded by paper: Zotyev, D. B., Alternative energy vs pseudo-science, ISJAEE. 2013. 8(130). P.131-136, is reviewed and commented. A comparison with the generally accepted energy conservation law in hydrodynamics reveals a disappointingly low scientific level of the reviewed papers (both pro- and contra- the dam-free concept), not excluding the published peer-reviewer reports. In the present version we emphasize that the ISJAEE journal published several papers, which neglect and reject the basic physical concepts, such as the Bernoulli integral, the energy conservation law in hydrodynamics, the wave function of photon and some others, with all these rejected concepts being far beyond the scientific scope of the journal. Some readers will be more concerned about the energy equation in hydrodynamics, in its theoretical form or in the Bernoulli integral form as being more traditional in technical hydromechanics. Some readers will be shocked with the statement that a photon does not possess the wave function. Overall, in this way or in that way, all readers will hardly stay unsurprised.

physics.gen-ph↗
arXiv2013

Four approaches to hydrodynamic Green's functions -- the Oseen tensors

We present four different ways of deriving the Oseen tensor which is the fundamental solution to the Stokes equations for an incompressible viscous fluid. This solution corresponds to a point force acting on an infinite fluid. The derivations follow the books of Kim & Karilla, Zapryanov & Tabakova, Dhont, and Pozrikidis.

physics.flu-dyn↗
arXiv2013

Marangoni spreading due to a localized alcohol supply on a thin water film

Bringing the interfaces of two miscible fluids into contact naturally generates strong gradients in surface tension. Here we investigate such a Marangoni-driven flow by continuously supplying isopropyl alcohol (IPA) on a film of water, using micron-sized droplets of IPA-water mixtures. These droplets create a localized depression in surface tension that leads to the opening of a circular and thin region in the water film. At the edge of the thin region, there is a rim growing and collecting the water of the film. We find that the spreading radius scales as $r \sim t^{1/2}$. This result can be explained from a balance between Marangoni and viscous stresses, assuming that the gradients in surface tension are smoothened out over the entire size of the circular opening. We derive a scaling law that accurately predicts the influence of the IPA flux as well as the thickness of the thin film at the interior of the spreading front.

physics.flu-dyn↗
arXiv2013

The flow around a macroscopical body by a colloid solution and the drag crisis

The motion of colloids in the flow field of a viscous liquid is investigated. The small colloid size compare to the macroscopical scale of the flow allow to calculate their velocity relative to that of the liquid. If the inner colloid density is larger then the density of the liquid the flow field has the domains where the colloid velocity is close to the liquid velocity. But in the domains with a strong braking of the liquid velocity the colloids are accelerated relative to the liquid. This effect is used for the qualitative explanation of the drag reduction in the flow around macroscopical bodies and in the pipes.

nlin.AO↗
arXiv2014

Global Regularity vs. Finite-Time Singularities: Some Paradigms on the Effect of Boundary Conditions and Certain Perturbations

In light of the question of finite-time blow-up vs. global well-posedness of solutions to problems involving nonlinear partial differential equations, we provide several cautionary examples which indicate that modifications to the boundary conditions or to the nonlinearity of the equations can effect whether the equations develop finite-time singularities. In particular, we aim to underscore the idea that in analytical and computational investigations of the blow-up of three-dimensional Euler and Navier-Stokes equations, the boundary conditions may need to be taken into greater account. We also examine a perturbation of the nonlinearity by dropping the advection term in the evolution of the derivative of the solutions to the viscous Burgers equation, which leads to the development of singularities not present in the original equation, and indicates that there is a regularizing mechanism in part of the nonlinearity. This simple analytical example corroborates recent computational observations in the singularity formation of fluid equations.

math.AP↗
arXiv2014

Prediction of temperature distribution in turbulent Rayleigh-Benard convection

A quantitative theory is developed for the vertical mean temperature profile (MTP) in turbulent Rayleigh-Benard convection (RBC), which explains the recent experimental and numerical observations of a logarithmic law by Ahlers et al.(Phys. Rev. Lett., 2012). A multi-layer model is formulated and quantified, whose predictions agree with DNS and experimental data for the Rayleigh-number (Ra) over seven decades. In particular, a thermal buffer layer follows a 1/7 scaling like the previously postulated mixing zone (Procaccia et al, Phys. Rev. A,1991), and yields a Ra-dependent log law constant. A new parameterization of Nu(Ra) dependence is proposed, based on the present multi-layer quantification of the bulk MTP.

