scholarly journals Bubble pinch-off in turbulence

2019 ◽  
Vol 116 (51) ◽  
pp. 25412-25417 ◽  
Author(s):  
Daniel J. Ruth ◽  
Wouter Mostert ◽  
Stéphane Perrard ◽  
Luc Deike
Keyword(s):  
Flow Field ◽  
Initial Conditions ◽  
The Self ◽  
Similar Process ◽  
Linear Perturbation ◽  
Bubble Shape ◽  
Complex Flow ◽  
Experimental Conditions ◽  
Initial Flow ◽  
Self Similar

Although bubble pinch-off is an archetype of a dynamical system evolving toward a singularity, it has always been described in idealized theoretical and experimental conditions. Here, we consider bubble pinch-off in a turbulent flow representative of natural conditions in the presence of strong and random perturbations, combining laboratory experiments, numerical simulations, and theoretical modeling. We show that the turbulence sets the initial conditions for pinch-off, namely the initial bubble shape and flow field, but after the pinch-off starts, the turbulent time at the neck scale becomes much slower than the pinching dynamics: The turbulence freezes. We show that the average neck size,d¯, can be described byd¯∼(t−t0)α, wheret0is the pinch-off or singularity time andα≈0.5, in close agreement with the axisymmetric theory with no initial flow. While frozen, the turbulence can influence the pinch-off through the initial conditions. Neck shape oscillations described by a quasi–2-dimensional (quasi-2D) linear perturbation model are observed as are persistent eccentricities of the neck, which are related to the complex flow field induced by the deformed bubble shape. When turbulent stresses are less able to be counteracted by surface tension, a 3-dimensional (3D) kink-like structure develops in the neck, causingd¯to escape its self-similar decrease. We identify the geometric controlling parameter that governs the appearance of these kink-like interfacial structures, which drive the collapse out of the self-similar route, governing both the likelihood of escaping the self-similar process and the time and length scale at which it occurs.

Critical microjets in collapsing cavities

1995 ◽  
Vol 290 ◽  
pp. 183-201 ◽  
Author(s):  
Michael S. Longuet-Higgins ◽  
Hasan Oguz
Keyword(s):  
Flow Field ◽  
Spherical Harmonic ◽  
Velocity Potential ◽  
Initial Conditions ◽  
Numerical Study ◽  
Critical Flow ◽  
Jet Formation ◽  
Initial Flow ◽  
The Family ◽  
Self Similar

Inward microjets are commonly observed in collapsing cavities, but here we show that jets with exceptionally high velocities and accelerations occur in certain critical flows dividing jet formation from bubble pinch-off. An example of the phenomenon occurs in the family of flows which evolve from a certain class of initial conditions: the initial flow field is that due to a moving point sink within the cavity.A numerical study of the critical flow shows that in the neighbourhood of microjet formation the flow is self-similar. The local accelerations, velocities and distances scale as tβ-2, tβ-1 and tβ respectively, where β = 0.575. The velocity potential is approximately a spherical harmonic of degree ¼.

scholarly journals Analysis of the self-similar solutions of a generalized Burger's equation with nonlinear damping

2001 ◽  
Vol 7 (3) ◽  
pp. 253-282 ◽  
Author(s):  
Ch. Srinivasa Rao ◽  
P. L. Sachdev ◽  
Mythily Ramaswamy
Keyword(s):  
Initial Conditions ◽  
Nonlinear Damping ◽  
Nonlinear Ordinary Differential Equation ◽  
The Self ◽  
Similar Reduction ◽  
Generalized Burgers Equation ◽  
Different Types ◽  
Self Similar ◽  
Parameter Ranges ◽  
Similar Solutions

The nonlinear ordinary differential equation resulting from the self-similar reduction of a generalized Burgers equation with nonlinear damping is studied in some detail. Assuming initial conditions at the origin we observe a wide variety of solutions – (positive) single hump, unbounded or those with a finite zero. The existence and nonexistence of positive bounded solutions with different types of decay (exponential or algebraic) to zero at infinity for specific parameter ranges are proved.

