scholarly journals On Rayleigh-Taylor and Richtmyer-Meshkov Dynamics With Inverse-Quadratic Power-Law Acceleration

2022 ◽  
Vol 7 ◽  
Author(s):  
D. L. Hill ◽  
S. I. Abarzhi
Keyword(s):  
Initial Conditions ◽  
Density Ratio ◽  
Three Dimensional ◽  
Early Time ◽  
Power Laws ◽  
Future Research ◽  
Continuous Family ◽  
Late Time ◽  
Time Dynamics ◽  
Plane Normal

Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities occur in many situations in Nature and technology from astrophysical to atomic scales, including stellar evolution, oceanic flows, plasma fusion, and scramjets. While RT and RM instabilities are sister phenomena, a link of RT-to-RM dynamics requires better understanding. This work focuses on the long-standing problem of RTI/RMI induced by accelerations, which vary as inverse-quadratic power-laws in time, and on RT/RM flows, which are three-dimensional, spatially extended and periodic in the plane normal to the acceleration direction. We apply group theory to obtain solutions for the early-time linear and late-time nonlinear dynamics of RT/RM coherent structure of bubbles and spikes, and investigate the dependence of the solutions on the acceleration’s parameters and initial conditions. We find that the dynamics is of RT type for strong accelerations and is of RM type for weak accelerations, and identify the effects of the acceleration’s strength and the fluid density ratio on RT-to-RM transition. While for given problem parameters the early-time dynamics is uniquely defined, the solutions for the late-time dynamics form a continuous family parameterised by the interfacial shear and include special solutions for RT/RM bubbles/spikes. Our theory achieves good agreement with available observations. We elaborate benchmarks that can be used in future research and in design of experiments and simulations, and that can serve for better understanding of RT/RM relevant processes in Nature and technology.

scholarly journals Dependence of Enstrophy Transport and Mixed Mass on Dimensionality and Initial Conditions in the Richtmyer–Meshkov Instability Induced Flows1

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Ye Zhou ◽  
Michael Groom ◽  
Ben Thornber
Keyword(s):  
Inertial Confinement Fusion ◽  
Initial Conditions ◽  
Broad Band ◽  
Initial Perturbation ◽  
Density Ratio ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Late Time ◽  
Production Term

Abstract This paper presents a comparative study of the enstrophy budget and mixed mass between two- and three-dimensional flows induced by Richtmyer–Meshkov instability (RMI). Specifically, the individual contributions to the enstrophy budget due to the production from baroclinicity and from vortex stretching (which vanishes in two-dimensional (2D) flow) are delineated. This is enabled by a set of two- and three-dimensional computations at Atwood 0.5 having both narrow- and broad-band perturbations. A further three-dimensional (3D) computation is conducted at Atwood 0.9 using an identical narrowband perturbation to the Atwood 0.5 case to examine the sensitivity to density ratio. The mixed mass is also considered with the goal to obtain insight on how faithfully a simplified calculation performed in two dimensions can capture the mixed mass for an inertial confinement fusion (ICF) or other practical application. It is shown that the late time power law decay of variable density enstrophy is substantially different in two and three dimensions for the narrowband initial perturbation. The baroclinic production term is negligible in three dimensions (aside from the initial shock interaction), as vortex stretching is larger by two orders of magnitude. The lack of vortex stretching considerably reduces the decay rate in both narrowband and broadband perturbations in two dimensions. In terms of mixed mass, the lack of vortex stretching reduces the mixed mass in two dimensions compared to three in all cases. In the broadband cases, the spectral bandwidth in the 2D case is wider; hence, there is a longer time period of sustained linear growth which reduces the normalized mixed mass further.