physics.flu-dyn↗
arXiv2014

Moist-entropic vertical adiabatic lapse rates: the standard cases and some lead towards inhomogeneous conditions

This note is a companion of Marquet and Geleyn (2013, {arXiv:1401.2379 [ao-ph]}), where adiabatic lapse rates $Γ_{ns}$ and $Γ_{sw}$ are derived for non-saturated ($Γ_{ns}$) or saturated ($Γ_{sw}$) parcel of moist-air. They are computed in terms of the vertical derivative of the moist-air entropy potential temperature $θ_s$ defined in Marquet (2011, {arXiv:1401.1097 [ao-ph]}). The saturated value $Γ_{sw}$ is rewritten in this note so that a more compact formulation is obtained. The new formulation for $Γ_{sw}$ is expressed in term of a weighting factor $C$. This factor may represent the proportion of an air parcel being in saturated conditions.

physics.ao-ph↗
arXiv2014

Acceleration feature points of unsteady shear flows

In this paper, we propose a novel framework to extract features such as vortex cores and saddle points in two-dimensional unsteady flows. This feature extraction strategy generalizes critical points of snapshot topology in a Galilean-invariant manner, allows to prioritize features according to their strength and longevity, enables to track the temporal evolution of features, is robust against noise and has no subjective parameters. These characteristics are realized via several constitutive elements. First, acceleration is employed as a feature identifier following Goto and Vassilicos (2006), thus ensuring Galilean invariance. Second, the acceleration magnitude is used as basis for a mathematically well-developed scalar field topology. The minima of this field are called acceleration feature points, a superset of the acceleration zeros. These points are discriminated into vortices and saddle points depending the spectral properties of the velocity Jacobian. Third, all operations are based on discrete topology for the scalar field with combinatorial algorithms. This parameter-free foundation allows (1) to use persistence as a physically meaningful importance measure to prioritize feature points, (2) ensures robustness since no differentiation and interpolation need to be performed with the data, and (3) enables a natural and robust tracking algorithm for the temporal feature evolution. In particular, we can track vortex merging events in an unsupervised manner. Data based analyses are presented for an incompressible periodic cylinder wake, an incompressible planar mixing layer and a weakly compressible planar jet. They demonstrate the power of the tracking approach, which provides a spatiotemporal hierarchy of the minima.

physics.flu-dyn↗
arXiv2014

A new class of exact solution of two-dimensional incompressible vortex motion

At present in the fluid mechanics, mostly one like to use the vortex as a basic physical quantity, such that some exact solutions is based on the vorticity evolution equation. For the vortex flow problem with axisymmetry, it is well known that there exists in the circulation as a mechanical system of basic physical quantities. In this paper, from the basic dynamic equation of the mechanical system, the self-similar solution, eigenvalue system into a self- consistent, new exact solutions of the two-dimensional circular symmetric vortex flow are obtained, and some further comparison are made with the known exact solutions. Key words: vortex motion, exact solution, eigenvalue system

physics.flu-dyn↗
arXiv2014

Numerical study of viscous starting flow past a flat plate

Viscous flow past a finite plate which is impulsively started in direction normal to itself is studied numerically using a high order mixed finite difference and semi-Lagrangian scheme. The goal is to resolve details of the vorticity generation at early times, and to determine the effect of viscosity on flow quantities such as the core trajectory and vorticity, and the shed circulation. Vorticity contours, streaklines and streamlines are presented for a range of Reynolds numbers $Re \in [250, 2000]$ and a range of times $t \in[0. 0002, 5]$. At early times, most of the vorticity is attached to the plate. The paper proposes a definition for the shed circulation at early as well as late times, and shows that it indeed represents vorticity that separates from the plate without reattaching. The contribution of viscous diffusion to the circulation shedding rate is found to be significant, but, interestingly, to depend only slightly on the value of the Reynolds number. The shed circulation and the vortex core trajectories follow scaling laws for inviscid self-similar flow over several decades in time. Scaling laws describing the core vorticity, core dissipation, boundary layer thickness, drag and lift forces in time and Reynolds number are also presented. The simulations provide benchmark results to evaluate, for example, simpler separation models such as point vortex and vortex sheet models.

