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 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.

scholarly journals Anisotropic evolution of D-dimensional FRW spacetime

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Chad Middleton ◽  
Bret A. Brouse ◽  
Scott D. Jackson
Keyword(s):  
Early Time ◽  
Scale Factor ◽  
Accelerated Expansion ◽  
Late Time ◽  
Time Behavior ◽  
Einstein Field Equations ◽  
Fluid Regime ◽  
Field Equations ◽  
Higher Dimensional ◽  
Walker Metric

AbstractWe examine the time evolution of the $$D=d+4$$D=d+4 dimensional Einstein field equations subjected to a flat Robertson-Walker metric where the 3D and higher-dimensional scale factors are allowed to evolve at different rates. We find the exact solution to these equations for a single fluid component, which yields two limiting regimes offering the 3D scale factor as a function of the time. The fluid regime solution closely mimics that described by 4D FRW cosmology, offering a late-time behavior for the 3D scale factor after becoming valid in the early universe, and can give rise to a late-time accelerated expansion driven by vacuum energy. This is shown to be preceded by an earlier volume regime solution, which offers a very early-time epoch of accelerated expansion for a radiation-dominated universe for $$d=1$$d=1. The time scales describing these phenomena, including the transition from volume to fluid regime, are shown to fall within a small fraction of the first second when the fundamental constants of the theory are aligned with the Planck time. This model potentially offers a higher-dimensional alternative to scalar-field inflationary theory and a consistent cosmological theory, yielding a unified description of early- and late-time accelerated expansions via a 5D spacetime scenario.

scholarly journals A general buoyancy–drag model for the evolution of the Rayleigh–Taylor and Richtmyer–Meshkov instabilities

2003 ◽  
Vol 21 (3) ◽  
pp. 347-353 ◽  
Author(s):  
YAIR SREBRO ◽  
YONI ELBAZ ◽  
OREN SADOT ◽  
LIOR ARAZI ◽  
DOV SHVARTS
Keyword(s):  
Temporal Evolution ◽  
Random Noise ◽  
Single Mode ◽  
Time Dependent ◽  
Late Time ◽  
Random Perturbations ◽  
Linear Stage ◽  
Drag Model ◽  
Characteristic Wavelength ◽  
Self Similar

The growth of a single-mode perturbation is described by a buoyancy–drag equation, which describes all instability stages (linear, nonlinear and asymptotic) at time-dependent Atwood number and acceleration profile. The evolution of a multimode spectrum of perturbations from a short wavelength random noise is described using a single characteristic wavelength. The temporal evolution of this wavelength allows the description of both the linear stage and the late time self-similar behavior. Model results are compared to full two-dimensional numerical simulations and shock-tube experiments of random perturbations, studying the various stages of the evolution. Extensions to the model for more complicated flows are suggested.

A general E-pulse scheme arising from the dual early-time/late-time behavior of radar scatterers

1994 ◽  
Vol 42 (9) ◽  
pp. 1336-1341 ◽  
Author(s):  
E.J. Rothwell ◽  
Kun-Mu Chen ◽  
D.P. Nyquist ◽  
P. Ilavarasan ◽  
J.E. Ross ◽  
...  
Keyword(s):  
Early Time ◽  
Late Time ◽  
Time Behavior

scholarly journals Restoring universality to the pinch-off of a bubble

2019 ◽  
Vol 116 (28) ◽  
pp. 13780-13784 ◽  
Author(s):  
Amir A. Pahlavan ◽  
Howard A. Stone ◽  
Gareth H. McKinley ◽  
Ruben Juanes
Keyword(s):  
Inkjet Printing ◽  
Initial Conditions ◽  
Capillary Tube ◽  
Early Time ◽  
Microfluidic Devices ◽  
Capillary Forces ◽  
Relative Importance ◽  
Scale Separation ◽  
Large Tank ◽  
Self Similar

The pinch-off of a bubble is an example of the formation of a singularity, exhibiting a characteristic separation of length and time scales. Because of this scale separation, one expects universal dynamics that collapse into self-similar behavior determined by the relative importance of viscous, inertial, and capillary forces. Surprisingly, however, the pinch-off of a bubble in a large tank of viscous liquid is known to be nonuniversal. Here, we show that the pinch-off dynamics of a bubble confined in a capillary tube undergo a sequence of two distinct self-similar regimes, even though the entire evolution is controlled by a balance between viscous and capillary forces. We demonstrate that the early-time self-similar regime restores universality to bubble pinch-off by erasing the system’s memory of the initial conditions. Our findings have important implications for bubble/drop generation in microfluidic devices, with applications in inkjet printing, medical imaging, and synthesis of particulate materials.