Three-dimensional wakes behind cylinders of square and circular cross-section: early and long-time dynamics

2019 ◽  
Vol 870 ◽  
pp. 419-432 ◽  
Author(s):  
G. Agbaglah ◽  
C. Mavriplis
Keyword(s):  
Circular Cylinder ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Early Time ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Square Cylinder ◽  
Saturation Regime ◽  
Time Dynamics ◽  
Significant Difference

The flow in the near wake of a square cylinder at Reynolds numbers of 205 and 225, corresponding to three-dimensional wake instability modes $A$ and $B$, respectively, and that of the square’s circumscribed circular cylinder are examined by using three-dimensional Navier–Stokes numerical simulations. At small times, prior to the streamwise vortex shedding, a self-similar velocity is observed in the wake and no significant difference is observed in the dynamics of the flows past the square and the circular cylinders. The exponential growth of the three-dimensional instability reaches a saturation regime during this early time for the considered Reynolds numbers. Vortical structures in the wake at long times and shedding frequencies are very close for the square and the circular cylinders. The flow separation on the forward top and bottom corners of the square cylinder have the effect of increasing its effective width, making it comparable with the diameter of the circumscribed circular cylinder. Thus, Floquet multipliers and modes of the associated three-dimensional instabilities are shown to be very close for the two cylinders when using the circumscribed circular cylinder as the basis for a characteristic length scale. Most importantly, the wavenumber with the maximum growth rate, for modes $A$ and $B$, is approximately identical for the two cylinders.

scholarly journals Early Time Modifications to the Buoyancy-Drag Model for Richtmyer–Meshkov Mixing

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
David L. Youngs ◽  
Ben Thornber
Keyword(s):  
Initial Conditions ◽  
Mean Field ◽  
Early Time ◽  
Growth Exponent ◽  
Late Time ◽  
Time Behavior ◽  
Mixing Zone ◽  
Drag Model ◽  
Model Based ◽  
Self Similar

Abstract The Buoyancy-Drag model is a simple model, based on ordinary differential equations, for estimating the growth in the width of a turbulent mixing zone at an interface between fluids of different densities due to Richtmyer–Meshkov and Rayleigh–Taylor instabilities. The model is calibrated to give the required self-similar behavior for mixing in simple situations. However, the early stages of the mixing process are very dependent on the initial conditions and modifications to the Buoyancy-Drag model are then needed to obtain correct results. In a recent paper, Thornber et al. (2017, “Late-Time Growth Rate, Mixing, and Anisotropy in the Multimode Narrowband Richtmyer–Meshkov Instability: The θ-Group Collaboration,” Phys. Fluids, 29, p. 105107), a range of three-dimensional simulation techniques was used to calculate the evolution of the mixing zone integral width due to single-shock Richtmyer–Meshkov mixing from narrowband initial random perturbations. Further analysis of the results of these simulations gives greater insight into the transition from the initial linear behavior to late-time self-similar mixing and provides a way of modifying the Buoyancy-Drag model to treat the initial conditions accurately. Higher-resolution simulations are used to calculate the early time behavior more accurately and compare with a multimode model based on the impulsive linear theory. The analysis of the iLES data also gives a new method for estimating the growth exponent, θ (mixing zone width ∼ tθ), which is suitable for simulations which do not fully reach the self-similar state. The estimates of θ are consistent with the theoretical model of Elbaz and Shvarts (2018, “Modal Model Mean Field Self-Similar Solutions to the Asymptotic Evolution of Rayleigh-Taylor and Richtmyer-Meshkov Instabilities and Its Dependence on the Initial Conditions,” Phys. Plasmas, 25, p. 062126).

scholarly journals On the “Early-Time” Evolution of Variables Relevant to Turbulence Models for the Rayleigh-Taylor Instability

2010 ◽  
Author(s):  
Bertrand Rollin ◽  
Malcolm J. Andrews
Keyword(s):  
Turbulence Model ◽  
Initial Conditions ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Early Time ◽  
Variable Density ◽  
Taylor Instability ◽  
Turbulent Regime ◽  
Rayleigh Taylor Instability

We present our progress toward setting initial conditions in variable density turbulence models. In particular, we concentrate our efforts on the BHR turbulence model [1] for turbulent Rayleigh-Taylor instability. Our approach is to predict profiles of relevant variables before fully turbulent regime and use them as initial conditions for the turbulence model. We use an idealized model of mixing between two interpenetrating fluids to define the initial profiles for the turbulence model variables. Velocities and volume fractions used in the idealized mixing model are obtained respectively from a set of ordinary differential equations modeling the growth of the Rayleigh-Taylor instability and from an idealization of the density profile in the mixing layer. A comparison between predicted profiles for the turbulence model variables and profiles of the variables obtained from low Atwood number three dimensional simulations show reasonable agreement.