physics.flu-dyn↗
arXiv2014

Least Squares Shadowing for Sensitivity Analysis of Turbulent Fluid Flows

Computational methods for sensitivity analysis are invaluable tools for aerodynamics research and engineering design. However, traditional sensitivity analysis methods break down when applied to long-time averaged quantities in turbulent fluid flow fields, specifically those obtained using high-fidelity turbulence simulations. This is because of a number of dynamical properties of turbulent and chaotic fluid flows, most importantly high sensitivity of the initial value problem, popularly known as the "butterfly effect". The recently developed least squares shadowing (LSS) method avoids the issues encountered by traditional sensitivity analysis methods by approximating the "shadow trajectory" in phase space, avoiding the high sensitivity of the initial value problem. The following paper discusses how the least squares problem associated with LSS is solved. Two methods are presented and are demonstrated on a simulation of homogeneous isotropic turbulence and the Kuramoto-Sivashinsky (KS) equation, a 4th order chaotic partial differential equation. We find that while LSS computes fairly accurate gradients, faster, more efficient linear solvers are needed to apply both LSS methods presented in this paper to larger simulations.

physics.comp-ph↗
arXiv2014

Analysis of the stability of stationary boundary friction modes in the framework of a synergetic model

A synergetic model describing the state of an ultrathin lubricant layer squeezed between two atomically smooth solid surfaces operating in the boundary friction mode has been developed further. To explain the presence of different operation modes of the system for various sets of its main parameters, the mathematical analysis of the synergetic model is carried out. The type of functioning a tribological system is described in accordance with the stability character of singular points, and the diagrams distinguishing various operation modes are obtained. Phase portraits corresponding to different stability types are plotted for all diagram areas. A stick-slip mode of motion that is often observed experimentally is described.

cond-mat.mes-hall↗
arXiv2014

Why bouncing droplets are a pretty good model of quantum mechanics

In 2005, Couder, Protiere, Fort and Badouad showed that oil droplets bouncing on a vibrating tray of oil can display nonlocal interactions reminiscent of the particle-wave associations in quantum mechanics; in particular they can move, attract, repel and orbit each other. Subsequent experimental work by Couder, Fort, Protiere, Eddi, Sultan, Moukhtar, Rossi, Molacek, Bush and Sbitnev has established that bouncing drops exhibit single-slit and double-slit diffraction, tunnelling, quantised energy levels, Anderson localisation and the creation/annihilation of droplet/bubble pairs. In this paper we explain why. We show first that the surface waves guiding the droplets are Lorentz covariant with the characteristic speed c of the surface waves; second, that pairs of bouncing droplets experience an inverse-square force of attraction or repulsion according to their relative phase, and an analogue of the magnetic force; third, that bouncing droplets are governed by an analogue of Schroedinger's equation where Planck's constant is replaced by an appropriate constant of the motion; and fourth, that orbiting droplet pairs exhibit spin-half symmetry and align antisymmetrically as in the Pauli exclusion principle. Our analysis explains the similarities between bouncing-droplet experiments and the behaviour of quantum-mechanical particles. It also enables us to highlight some differences, and to predict some surprising phenomena that can be tested in feasible experiments.

quant-ph↗
arXiv2014

Compressible Hydrodynamic Mean-Field Equations in Spherical Geometry and their Application to Turbulent Stellar Convection Data

We present a statistical analysis of turbulent convection in stars within our Reynolds-Averaged Navier Stokes (RANS) framework in spherical geometry which we derived from first principles. The primary results reported in this document include: (1) an extensive set of mean-field equations for compressible, multi-species hydrodynamics, and (2) corresponding mean-field data computed from various simulation models. Some supplementary scale analysis data is also presented. The simulation data which is presented includes: (1) shell convection during oxygen burning in a 23 solar mass supernova progenitor, (2) envelope convection in a 5 solar mass red giant, (3) shell convection during the helium flash, and (4) a hydrogen injection flash in a 1.25 solar mass star. These simulations have been partially described previously in Meakin [2006], Meakin and Arnett [2007a,b, 2010], Arnett et al. [2009, 2010], Viallet et al. [2011, 2013a,b] and Mocak et al. [2009, 2011]. New data is also included in this document with several new domain and resolution configurations as well as some variations in the physical model such as convection zone depth and driving source term. The long term goal of this work is to aid in the development of more sophisticated models for treating hydrodynamic phenomena (e.g., turbulent convection) in the field of stellar evolution by providing a direct link between 3D simulation data and the mean fields which are modeled by 1D stellar evolution codes. As such, this data can be used to test previously proposed turbulence models found in the literature and sometimes used in stellar modeling. This data can also serve to test basic physical principles for model building and inspire new prescriptions for use in 1D evolution codes.

astro-ph.SR↗