scholarly journals Asymptotic solution for high-vorticity regions in incompressible three-dimensional Euler equations

2017 ◽  
Vol 813 ◽  
Author(s):  
D. S. Agafontsev ◽  
E. A. Kuznetsov ◽  
A. A. Mailybaev
Keyword(s):  
Exact Solution ◽  
Shear Flow ◽  
Asymptotic Solution ◽  
Euler Equations ◽  
Asymmetry Parameter ◽  
Large Scale ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Pseudospectral Method ◽  
Detailed Comparison

Incompressible three-dimensional Euler equations develop high vorticity in very thin pancake-like regions from generic large-scale initial conditions. In this work, we propose an exact solution of the Euler equations for the asymptotic pancake evolution. This solution combines a shear flow aligned with an asymmetric straining flow, and is characterized by a single asymmetry parameter and an arbitrary transversal vorticity profile. The analysis is based on detailed comparison with numerical simulations performed using a pseudospectral method in anisotropic grids of up to $972\times 2048\times 4096$.

Three‐dimensional primary zero‐offset reflections

Geophysics ◽  
1993 ◽  
Vol 58 (5) ◽  
pp. 692-702 ◽  
Author(s):  
Peter Hubral ◽  
Jorg Schleicher ◽  
Martin Tygel
Keyword(s):  
Ray Tracing ◽  
Large Scale ◽  
Initial Conditions ◽  
Fresnel Zone ◽  
Three Dimensional ◽  
Normal Incidence ◽  
Careful Analysis ◽  
Point Sources ◽  
Dynamic Ray Tracing ◽  
Zero Offset

Zero‐offset reflections resulting from point sources are often computed on a large scale in three‐dimensional (3-D) laterally inhomogeneous isotropic media with the help of ray theory. The geometrical‐spreading factor and the number of caustics that determine the shape of the reflected pulse are then generally obtained by integrating the so‐called dynamic ray‐tracing system down and up to the two‐way normal incidence ray. Assuming that this ray is already known, we show that one integration of the dynamic ray‐tracing system in a downward direction with only the initial condition of a point source at the earth’s surface is in fact sufficient to obtain both results. To establish the Fresnel zone of the zero‐offset reflection upon the reflector requires the same single downward integration. By performing a second downward integration (using the initial conditions of a plane wave at the earth’s surface) the complete Fresnel volume around the two‐way normal ray can be found. This should be known to ascertain the validity of the computed zero‐offset event. A careful analysis of the problem as performed here shows that round‐trip integrations of the dynamic ray‐tracing system following the actually propagating wavefront along the two‐way normal ray need never be considered. In fact some useful quantities related to the two‐way normal ray (e.g., the normal‐moveout velocity) require only one single integration in one specific direction only. Finally, a two‐point ray tracing for normal rays can be derived from one‐way dynamic ray tracing.

scholarly journals Single-Interface Richtmyer–Meshkov Turbulent Mixing at the Los Alamos Vertical Shock Tube

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
B. M. Wilson ◽  
R. Mejia-Alvarez ◽  
K. P. Prestridge
Keyword(s):  
Mach Number ◽  
Shock Tube ◽  
Large Scale ◽  
Initial Conditions ◽  
National Laboratory ◽  
Three Dimensional ◽  
Los Alamos ◽  
Single Interface ◽  
Small Scales ◽  
Planar Laser

Mach number and initial conditions effects on Richtmyer–Meshkov (RM) mixing are studied by the vertical shock tube (VST) at Los Alamos National Laboratory (LANL). At the VST, a perturbed stable light-to-heavy (air–SF6, A = 0.64) interface is impulsively accelerated with a shock wave to induce RM mixing. We investigate changes to both large and small scales of mixing caused by changing the incident Mach number (Ma = 1.3 and 1.45) and the three-dimensional (3D) perturbations on the interface. Simultaneous density (quantitative planar laser-induced fluorescence (PLIF)) and velocity (particle image velocimetry (PIV)) measurements are used to characterize preshock initial conditions and the dynamic shocked interface. Initial conditions and fluid properties are characterized before shock. Using two types of dynamic measurements, time series (N = 5 realizations at ten locations) and statistics (N = 100 realizations at a single location) of the density and velocity fields, we calculate several mixing quantities. Mix width, density-specific volume correlations, density–vorticity correlations, vorticity, enstrophy, strain, and instantaneous dissipation rate are examined at one downstream location. Results indicate that large-scale mixing, such as the mix width, is strongly dependent on Mach number, whereas small scales are strongly influenced by initial conditions. The enstrophy and strain show focused mixing activity in the spike regions.