scholarly journals SHOCK WAVE COLLISIONS IN AdS5: APPROXIMATE NUMERICAL SOLUTIONS

2011 ◽  
Vol 22 (12) ◽  
pp. 1317-1342 ◽  
Author(s):  
BIN WU ◽  
PAUL ROMATSCHKE
Keyword(s):  
Shock Wave ◽  
Black Hole ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Early Time ◽  
Heavy Ion ◽  
Late Time ◽  
Time Behavior ◽  
Ion Collisions ◽  
Bulk System

We numerically study the evolution of a boost-invariant [Formula: see text] SYM medium using AdS/CFT . We consider a toy model for the collision of gravitational shock waves, finding that the energy density first increases, reaches a maximum and then starts to decrease, matching hydrodynamics for late times. For the initial conditions we consider, the hydrodynamic scale governing the late time behavior is to very good approximation determined by the area of the black hole horizon at initial times. Our results provide a toy model for the early time evolution of the bulk system in heavy-ion collisions at RHIC and the LHC.

Impact and Dispersion of Liquid Filled Cylinders

2006 ◽  
Vol 128 (6) ◽  
pp. 1295-1307
Author(s):  
John Borg ◽  
Susan Bartyczak ◽  
Nancy Swanson ◽  
John R. Cogar
Keyword(s):  
Vacuum Chamber ◽  
Early Time ◽  
Impact Dynamics ◽  
Expansion Velocity ◽  
Late Time ◽  
Thin Wall ◽  
Computational Results ◽  
Time Dynamics ◽  
Cylindrical Target ◽  
The Impact

The computational and experimental results of impact loading a thin wall liquid filled cylindrical target within a vacuum chamber are presented. The impact velocity ranges from 2.2 to 4.2km∕s. Both experimental and computational results are presented. It will be shown that impact dynamics and the early time fluid expansion are well modeled and understood. This includes the mass distribution and resulting expansion velocity. However, the late time dynamics, which includes the liquid breakup and droplet formation process of impacted liquid filled cylinders, is not well understood.

THREE-DIMENSIONAL LATTICE BOLTZMANN MODEL RESULTS FOR COMPLEX FLUIDS ORDERING

2005 ◽  
Vol 16 (12) ◽  
pp. 1819-1830
Author(s):  
G. AMATI ◽  
F. MASSAIOLI ◽  
G. GONNELLA ◽  
AIGUO XU ◽  
A. LAMURA
Keyword(s):  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Three Dimensions ◽  
Lattice Boltzmann Model ◽  
Domain Growth ◽  
Late Time ◽  
Extended Defects ◽  
Time Dynamics ◽  
Boltzmann Method

The kinetics of domain growth of fluid mixtures quenched from a disordered to a lamellar phase has been studied in three dimensions. We use a numerical approach based on the lattice Boltzmann method (LBM). A novel implementation for LBM which "fuses" the collision and streaming steps is used in order to reduce memory and bandwidth requirements. We find that extended defects between stacks of lamellae with different orientation dominate the late time dynamics.

scholarly journals Approach and separation of quantised vortices with balanced cores

2016 ◽  
Vol 808 ◽  
pp. 641-667 ◽  
Author(s):  
C. Rorai ◽  
J. Skipper ◽  
R. M. Kerr ◽  
K. R. Sreenivasan
Keyword(s):  
Scaling Laws ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Physical Space ◽  
Power Laws ◽  
Density Fluctuations ◽  
Field Equations ◽  
Accurate Identification ◽  
Vortex Lines ◽  
Mean Field Equations

