scholarly journals Modulated waves in a periodically driven annular cavity

2010 ◽  
Vol 667 ◽  
pp. 336-357 ◽  
Author(s):  
H. M. BLACKBURN ◽  
J. M. LOPEZ
Keyword(s):  
Symmetry Group ◽  
Temporal Dynamics ◽  
Travelling Waves ◽  
Temporal Structure ◽  
Three Dimensional ◽  
Spanwise Direction ◽  
Two Dimensional ◽  
Periodically Driven ◽  
Spatio Temporal ◽  
Temporal Symmetry

Time-periodic flows with spatio-temporal symmetry Z2 × O(2) – invariance in the spanwise direction generating the O(2) symmetry group and a half-period-reflection symmetry in the streamwise direction generating a spatio-temporal Z2 symmetry group – are of interest largely because this is the symmetry group of periodic laminar two-dimensional wakes of symmetric bodies. Such flows are the base states for various three-dimensional instabilities; the periodically shedding two-dimensional circular cylinder wake with three-dimensional modes A and B being the generic example. However, it is not easy to physically realize the ideal flows owing to the presence of end effects and finite spanwise geometries. Flows past rings are sometimes advanced as providing a relevant idealization, but in fact these have symmetry group O(2) and only approach Z2 × O(2) symmetry in the infinite aspect ratio limit. The present work examines physically realizable periodically driven annular cavity flows that possess Z2 × O(2) spatio-temporal symmetry. The flows have three distinct codimension-1 instabilities: two synchronous modes (A and B), and two manifestations of a quasi-periodic (QP) mode, either as modulated standing waves or modulated travelling waves. It is found that the curvature of the system can determine which of these modes is the first to become unstable with increasing Reynolds number, and that even in the nonlinear regime near onset of three-dimensional instabilities the dynamics are dominated by mixed modes with complicated spatio-temporal structure. Supplementary movies illustrating the spatio-temporal dynamics are available at journals.cambridge.org/flm.

Spatio-temporal dynamics of a periodically driven cavity flow

2003 ◽  
Vol 478 ◽  
pp. 197-226 ◽  
Author(s):  
M. J. VOGEL ◽  
A. H. HIRSA ◽  
J. M. LOPEZ
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Three Dimensional ◽  
Spanwise Direction ◽  
Two Dimensional ◽  
Measured Velocity ◽  
Time Symmetry ◽  
Time Flow ◽  
Time Periodic

The flow in a rectangular cavity driven by the sinusoidal motion of the floor in its own plane has been studied both experimentally and computationally over a broad range of parameters. The stability limits of the time-periodic two-dimensional base state are of primary interest in the present study, as it is within these limits that the flow can be used as a viable surface viscometer (as outlined theoretically in Lopez & Hirsa 2001). Three flow regimes have been found experimentally in the parameter space considered: an essentially two-dimensional time-periodic flow, a time-periodic three-dimensional flow with a cellular structure in the spanwise direction, and a three-dimensional irregular (in both space and time) flow. The system poses a space–time symmetry that consists of a reflection about the vertical mid-plane together with a half-period translation in time (RT symmetry); the two-dimensional base state is invariant to this symmetry. Computations of the two-dimensional Navier–Stokes equations agree with experimentally measured velocity and vorticity to within experimental uncertainty in parameter regimes where the flow is essentially uniform in the spanwise direction, indicating that in this cavity with large spanwise aspect ratio, endwall effects are small and localized for these cases. Two classes of flows have been investigated, one with a rigid no-slip top and the other with a free surface. The basic states of these two cases are quite similar, but the free-surface case breaks RT symmetry at lower forcing amplitudes, and the structure of the three-dimensional states also differs significantly between the two classes.

scholarly journals Transitions to three-dimensional flows in a cylinder driven by oscillations of the sidewall

2011 ◽  
Vol 681 ◽  
pp. 515-536 ◽  
Author(s):  
C. PANADES ◽  
F. MARQUES ◽  
J. M. LOPEZ
Keyword(s):  
Bluff Body ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Theoretical Predictions ◽  
Spatio Temporal ◽  
Nonlinear Solutions ◽  
First Time ◽  
Temporal Symmetry ◽  
Codimension Two Bifurcation

The transition from two-dimensional to three-dimensional flows in a finite circular cylinder driven by an axially oscillating sidewall is explored in detail. The complete symmetry group of this flow, including a spatio-temporal symmetry related to the oscillating sidewall, is Z2 × O(2). Previous studies in flows with the same symmetries, such as symmetric bluff-body wakes and periodically forced rectangular cavities, were unable to obtain the theoretically predicted bifurcation to modulated travelling waves. In the simpler cylindrical geometry, where the azimuthal direction is physically periodic, we have found these predicted modulated travelling waves as stable fully saturated nonlinear solutions for the first time. A careful analysis of the base states and their linear stability identifies different parameter regimes where three-dimensional states are either synchronous with the forcing or quasi-periodic, corresponding to different symmetry-breaking processes. These results are in good agreement with theoretical predictions and previous results in similar flows. These different regimes are separated by three codimension-two bifurcation points that are yet to be fully analysed theoretically. Finally, the saturated nonlinear states and their properties in different parameter regimes are analysed.

