Time‐dependent inviscid vortices in global self‐similar expansion

1994 ◽  
Vol 6 (1) ◽  
pp. 253-262 ◽  
Author(s):  
B. C. Low
Keyword(s):  
Time Dependent ◽  
Self Similar

Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Cylinder With Time-Dependent Axial Velocity and Uniform Transpiration

2004 ◽  
Vol 126 (6) ◽  
pp. 997-1005 ◽  
Author(s):  
R. Saleh ◽  
A. B. Rahimi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Axial Velocity ◽  
Time Dependent ◽  
Navier Stokes ◽  
Flow And Heat Transfer ◽  
Moving Cylinder ◽  
Self Similar ◽  
Suction Rate ◽  
Axial Speed

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite moving cylinder with time-dependent axial velocity and with uniform normal transpiration Uo are investigated. The impinging free stream is steady and with a constant strain rate k¯. An exact solution of the Navier–Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the axial velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may move with constant speed, with exponentially increasing–decreasing axial velocity, with harmonically varying axial speed, or with accelerating–decelerating oscillatory axial speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semisimilar solutions of the unsteady Navier–Stokes and energy equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent axial velocity of the cylinder is a step-function, and a ramp function. All the solutions above are presented for Reynolds numbers, Re=ka¯2/2υ, ranging from 0.1 to 100 for different values of dimensionless transpiration rate, S=Uo/ka¯, where a is cylinder radius and υ is kinematic viscosity of the fluid. Absolute value of the shear-stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear- stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder moving with certain exponential axial velocity function at any particular value of Reynolds number and suction rate is axially stress-free. The heat transfer coefficient increases with the increasing suction rate, Reynolds number, Prandtl number, oscillation frequency and amplitude. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration. It is shown that a cylinder with certain type of exponential wall temperature exposed to a temperature difference has no heat transfer.

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.

LOGISTIC MAPPING WITH A TIME-DEPENDENT SYSTEM-PARAMETER AND ITS ATTRACTOR BASINS WITH SELF-SIMILAR STRUCTURE

2004 ◽  
Vol 14 (07) ◽  
pp. 2407-2416 ◽  
Author(s):  
JOUSUKE KUROIWA ◽  
TAKAFUMI MIKI
Keyword(s):  
System Parameter ◽  
Time Dependent ◽  
Chaotic Attractors ◽  
Self Similarity ◽  
Initial Values ◽  
Logistic Mapping ◽  
Periodic Attractors ◽  
Self Similar ◽  
Basins Of Attractions ◽  
Time Dependent System

In this paper, logistic mapping with a time-dependent system-parameter (referred as "LMTD") is proposed. In various choices of time dependence, the periodic one has been tried in order to investigate the dynamical properties of LMTD. In certain parameter regions, two different attractors coexist depending on the initial values, for instances, two different chaotic attractors, two different periodic attractors, or two periodic/chaotic attractors. In addition, the whole configuration space of the initial values forms basins of attractions of which structures indicate self-similarity.

Axisymmetric Stagnation—Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time-Dependent Angular Velocity and Uniform Transpiration

2006 ◽  
Vol 129 (1) ◽  
pp. 106-115 ◽  
Author(s):  
A. B. Rahimi ◽  
R. Saleh
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Angular Velocity ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer ◽  
Self Similar

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite rotating circular cylinder with transpiration U0 are investigated when the angular velocity and wall temperature or wall heat flux all vary arbitrarily with time. The free stream is steady and with a strain rate of Γ. An exact solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by the use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the angular velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may rotate with constant speed, with exponentially increasing/decreasing angular velocity, with harmonically varying rotation speed, or with accelerating/decelerating oscillatory angular speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent rotation velocity of the cylinder is, for example, a step-function. All the solutions above are presented for Reynolds numbers, Re=Γa2∕2υ, ranging from 0.1 to 1000 for different values of Prandtl number and for selected values of dimensionless transpiration rate, S=U0∕Γa, where a is cylinder radius and υ is kinematic viscosity of the fluid. Dimensionless shear stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder rotating with certain exponential angular velocity function and at particular value of Reynolds number is azimuthally stress-free. Heat transfer is independent of cylinder rotation and its coefficient increases with the increasing suction rate, Reynolds number, and Prandtl number. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration.