Time-Resolved Stereo PIV Measurements of Flow Fields Inside a Rotating Cavity

2014 ◽  
Author(s):  
Junya Kouwa ◽  
Takahisa Nagao ◽  
Shinsuke Matsuno ◽  
Yukie Sasaki ◽  
Koutarou Hisaeda
Keyword(s):  
Flow Field ◽  
Flow Structure ◽  
Flow Fields ◽  
Experimental Result ◽  
Rossby Number ◽  
Complex Flow ◽  
Experimental Conditions ◽  
Time Resolved ◽  
Rotating Cavity ◽  
Structure Of Flow

This paper describes the experimental and numerical results of flow fields inside a rotor-stator rotating cavity. The rotational speeds and the axial throughflow are varied as experimental conditions. In the experiment, 3-components velocity vectors on the r–θ and r–z sections are obtained by a stereo dynamic PIV system to understand complex flow fields in detail such as flow structure and unsteadiness. A large eddy simulation (LES) is also carried out to confirm the analytical capability for the rotating cavity and to complement the understanding of the flow field. From the results, axisymmetric steady flow fields are observed under high Rossby number conditions, while several vortices are captured in the cavity in the r – θ section under low Rossby number conditions. The visualization results with seeding tracers for PIV show the flow structure of flow fields. LES can predict the flow field of the experimental result and the behavior of vortices which are varied as to the change of Ro conditions.

Self-similar and asymptotic solutions for a one-dimensional Vlasov beam

1983 ◽  
Vol 29 (1) ◽  
pp. 139-142 ◽  
Author(s):  
J. R. Burgan ◽  
M. R. Feix ◽  
E. Fijalkow ◽  
A. Munier
Keyword(s):  
Asymptotic Solution ◽  
Initial Conditions ◽  
The Self ◽  
Similar Solution ◽  
Asymptotic Solutions ◽  
One Dimensional ◽  
Self Similar Solution ◽  
Self Similar ◽  
New Equation

Rescaling transformations bringing friction terms in the new equation are used to obtain the asymptotic solution of a one-dimensional, one-species beam. It is shown that for all possible initial conditions this asymptotic solution coincides with the self-similar solution.

Instantaneous three-dimensional concentration measurements in the self-similar region of a round high-Schmidt-number jet

1994 ◽  
Vol 279 ◽  
pp. 313-350 ◽  
Author(s):  
M. Yoda ◽  
L. Hesselink ◽  
M. G. Mungal
Keyword(s):  
Concentration Gradient ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Concentration Field ◽  
The Self ◽  
Gradient Field ◽  
Geometrical Parameters ◽  
Similar Region ◽  
Self Similar ◽  
Local Topology

The virtually instantaneous three-dimensional concentration fields in the self-similar region of natural or unexcited, circularly excited and weakly buoyant round jets of Reynolds number based on nozzle diameter of 1000 to 4000 are measured experimentally at a spatial resolution of the order of the Kolmogorov length scale. Isoconcentration surfaces are extracted from the concentration field. These surfaces along with their geometrical parameters are used to deduce the structure and modal composition of the jet. The concentration gradient field is calculated, and its local topology is classified using critical-point concepts.Large-scale structure is evident in the form of ‘clumps’ of higher-concentration jet fluid. The structure, which has a downstream extent of about the local jet diameter, is roughly axisymmetric with a conical downstream end. This structure appears to be present only in fully turbulent jets. The antisymmetric two-dimensional images previously thought to be axial slices of an expanding spiral turn out in our data to instead be slices of a simple sinusoid in three dimensions. This result suggests that the helical mode, when present, is in the form of a pair of counter-rotating spirals, or that the +1 and −1 modes are simultaneously present in the flow, with their relative phase set by initial conditions.In terms of local structure, regions with a large magnitude in concentration gradient are shown to have a local topology which is roughly axisymmetric and compressed along the axis of symmetry. Such regions, which would be locally planar and sheet-like, may correspond to the superposition of several of the layer-like structures which are the basic structure of the fine-scale passive scalar field (Buch & Dahm 1991; Ruetsch & Maxey 1991).