The Aerodynamics of Three-Dimensional Vaned Diffusers in Industrial Centrifugal Compressors

2005 ◽  
Author(s):  
Ahmed Abdelwahab
Keyword(s):  
Centrifugal Compressor ◽  
Dynamic Pressure ◽  
Three Dimensional ◽  
Pressure Recovery ◽  
Navier Stokes ◽  
Spanwise Direction ◽  
Two Dimensional ◽  
Blade Loading ◽  
Recovery Capacity ◽  
Close Proximity

Vaned diffusers have been used successfully as efficient and compact dynamic pressure recovery devices in industrial centrifugal compressor stages. Typically such diffusers consist of a cascade of two-dimensional blades distributed circumferentially at close proximity to the impeller exit. In this paper three low-solidity diffuser blade geometries are numerically investigated. The first geometry employs variable stagger stacking of similar blade sections along the blade span. The second employs linearly inclined stacking to generate blade lean along the diffuser span. The third geometry employs the conventional two-dimensional low-solidity diffuser geometry with no variable stagger or lean. The variable stagger blade arrangement has the potential of better aligning the diffuser leading edges with the highly non-uniform flow leaving the impeller. Both variable stagger and linearly leaned diffuser blade arrangements, however, have the effect of redistributing the blade loading and flow streamlines in the spanwise direction leading to improved efficiency and pressure recovery capacity of the diffuser. In this paper a description of the proposed diffuser geometries is presented. The results of Three-dimensional Navier-Stokes numerical simulations of the three centrifugal compressor arrangements are discussed. Comparisons between the performance of the two and three-dimensional diffuser blade geometries are presented. The comparisons indeed show that the variable stagger and leaned diffusers present an improvement in the diffuser operating range and pressure recovery capacity over the conventional two-dimensional diffuser geometry.

Three-dimensional disturbances to a mixing layer in the nonlinear critical-layer regime

1995 ◽  
Vol 291 ◽  
pp. 57-81 ◽  
Author(s):  
S. M. Churilov ◽  
I. G. Shukhman
Keyword(s):  
Travelling Waves ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Critical Layer ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
New Type ◽  
Two Stages

We consider the nonlinear spatial evolution in the streamwise direction of slightly three-dimensional disturbances in the form of oblique travelling waves (with spanwise wavenumber kz much less than the streamwise one kx) in a mixing layer vx = u(y) at large Reynolds numbers. A study is made of the transition (with the growth of amplitude) to the regime of a nonlinear critical layer (CL) from regimes of a viscous CL and an unsteady CL, which we have investigated earlier (Churilov & Shukhman 1994). We have found a new type of transition to the nonlinear CL regime that has no analogy in the two-dimensional case, namely the transition from a stage of ‘explosive’ development. A nonlinear evolution equation is obtained which describes the development of disturbances in a regime of a quasi-steady nonlinear CL. We show that unlike the two-dimensional case there are two stages of disturbance growth after transition. In the first stage (immediately after transition) the amplitude A increases as x. Later, at the second stage, the ‘classical’ law A ∼ x2/3 is reached, which is usual for two-dimensional disturbances. It is demonstrated that with the growth of kz the region of three-dimensional behaviour is expanded, in particular the amplitude threshold of transition to the nonlinear CL regime from a stage of ‘explosive’ development rises and therefore in the ‘strongly three-dimensional’ limit kz = O(kx) such a transition cannot be realized in the framework of weakly nonlinear theory.

FREEMAN'S K MODELS AS RESERVOIR COMPUTING ARCHITECTURES

2009 ◽  
Vol 05 (01) ◽  
pp. 265-286
Author(s):  
MUSTAFA C. OZTURK ◽  
JOSE C. PRINCIPE
Keyword(s):  
Computational Models ◽  
Temporal Dynamics ◽  
Temporal Structure ◽  
Reservoir Computing ◽  
Short Term ◽  
System Parameters ◽  
History Of ◽  
Spatio Temporal ◽  
Universal Approximators ◽  
Theoretical Results

Walter Freeman in his classic 1975 book "Mass Activation of the Nervous System" presented a hierarchy of dynamical computational models based on studies and measurements done in real brains, which has been known as the Freeman's K model (FKM). Much more recently, liquid state machine (LSM) and echo state network (ESN) have been proposed as universal approximators in the class of functionals with exponential decaying memory. In this paper, we briefly review these models and show that the restricted K set architecture of KI and KII networks share the same properties of LSM/ESNs and is therefore one more member of the reservoir computing family. In the reservoir computing perspective, the states of the FKM are a representation space that stores in its spatio-temporal dynamics a short-term history of the input patterns. Then at any time, with a simple instantaneous read-out made up of a KI, information related to the input history can be accessed and read out. This work provides two important contributions. First, it emphasizes the need for optimal readouts, and shows how to adaptively design them. Second, it shows that the Freeman model is able to process continuous signals with temporal structure. We will provide theoretical results for the conditions on the system parameters of FKM satisfying the echo state property. Experimental results are presented to illustrate the validity of the proposed approach.