Self-Organization in Three-Dimensional Hydrodynamic Turbulence Self-Organization in Three-Dimensional Hydrodynamic Turbulence

1990 ◽  
Vol 45 (9-10) ◽  
pp. 1059-1073 ◽  
Author(s):  
G. Knorr ◽  
J. P. Lynov ◽  
H. L. Pécseli
Keyword(s):  
Euler Equations ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Self Organization ◽  
Two Dimensional ◽  
Hydrodynamic Turbulence ◽  
Available Energy ◽  
Wave Numbers ◽  
Negative Helicity ◽  
Incompressible Euler

Abstract The three-dimensional incompressible Euler equations are expanded in eigenflows of the curl operator, which represent positive and negative helicity flows in a particularly simple and convenient way. Four different basic types of interactions between eigenflows are found. Two represent an "inverse cascade", the interaction familiar from the two-dimensional Euler equations, in which only modes of the same sign of the helicity interact. The other two interactions mix positive and negative helicity modes. Only these interactions can transport all of the available energy to higher wave numbers. Initial conditions, which lead to the appearance of structures and self-organization, are discussed.

scholarly journals The fate of random initial vorticity distributions for two-dimensional Euler equations on a sphere

2015 ◽  
Vol 786 ◽  
pp. 1-4 ◽  
Author(s):  
Paul K. Newton
Keyword(s):  
Numerical Simulations ◽  
Euler Equations ◽  
Large Scale ◽  
Initial Conditions ◽  
Infinite Family ◽  
Small Scale ◽  
Two Dimensional ◽  
Random Initial Conditions ◽  
Long Time ◽  
Initial Vorticity

The paper by Dritschel et al. (J. Fluid Mech., vol. 783, 2015, pp. 1–22) describes the long-time behaviour of inviscid two-dimensional fluid dynamics on the surface of a sphere. At issue is whether the flow settles down to an equilibrium or whether, for generic (random) initial conditions, the long-time solution is periodic, quasi-periodic or chaotic. While it might be surprising that this issue is not settled in the literature, it is important to keep in mind that the Euler equations form a dissipationless Hamiltonian system, hence the set of equations only redistributes the initial vorticity, generating smaller and smaller scales, while keeping kinetic energy, angular impulse and an infinite family of vorticity moments (Casimirs) intact. While special solutions that never settle down to an equilibrium state can be constructed using point vortices, vortex patches and other distributions, the fate of random initial conditions is a trickier problem. Previous statistical theories indicate that the long-time state should be a stationary large-scale distribution of vorticity. By carrying out careful numerical simulations using two different methods, the authors make a compelling case that the generic long-time state resembles a large-scale oscillating quadrupolar vorticity field, surrounded by persistent small-scale vortices. While numerical simulations can never conclusively settle this issue, the results might help guide future theories that seek to prove the existence of such an interesting dynamical long-time state.

Linear instability of low Reynolds number massively separated flow around three NACA airfoils

2016 ◽  
Vol 811 ◽  
pp. 701-741 ◽  
Author(s):  
W. He ◽  
R. S. Gioria ◽  
J. M. Pérez ◽  
V. Theofilis
Keyword(s):  
Reynolds Number ◽  
Short Wavelength ◽  
Large Scale ◽  
Initial Conditions ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Separated Flow ◽  
Linear Stability Theory ◽  
Instability Analysis ◽  
Stall Cells