scholarly journals Particle acceleration at colliding shock waves

2020 ◽  
Vol 494 (3) ◽  
pp. 3166-3176 ◽  
Author(s):  
T Vieu ◽  
S Gabici ◽  
V Tatischeff
Keyword(s):  
Shock Waves ◽  
High Energy ◽  
Time Dependent ◽  
Shock Acceleration ◽  
Diffusive Shock Acceleration ◽  
Mathematical Methods ◽  
Accretion Flows ◽  
Self Similar Solution ◽  
Self Similar ◽  
Accelerated Particles

ABSTRACT We model the diffusive shock acceleration of particles in a system of two colliding shock waves and present a method to solve the time-dependent problem analytically in the test-particle approximation and high energy limit. In particular, we show that in this limit the problem can be analysed with the help of a self-similar solution. While a number of recent works predict hard (E−1) spectra for the accelerated particles in the stationary limit, or the appearance of spectral breaks, we found instead that the spectrum of accelerated particles in a time-dependent collision follows quite closely the canonical E−2 prediction of diffusive shock acceleration at a single shock, except at the highest energy, where a hardening appears, originating a bumpy feature just before the exponential cut-off. We also investigated the effect of the reacceleration of pre-existing cosmic rays by a system of two shocks, and found that under certain conditions spectral features can appear in the cut-off region. Finally, the mathematical methods presented here are very general and could be easily applied to a variety of astrophysical situations, including for instance standing shocks in accretion flows, diverging shocks, backward collisions of a slow shock by a faster shock, and wind–wind or shock–wind collisions.

scholarly journals The structure of nearly isothermal, adiabatic shock waves

2020 ◽  
Vol 496 (1) ◽  
pp. L43-L47
Author(s):  
Eric R Coughlin
Keyword(s):  
Shock Wave ◽  
Contact Discontinuity ◽  
Time Dependent ◽  
Fluid Density ◽  
Leading Order ◽  
Energy Conserving ◽  
Post Shock ◽  
Adiabatic Shock ◽  
Self Similar ◽  
Ambient Gas

ABSTRACT An explosively generated shock wave with time-dependent radius R(t) is characterized by a phase in which the shocked gas becomes radiative with an effective adiabatic index γ ≃ 1. Using the result that the post-shock gas is compressed into a shell of width ΔR/R ≃ δ, where δ = γ − 1, we show that a choice of self-similar variable that exploits this compressive behaviour in the limit that γ → 1 naturally leads to a series expansion of the post-shock fluid density, pressure, and velocity in the small quantity δ. We demonstrate that the leading-order (in δ) solutions, which are increasingly accurate as γ → 1, can be written in simple, closed forms when the fluid is still approximated to be in the energy-conserving regime (i.e. the Sedov–Taylor limit), and that the density declines exponentially rapidly with distance behind the shock. We also analyse the solutions for the bubble surrounding a stellar or galactic wind that interacts with its surroundings, and derive expressions for the location of the contact discontinuity that separates the shocked ambient gas from the shocked wind. We discuss the implications of our findings in the context of the dynamical stability of nearly isothermal shocks.