scholarly journals Estimation of the self-similarity parameter in long memory processes

1970 ◽  
Vol 38 ◽  
pp. 32-37 ◽  
Author(s):  
MMA Sarker
Keyword(s):  
Long Memory ◽  
The Self ◽  
Similar Process ◽  
Long Range Dependence ◽  
Self Similarity ◽  
Similarity Parameter ◽  
Data Set ◽  
Memory Processes ◽  
Long Memory Processes ◽  
Self Similar

Long memory processes, where positive correlations between observations far apart in time and space decay very slowly to zero with increasing time lag, occur quite frequently in fields such as hydrology and economics. Stochastic processes that are invariant in distribution under judicious scaling of time and space, called self-similar process, can parsimoniously model the long-run properties of phenomena exhibiting long-range dependence. Four of the heuristic estimation approaches have been presented in this study so that the self-similarity parameter, H that gives the correlation structure in long memory processes, can be effectively estimated. Finally, the methods presented in this paper were applied to two observed time series, namely Nile River Data set and the VBR (Variable- Bit-Rate) data set. The estimated values of H for two data sets found from different methods suggest that all methods are not equally good for estimation. Keywords: Long memory process, long-range dependence, Self-similar process, Hurst Parameter, Gaussian noise. DOI: 10.3329/jme.v38i0.898 Journal of Mechanical Engineering Vol.38 Dec. 2007 pp.32-37  

Annular self-similar solutions in ideal magnetogasdynamics

2008 ◽  
Vol 74 (4) ◽  
pp. 531-554 ◽  
Author(s):  
R. M. LOCK ◽  
A. J. MESTEL
Keyword(s):  
Magnetic Field ◽  
Initial Value Problem ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
The Self ◽  
Initial Value ◽  
Azimuthal Magnetic Field ◽  
Self Similar ◽  
Similar Solutions ◽  
Z Pinch

AbstractWe consider the possibility of self-similar solutions describing the implosion of hollow cylindrical annuli driven by an azimuthal magnetic field, in essence a self-similar imploding liner z-pinch. We construct such solutions for gasdynamics, for ideal ‘β=0’ plasma and for ideal magnetogasdynamics (MGD). In the latter two cases some quantities are singular at the annular boundaries. Numerical solutions of the full ideal MGD initial value problem indicate that the self-similar solutions are not attractive for arbitrary initial conditions, possibly as a result of flux-freezing.

scholarly journals Statistical models of network traffic

Connectivity ◽  
2021 ◽  
Vol 149 (1) ◽  
Author(s):  
N. M. Yakymchuk ◽  
Keyword(s):  
Network Traffic ◽  
High Speed ◽  
Packet Switching ◽  
Telecommunication Networks ◽  
The Self ◽  
Statistical Characteristics ◽  
Similar Process ◽  
Data Traffic ◽  
Similarity Parameter ◽  
Self Similar

The article considers the issues of statistical modeling of traffic in telecommunication networks with packet switching. The simulation results are used in the development of network technical condition management systems, in particular, diagnostics, troubleshooting and network configuration management. The peculiarities of congestion control of separate network segments are emphasized. With improper analysis the overload condition can be mistaken for equipment failure. Therefore, control and elimination of congestion is a statistical task. The concept of end-to-end network diagnostics is considered. This concept provides for effective assessment of the quality of functioning of all network components taking into account their interrelationships. The main issues are the interaction of equipment, inefficient configuration, improper network organization and user operation. Methods of traffic statistical control characteristics based on perforated and marker bucket algorithms are analyzed. A feature of these algorithms is the formation of a strict output stream at a rate that does not depend on the non-uniformity of the input stream. The possibility of improving the token bucket algorithm by adapting to changes in the statistical characteristics of traffic is shown. To solve this problem, statistical mathematical models of network traffic are built. Data traffic circulating in telecommunication networks by packet switching has self-similar (fractal) properties. The self-similar process retains its properties when considered at different time scales (invariance to scale changes). The degree of statistical stability of the process with multiple scaling is determined by the Hirst parameter (the self-similarity parameter). Graphs of statistical characteristics of low-speed and high-speed data traffic are obtained. Their comparative analysis is carried out.