Two- and three-dimensional modal and non-modal instability mechanisms of steady spanwise-homogeneous laminar separated flow over airfoil profiles, placed at large angles of attack against the oncoming flow, have been investigated using global linear stability theory. Three NACA profiles of distinct thickness and camber were considered in order to assess geometry effects on the laminar–turbulent transition paths discussed. At the conditions investigated, large-scale steady separation occurs, such that Tollmien–Schlichting and cross-flow mechanisms have not been considered. It has been found that the leading modal instability on all three airfoils is that associated with the Kelvin–Helmholtz mechanism, taking the form of the eigenmodes known from analysis of generic bluff bodies. The three-dimensional stationary eigenmode of the two-dimensional laminar separation bubble, associated in earlier analyses with the formation on the airfoil surface of large-scale separation patterns akin to stall cells, is shown to be more strongly damped than the Kelvin–Helmholtz mode at all conditions examined. Non-modal instability analysis reveals the potential of the flows considered to sustain transient growth which becomes stronger with increasing angle of attack and Reynolds number. Optimal initial conditions have been computed and found to be analogous to those on a cascade of low pressure turbine blades. By changing the time horizon of the analysis, these linear optimal initial conditions have been found to evolve into the Kelvin–Helmholtz mode. The time-periodic base flows ensuing linear amplification of the Kelvin–Helmholtz mode have been analysed via temporal Floquet theory. Two amplified modes have been discovered, having characteristic spanwise wavelengths of approximately 0.6 and 2 chord lengths, respectively. Unlike secondary instabilities on the circular cylinder, three-dimensional short-wavelength perturbations are the first to become linearly unstable on all airfoils. Long-wavelength perturbations are quasi-periodic, standing or travelling-wave perturbations that also become unstable as the Reynolds number is further increased. The dominant short-wavelength instability gives rise to spanwise periodic wall-shear patterns, akin to the separation cells encountered on airfoils at low angles of attack and the stall cells found in flight at conditions close to stall. Thickness and camber have quantitative but not qualitative effect on the secondary instability analysis results obtained.

scholarly journals Impacts of pre-initial conditions on anisotropic separate universe simulations: a boosted tidal response in the epoch of reionization

2020 ◽  
Vol 500 (1) ◽  
pp. 1018-1028
Author(s):  
Shogo Masaki ◽  
Takahiro Nishimichi ◽  
Masahiro Takada
Keyword(s):  
Structure Formation ◽  
Large Scale ◽  
Particle Distribution ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Initial Anisotropy ◽  
Anisotropic Expansion ◽  
Local Background ◽  
Systematic Effects ◽  
Spatial Coordinates

ABSTRACT To generate initial conditions for cosmological N-body simulations, one needs to prepare a uniform distribution of simulation particles, the so-called pre-initial condition (pre-IC). The standard method to construct the pre-IC is to place the particles on the lattice grids evenly spaced in the three-dimensional spatial coordinates. However, even after the initial displacement of each particle according to cosmological perturbations, the particle distribution remains to display an artificial anisotropy. Such an artefact causes systematic effects in simulations at later time until the evolved particle distribution sufficiently erases the initial anisotropy. In this paper, we study the impacts of the pre-IC on the anisotropic separate universe simulation, where the effect of large-scale tidal field on structure formation is taken into account using the anisotropic expansion in a local background (simulation volume). To quantify the impacts, we compare the simulations employing the standard grid pre-IC and the glass one, where the latter is supposed to suppress the initial anisotropy. We show that the artificial features in the grid pre-IC simulations are seen until z ∼ 9, while the glass pre-IC simulations appear to be stable and accurate over the range of scales we study. From these results we find that a coupling of the large-scale tidal field with matter clustering is enhanced compared to the leading-order prediction of perturbation theory in the quasi-non-linear regime in the redshift range 5 ≲ z ≲ 15, indicating the importance of tidal field on structure formation at such high redshifts, e.g. during the epoch of reionization.

Massively Parallelized Simulation of Deflagration-to-Detonation Transition in a Konvoi-Type Pressurized Water Reactor

2016 ◽  
Author(s):  
Josef Hasslberger ◽  
Peter Katzy ◽  
Thomas Sattelmayer ◽  
Lorenz R. Boeck
Keyword(s):  
Large Scale ◽  
Initial Conditions ◽  
Combustion Process ◽  
Three Dimensional ◽  
Pressurized Water Reactor ◽  
Pressurized Water ◽  
Flow Solver ◽  
Water Reactor ◽  
Highly Sensitive ◽  
Transition Criteria

For the purpose of nuclear safety analysis, a reactive flow solver has been developed to determine the hazard potential of large-scale hydrogen explosions. Without using empirical transition criteria, the whole combustion process (including DDT) is computed within a single solver framework. In this paper, we present massively parallelized three-dimensional explosion simulations in a full-scale pressurized water reactor of the Konvoi type. Several generic DDT scenarios in globally lean hydrogen-air mixtures are examined to assess the importance of different input parameters. It is demonstrated that the explosion process is highly sensitive to mixture composition, ignition location and thermodynamic initial conditions. Pressure loads on the confining structure show a profoundly dynamic behavior depending on the position in the containment.