Modelling intrusions through quiescent and moving ambients

2015 ◽  
Vol 771 ◽  
pp. 370-406 ◽  
Author(s):  
Christopher G. Johnson ◽  
Andrew J. Hogg ◽  
Herbert E. Huppert ◽  
R. Stephen J. Sparks ◽  
Jeremy C. Phillips ◽  
...  
Keyword(s):  
Volcanic Eruptions ◽  
Lateral Spreading ◽  
Time Dependent ◽  
Neutral Buoyancy ◽  
Narrow Region ◽  
Shallow Layer ◽  
Buoyancy Forces ◽  
Self Similar ◽  
Inertial Regime

Volcanic eruptions commonly produce buoyant ash-laden plumes that rise through the stratified atmosphere. On reaching their level of neutral buoyancy, these plumes cease rising and transition to horizontally spreading intrusions. Such intrusions occur widely in density-stratified fluid environments, and in this paper we develop a shallow-layer model that governs their motion. We couple this dynamical model to a model for particle transport and sedimentation, to predict both the time-dependent distribution of ash within volcanic intrusions and the flux of ash that falls towards the ground. In an otherwise quiescent atmosphere, the intrusions spread axisymmetrically. We find that the buoyancy-inertial scalings previously identified for continuously supplied axisymmetric intrusions are not realised by solutions of the governing equations. By calculating asymptotic solutions to our model we show that the flow is not self-similar, but is instead time-dependent only in a narrow region at the front of the intrusion. This non-self-similar behaviour results in the radius of the intrusion growing with time $t$ as $t^{3/4}$, rather than $t^{2/3}$ as suggested previously. We also identify a transition to drag-dominated flow, which is described by a similarity solution with radial growth now proportional to $t^{5/9}$. In the presence of an ambient wind, intrusions are not axisymmetric. Instead, they are predominantly advected downstream, while at the same time spreading laterally and thinning vertically due to persistent buoyancy forces. We show that close to the source, this lateral spreading is in a buoyancy-inertial regime, whereas far downwind, the horizontal buoyancy forces that drive the spreading are balanced by drag. Our results emphasise the important role of buoyancy-driven spreading, even at large distances from the source, in the formation of the flowing thin horizontally extensive layers of ash that form in the atmosphere as a result of volcanic eruptions.

Thermal conductivity in a laser-created plasma heated by inverse bremsstrahlung absorption

1982 ◽  
Vol 28 (1) ◽  
pp. 65-92 ◽  
Author(s):  
R. Balescu
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Temperature Gradient ◽  
Heat Conductivity ◽  
Time Dependent ◽  
Reference State ◽  
Inverse Bremsstrahlung ◽  
Conduction Theory ◽  
Self Similar ◽  
Inverse Bremsstrahlung Absorption

The heat conductivity of a laser-created plasma heated by inverse bremsstrahlung absorption is investigated in the vicinity of a self-similar state (SSS), taken as reference state. Under certain conditions, the slowly varying macroscopic quantities obey true, local hydrodynamical equations and a well-defined, positive, heat conductivity exists. The latter is strongly time-dependent through the unperturbed temperature. Its value, compared to the classical heat conductivity at the same temperature, shows a reduction of about 20%. It is shown that, for high intensities and/or long wavelengths, the linear heat conduction theory necessarily breaks down, even if the temperature gradient is very small.

scholarly journals Time-dependent neutral-plasma isothermal expansions into a vacuum

2008 ◽  
Vol 26 (4) ◽  
pp. 671-675 ◽  
Author(s):  
Y. Huang ◽  
X. Duan ◽  
X. Lan ◽  
Z. Tan ◽  
N. Wang ◽  
...  
Keyword(s):  
Electric Field ◽  
Coordinate System ◽  
Linear Increase ◽  
Time Dependent ◽  
Analytic Model ◽  
Hot Electron ◽  
Self Similar ◽  
Neutral Plasma ◽  
Similar Solutions ◽  
Time Dependent Solution

AbstractA time-dependent solution for neutral-plasma isothermal expansions into a vacuum in a special-transformation coordinate system is obtained. In this new coordinate system, the special self-similar solutions of it were given by Huang and co-workers (Appl. Phys. Lett. 92, 031501). Combining the time-dependent solution and the quasi-linear increase of the electron density due to the hot-electron recirculation, an analytic model is proposed to reveal the influence of the hot-electron recirculation on the increase of electric field and on the acceleration of ions of different masses and charges.

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