Freely draining gravity currents in porous media: Dipole self-similar solutions with and without capillary retention

2007 ◽  
Vol 18 (3) ◽  
pp. 337-362 ◽  
Author(s):  
JOCHONIA S. MATHUNJWA ◽  
ANDREW J. HOGG
Keyword(s):  
Unsaturated Flow ◽  
Multiple Scales ◽  
Initial Conditions ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Theoretical Predictions ◽  
Analytic Expressions ◽  
Self Similar ◽  
Similar Solutions

We analyse the two-dimensional, gravitationally-driven spreading of fluid through a porous medium overlying a horizontal impermeable boundary from which fluid can drain freely at one end. Under the assumption that none of the intruding fluid is retained within the pores in the trail of the current, the motion of the current is described by the dipole self-similar solution of the first kind derived by Barenblatt and Zel'dovich (1957). We show that small perturbations of arbitrary shape imposed on this solution decay in time, indicating that the self-similar solution is linearly stable. We use the connection between the perturbation eigenfunctions and symmetry transformations of the self-similar solution to demonstrate that variables can always be specified in terms of which the rate of decay of the perturbations is maximised. Unsaturated flow can be modelled by assuming that a constant fraction of the fluid is retained within the pores by capillary action in the trail of the current. It has been shown (Barenblatt and Zel'dovich, 1998; Ingerman and Shvets, 1999) that in this case, the motion of the current is described by a self-similar solution of the second kind characterised by an anomalous exponent. We derive leading-order analytic expressions for the anomalous exponent and the self-similar quantities valid for small values of the fraction of fluid retained using direct asymptotic analysis and by using a novel application of the method of multiple scales. The latter offers a number of advantages and permits the evolution of the current to be clearly connected with its initial conditions in a way not possible with conventional approaches. We demonstrate that the theoretical predictions provided by these expressions are in excellent agreement with results from the numerical integration of the governing equations.

High-speed unsteady flows around spiked-blunt bodies

2009 ◽  
Vol 632 ◽  
pp. 69-96 ◽  
Author(s):  
ARGYRIS G. PANARAS ◽  
DIMITRIS DRIKAKIS
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
High Speed ◽  
Initial Conditions ◽  
Separation Bubble ◽  
Spike Length ◽  
Initial Flow ◽  
Flow Development ◽  
Stable Conditions ◽  
Blunt Bodies

This paper presents a detailed investigation of unsteady supersonic and hypersonic flows around spiked-blunt bodies, including the investigation of the effects of the flow field initialization on the flow results. Past experimental research has shown that if the geometry of a spiked-blunt body is such that a shock formation consisting of an oblique foreshock and a bow aftershock appears, then the flow may be unsteady. The unsteady flow is characterized by periodic radial inflation and collapse of the conical separation bubble formed around the spike (pulsation). Beyond a certain spike length the flow is ‘stable’, i.e. steady or mildly oscillating in the radial direction. Both unsteady and ‘stable’ conditions have been reported when increasing or decreasing the spike length during an experimental test and, additionally, hysteresis effects have been observed. The present study reveals that for certain geometries the numerically simulated flow depends strongly on the assumed initial flow field, including the occurrence of bifurcations due to inherent hysteresis effects and the appearance of unsteady flow modes. Computations using several different configurations reveal that the transient (initial) flow development corresponds to a nearly inviscid flow field characterized by a foreshock–aftershock interaction. When the flow is pulsating, the further flow development is not sensitive to initial conditions, whereas for an oscillating or almost ‘steady’ flow, the flow development depends strongly on the assumed initial flow field.

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