The scaling laws for the reconnection of isolated pairs of quantised vortices are characterised by numerically integrating the three-dimensional Gross–Pitaevskii equations, the simplest mean-field equations for a quantum fluid. The primary result is the identification of distinctly different temporal power laws for the pre- and post-reconnection separation distances $\unicode[STIX]{x1D6FF}(t)$ for two configurations. For the initially anti-parallel case, the scaling laws before and after the reconnection time $t_{r}$ obey the dimensional $\unicode[STIX]{x1D6FF}\sim |t_{r}-t|^{1/2}$ prediction with temporal symmetry about $t_{r}$ and physical space symmetry about the mid-point between the vortices $x_{r}$. The extensions of the vortex lines close to reconnection form the edges of an equilateral pyramid. For all of the initially orthogonal cases, $\unicode[STIX]{x1D6FF}\sim |t_{r}-t|^{1/3}$ before reconnection and $\unicode[STIX]{x1D6FF}\sim |t-t_{r}|^{2/3}$ after reconnection are respectively slower and faster than the dimensional prediction. For both configurations, smooth scaling laws are generated due to two innovations. The first innovation is to use an initial low-energy vortex-core density profile that suppresses unwanted density fluctuations as the vortices evolve in time. The other innovation is the accurate identification of the position of the vortex cores from a pseudo-vorticity constructed on the three-dimensional grid from the gradients of the wave function. These trajectories allow us to calculate the Frenet–Serret frames and the curvature of the vortex lines, secondary results that might hold clues for the origin of the differences between the scaling laws of the two configurations. Reconnection takes place in a reconnection plane defined by the average tangents $\boldsymbol{T}_{av}$ and curvature normal $\boldsymbol{N}_{av}$ directions of the pseudo-vorticity curves at the points of closest approach, at time $t\approx t_{r}$. To characterise the structure further, lines are drawn that connect the four arms that extend from the reconnection plane, from which four angles $\unicode[STIX]{x1D703}_{i}$ between the lines are defined. Their sum is convex or hyperbolic, that is $\sum _{i=1,4}\unicode[STIX]{x1D703}_{i}>360^{\circ }$, for the orthogonal cases, as opposed to the acute angles of the pyramid found for the anti-parallel initial conditions.

scholarly journals Three-dimensional simulations and analysis of the nonlinear stage of the Rayleigh-Taylor instability

1995 ◽  
Vol 13 (3) ◽  
pp. 423-440 ◽  
Author(s):  
J. Hecht ◽  
D. Ofer ◽  
U. Alon ◽  
D. Shvarts ◽  
S.A. Orszag ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Spherical Geometry ◽  
Taylor Instability ◽  
Three Dimensions ◽  
Type Model ◽  
Late Time ◽  
Nonlinear Stage ◽  
Rayleigh Taylor Instability ◽  
Atwood Number

The nonlinear stage in the growth of the Rayleigh-Taylor instability in three dimensions (3D) is studied using a 3D multimaterial hydrodynamic code. The growth of a single classical 3D square and rectangular modes is compared to the growth in planar and cylindrical geometries and found to be close to the corresponding cylindrical mode, which is in agreement with a new Layzer-type model for 3D bubble growth. The Atwood number effect on the final shape of the instability is demonstrated. Calculations in spherical geometry of the late deceleration stage of a typical ICF pellet have been performed. The different late time shapes obtained are shown to be a result of the initial conditions and the high Atwood number. Finally, preliminary results of calculations of two-mode coupling and random perturbations growth in 3D are presented.

scholarly journals Observational constraints on complex quintessence with attractive self-interaction

2021 ◽  
Vol 503 (3) ◽  
pp. 4008-4015
Author(s):  
Belen Carvente ◽  
Víctor Jaramillo ◽  
Celia Escamilla-Rivera ◽  
Darío Núñez
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Early Time ◽  
Mass Term ◽  
Scalar Fields ◽  
Einstein Condensate ◽  
Late Time ◽  
Complex Scalar ◽  
Time Dynamics ◽  
Complex Scalar Field

ABSTRACT In this paper, we consider that dark energy could be described solely by a complex scalar field with a Bose–Einstein condensate-like potential (denoted as CSFDE), that is, with a self-interaction and a mass term. In particular, we analyse a solution that in a fast oscillation regime at late times behaves as a cosmological constant. Our proposal adequately describes the standard homogeneous and flat Fridman dynamics. Furthermore, in this quintessence–complex scalar field scenario, it is possible to mimic the dynamics related to dark energy. However, when the precision cosmological tests are implemented in this landscape, the generic equation of state derived for this model in a restricted regime of ai (which corresponds to the scale factor at which the scalar field turns on) cannot be constrained by late-time current observations, since the analysis constraints solely the scalar field parameters within values ruled out by the theoretical model. This result is a clear hint to consider future CSFDE models with, for instance, two scalar fields in order to study the early-time dynamics of the Universe.

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