The influence of capillary effects on the drainage of a viscous gravity current into a deep porous medium

2017 ◽  
Vol 817 ◽  
pp. 514-559 ◽  
Author(s):  
Ying Liu ◽  
Zhong Zheng ◽  
Howard A. Stone
Keyword(s):  
Porous Medium ◽  
Gravity Current ◽  
Early Time ◽  
Late Time ◽  
Time Period ◽  
Gravity Driven ◽  
Drainage Problem ◽  
Self Similar ◽  
The One ◽  
Similar Solutions

The drainage of a viscous gravity current into a deep porous medium driven by both the gravitational and capillary forces is considered in two steps. We first study the one-dimensional case where a layer of fluid drains vertically into an infinitely deep porous medium. We determine a transition from the capillary-driven regime to the gravity-driven regime as time proceeds. Second, we solve the coupled spreading and drainage problem. There are no self-similar solutions of the problem for the entire time period, so asymptotic analyses are developed for the height, depth and front location in both the early-time and the late-time periods. In addition, we present numerical results of the governing partial differential equations, which agree well with the self-similar solutions in the appropriate asymptotic limits.

scholarly journals Technical Note: A simple generalization of the Brutsaert and Nieber analysis

2014 ◽  
Vol 11 (11) ◽  
pp. 12519-12530
Author(s):  
T. L. Chor ◽  
N. L. Dias
Keyword(s):  
Mathematical Formulation ◽  
Early Time ◽  
Technical Note ◽  
Soil Parameters ◽  
Late Time ◽  
Time Behavior ◽  
Water Stream ◽  
Discharge Data ◽  
Simple Generalization ◽  
Predicted Values

Abstract. The Brutsaert and Nieber (1977) analysis is a well known method that can estimate soil parameters given discharge data for some aquifers. It has been used for several cases where the observed late-time behavior of the recession suggests that the water stream that is adjacent to the aquifer has non-zero depth. However, its mathematical formulation is, strictly speaking, not capable of reproducing these real-case scenarios since the early time behavior is based on a solution for which the aquifer stream has zero depth (Polubarinova-Kochina, 1962). We propose a simple generalization for the Brutsaert and Nieber (1977) method that can estimate soil parameters for aquifers discharging into a water stream of finite non-zero depth. The generalization is based on already available solutions by Polubarinova-Kochina (1962), Chor et al. (2013) and Dias et al. (2014) and can be readily implemented with little effort. A sensitivity analysis shows that the modification can have significant impact on the predicted values of the drainable porosity.

On the universality of turbulent axisymmetric wakes

2012 ◽  
Vol 710 ◽  
pp. 419-452 ◽  
Author(s):  
John A. Redford ◽  
Ian P. Castro ◽  
Gary N. Coleman
Keyword(s):  
Reynolds Number ◽  
Initial Conditions ◽  
Early Time ◽  
Spherical Body ◽  
Temporal Variations ◽  
Inertial Subrange ◽  
Time Period ◽  
Self Similar ◽  
Early Time Period ◽  
Molecular Viscosity

AbstractDirect numerical simulations (DNS) of two time-dependent, axially homogeneous, axisymmetric turbulent wakes having very different initial conditions are presented in order to assess whether they reach a universal self-similar state as classically hypothesized by Townsend. It is shown that an extensive early-time period exists during which the two wakes are individually self-similar with wake widths growing like$\delta \propto {t}^{1/ 3} $, as predicted by classical dimensional analysis, but have very different growth rates and are thus not universal. Subsequently, however, the turbulence adjusts to yield, eventually, wakes that are structurally identical and have the same growth rate (also with$\delta \propto {t}^{1/ 3} $) so provide clear evidence of a universal, self-similar state. The former non-universal but self-similar state extends, in terms of a spatially equivalent flow behind a spherical body of diameter$d$, to a distance of$O(3000d)$whereas the final universal state does not appear before$O(5000d)$(and exists despite relatively low values of the Reynolds number and no evidence of a spectral${\kappa }^{\ensuremath{-} 5/ 3} $inertial subrange). Universal wake evolution is therefore likely to be rare in practice. Despite its low Reynolds number, the flow does not exhibit the sometime-suggested alternative self-similar behaviour with$\delta \propto {t}^{1/ 2} $(as for the genuinely laminar case) at large times (or, equivalently, distances), since the eddy viscosity remains large compared to the molecular viscosity and its temporal variations are not negligible.

scholarly journals Unified Inflation and Late-Time Accelerated Expansion with Exponential and R2 Corrections in Modified Gravity

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 794
Author(s):  
Luis Granda
Keyword(s):  
Modified Gravity ◽  
Initial Conditions ◽  
Gravity Models ◽  
Accelerated Expansion ◽  
Late Time ◽  
Time Behavior ◽  
De Sitter ◽  
Cosmological Observations ◽  
Leading Term ◽  
The Stability

Modified gravity models with and exponential function of curvature and R 2 corrections are proposed. At low curvature, the model explains the matter epoch and the late time accelerated expansion while at the inflation epoch the leading term is R 2 . At R → 0 the cosmological constant disappears, giving unified description of inflation and dark energy in pure geometrical context. The models satisfy the stability conditions, pass local tests and are viable in the ( r , m ) -plane, where the trajectories connect the saddle matter dominated critical point ( r = − 1 , m = 0 ) with the late time de Sitter attractor at r = − 2 and 0 < m ≤ 1 . Initial conditions were found, showing that the density parameters evolve in a way consistent with current cosmological observations, predicting late time behavior very close to the Λ CDM with future universe evolving towards the de Sitter attractor.

Sign in / Sign up

Export Citation Format

Share Document