scholarly journals Directional solidification of a binary alloy into a cellular convective flow: localized morphologies

1999 ◽  
Vol 395 ◽  
pp. 253-270 ◽  
Author(s):  
Y.-J. CHEN ◽  
S. H. DAVIS
Keyword(s):  
Directional Solidification ◽  
Binary Alloy ◽  
Temporal Dynamics ◽  
Three Dimensional ◽  
Multiple Scale ◽  
Solute Diffusion ◽  
Two Dimensional ◽  
Morphological Instability ◽  
Flow Strength ◽  
Weakly Nonlinear

A steady, two-dimensional cellular convection modifies the morphological instability of a binary alloy that undergoes directional solidification. When the convection wavelength is far longer than that of the morphological cells, the behaviour of the moving front is described by a slow, spatial–temporal dynamics obtained through a multiple-scale analysis. The resulting system has a parametric-excitation structure in space, with complex parameters characterizing the interactions between flow, solute diffusion, and rejection. The convection in general stabilizes two-dimensional disturbances, but destabilizes three-dimensional disturbances. When the flow is weak, the morphological instability is incommensurate with the flow wavelength, but as the flow gets stronger, the instability becomes quantized and forced to fit into the flow box. At large flow strength the instability is localized, confined in narrow envelopes. In this case the solutions are discrete eigenstates in an unbounded space. Their stability boundaries and asymptotics are obtained by a WKB analysis. The weakly nonlinear interaction is delivered through the Lyapunov–Schmidt method.

Flow over a thin circular disk at low to moderate Reynolds numbers

2008 ◽  
Vol 605 ◽  
pp. 253-262 ◽  
Author(s):  
A. R. SHENOY ◽  
C. KLEINSTREUER
Keyword(s):  
Lift Coefficient ◽  
Three Dimensional ◽  
Circular Disk ◽  
Vortex Structures ◽  
Separation Region ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Vortex Loops ◽  
Spatio Temporal ◽  
Temporal Symmetry

Computation of viscous flow over a circular disk of aspect ratio 10 (thickness/diameter) in the Reynolds number (Re) range of 10 to 300 was performed. The following flow regimes were observed: (I) steady axisymmetric flow when Re < 135, with the presence of a toroidal vortex behind the disk; (II) regular bifurcation with loss of azimuthal symmetry but with planar symmetry and a double-threaded wake, for 135 ≤ Re < 155; (III) three-dimensional flow with periodic shedding of double-sided hairpin-shaped vortex structures and periodic motion of the separation region for 155 ≤ Re < 172; (IV) regular shedding of double-sided hairpin-shaped vortex structures with planar and spatio-temporal symmetry for 172 ≤ Re < 280; (V) periodic three-dimensional flow with irregular rotation of the separation region when Re = 280–300. This transition process for the disk differs from that for the sphere as we observe a loss of the symmetry plane in Regime III due to a twisting motion of the axial vorticity strands in the wake of the disk. The periodic flow was characterized by double-sided hairpin structures, unlike the one-sided vortex loops observed for the sphere. This resulted in the drag coefficient oscillating at twice the frequency of the axial velocity. In Regime IV, the vortex loops were shed from diametrically opposite locations and with equal strength, resulting in the lift coefficient oscillating symmetrically about a zero mean. These results imply the presence of spatio-temporal symmetry.

scholarly journals Modeling the Spatio-Temporal Dynamics of a Population with Age Structure and Long-Range Interactions: Synchronization and Clustering

2019 ◽  
Vol 14 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Matvey Kulakov ◽  
E.Ya. Frisman
Keyword(s):  
Mathematical Model ◽  
Model Equation ◽  
Temporal Dynamics ◽  
Local Population ◽  
Two Dimensional ◽  
Attraction Basin ◽  
Local Populations ◽  
Long Range Interactions ◽  
Spatio Temporal ◽  
Formation Of Groups

The paper proposed a mathematical model for spatio-temporal dynamics of two-age populations coupled by migration living on a two-dimensional areal. The model equation is a system of nonlocal coupled two-dimensional maps. We considered cases when populations are coupled in a certain neighborhood of different form: circle, square or rhombus. Special attention is paid to the situation when the intensity of the migrants flow between the territories decreases with increasing distance between them. For this model we study the conditions for the formation of groups of synchronous populations or clusters that form, in space, typical structures like spots or stripes mixed with solitary states. It is shown that the dynamics, in time, of different clusters may differ significantly and may not be coherent and correspond to several simultaneous multistable regimes or potential states of the local population. Such spatio-temporal regimes are forced and are caused by impacts or perturbations on a single or several populations when their number falls into the attraction basin of another regime. With strong coupling, such clusters are rare and are represented by single outbursts or solitary states. However, the decrease in the coupling strength leads to the fact that these outbursts cause oscillations of their neighbors, and in their neighborhood a cluster of solitary states is formed which is surrounded by subpopulations with a different type of dynamics. It was found that the interaction of different type of clusters leads to the formation of a large number of groups with transitional dynamics that were not described for local populations.

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