Molecular-Dynamics Simulations Of Fracture: An Overview Of System Size And Other Effects

1995 ◽  
Vol 409 ◽  
Author(s):  
B. L. Holian ◽  
S.J. Zhou ◽  
P.S. Lomdahl ◽  
N. Gronbech-Jensen ◽  
D.M. Beazley ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Crack Propagation ◽  
Large Scale ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Crack Tip ◽  
System Size ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Dislocation Loops

AbstractWe have studied brittle and ductile behavior and their dependence on system size and interaction potentials, using molecular-dynamics (MD) simulations. By carefully embedding a single sharp crack in two- and three-dimensional crystals, and using a variant of the efficient sound-absorbing reservoir of Holian and Ravelo [Phys. Rev. B 51, 11275 (1995)], we have been able to probe both the static and dynamic crack regimes. Our treatment of boundary and initial conditions allows us to elucidate early crack propagation mechanisms under delicate overloading, all the way up to the more extreme dynamic crack-propagation regime, for much longer times than has been possible heretofore (before unwanted boundary effects predominate). For example, we have used graphical display of atomic velocities, forces, and potential energies to expose the presence of localized phonon-like modes near the moving crack tip, just prior to dislocation emission and crack-branching events. We find that our careful MD method is able to reproduce the ZCT brittle-ductile criterion for short-range pair potentials [static lattice Green's function calculations of Zhou, Carlsson, and Thomson, Phys. Rev. Letters 72, 852 (1994)].We report on progress we have made in large-scale 3D simulations in samples that are thick enough to display realistic behavior at the crack tip, including emission of dislocation loops. Such. calculations, using our careful treatment of boundary and initial conditions - especially important in 3D - have the promise of opening up new vistas in fracture research.

scholarly journals Flux Separation in Photospheric Magnetoconvection

2001 ◽  
Vol 203 ◽  
pp. 219-221 ◽  
Author(s):  
N. O. Weiss ◽  
M. R. E. Proctor
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Numerical Experiments ◽  
Large Scale ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Small Scale ◽  
The Sun ◽  
Intermediate Regime ◽  
Magnetic Features

Numerical experiments on three-dimensional magnetoconvection in a stratified compressible layer reveal a range of different patterns, depending on the strength of the imposed magnetic field. As the field is decreased there is a transition from small-scale plumes, in the magnetically dominated regime, to large-scale vigorous plumes when the field is dominated by the motion. In the intermediate regime magnetic flux separates from the motion, so that there are almost field-free regions, with clusters of vigorous plumes, surrounded by regions where the Lorentz force is strong enough to control the dynamics. There is a range of field strengths where either small-scale plumes or flux-separated solutions can persist, depending on initial conditions for the computation. These results can be related to magnetic features at the surface of the Sun.

The general and asymptotic solution of the elastic wave equation in an unbounded medium

1993 ◽  
Vol 441 (1911) ◽  
pp. 157-167
Keyword(s):  
Exact Solution ◽  
General Solution ◽  
Asymptotic Solution ◽  
Vector Fields ◽  
Initial Conditions ◽  
Displacement Vector ◽  
Elastic Solid ◽  
Elastic Field ◽  
Field Energy ◽  
Unbounded Medium

New forms and new properties are given for the general solution of the three-dimensional dynamic equation for the displacement vector in an isotropic linear elastic solid. The general initial value problem in an unbounded medium with no sources is solved. The general solution at an arbitrary time is given in terms of two asymptotic vector fields. One is thereby able to obtain the complete and exact solution, including initial conditions, which corresponds to a specified or desired asymptotic solution, valid for large times in the future. The complete elastic field energy of an arbitrary exact solution is also shown to depend, in a simple way, only on the two asymptotic vector fields.

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