scholarly journals Vortex pairing in jets as a global Floquet instability: modal and transient dynamics

2019 ◽  
Vol 862 ◽  
pp. 951-989 ◽  
Author(s):  
Léopold Shaabani-Ardali ◽  
Denis Sipp ◽  
Lutz Lesshafft
Keyword(s):  
Global Analysis ◽  
Growth Dynamics ◽  
Vortex Street ◽  
Single Frequency ◽  
Natural Occurrence ◽  
Transient Growth ◽  
Laminar Jet ◽  
Vortex Pairing ◽  
Value Decomposition ◽  
Time Periodic

The spontaneous pairing of rolled-up vortices in a laminar jet is investigated as a global secondary instability of a time-periodic spatially developing vortex street. The growth of subharmonic perturbations, associated with vortex pairing, is analysed both in terms of modal Floquet instability and in terms of transient growth dynamics. The article has the double objective to outline a toolset for the global analysis of time-periodic flows, and to leverage such an analysis for a fresh view on the vortex pairing phenomenon. Axisymmetric direct numerical simulations (DNS) of jets with single-frequency inflow forcing are performed, in order to identify combinations of the Reynolds and Strouhal numbers for which vortex pairing is naturally observed. The same DNS calculations are then repeated with an added time-delay control term, which artificially suppresses pairing, so as to obtain time-periodic unpaired base flows for linear stability analysis. It is demonstrated that the natural occurrence of vortex pairing in nonlinear DNS coincides with a linear subharmonic Floquet instability of the underlying unpaired vortex street. However, DNS results suggest that the onset of pairing involves much stronger temporal growth of subharmonic perturbations than that predicted by modal Floquet analysis, as well as a spatial distribution of these fast-growing perturbation structures that is inconsistent with the unstable Floquet mode. Singular value decomposition of the phase-shift operator (the operator that maps a given perturbation field to its state one flow period later) is performed for an analysis of optimal transient growth in the vortex street. Non-modal mechanisms near the jet inlet are thus found to provide a fast route towards the limit-cycle regime of established vortex pairing, in good agreement with DNS observations. It is concluded that modal Floquet analysis accurately predicts the parameter regime where sustained vortex pairing occurs, but that the bifurcation scenario under typical conditions is dominated by transient growth phenomena.

scholarly journals Study of Microwave Tomography Measurement Setup Configurations for Breast Cancer Detection Based on Breast Compression

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Alvaro Diaz-Bolado ◽  
Paul-Andre Barriere ◽  
Jean-Jacques Laurin
Keyword(s):  
Breast Cancer ◽  
Image Quality ◽  
Cancer Detection ◽  
Synthetic Data ◽  
Singular Value ◽  
Breast Cancer Detection ◽  
Single Frequency ◽  
Microwave Tomography ◽  
Breast Compression ◽  
Value Decomposition

Microwave tomography (MT) measurement setups for different configurations based on breast compression are compared to classical circular measurement setups. Configurations based on compression allow measuring the evanescent component of the scattered field and lead to a compact measurement setup that allows direct image comparison with a standard mammography system. The different configurations are compared based on the singular value decomposition (SVD) of the radiation operator for a 2D TM case. This analysis allows determining under which conditions the image quality obtained from the reconstructions can be enhanced. These findings are confirmed by a series of reconstructions of breast phantoms based on synthetic data obtained at a single frequency of operation.

Numerical Simulation of Mixing Enhancement and Suppression in Two-Dimensional Mixing Layer

2011 ◽  
Author(s):  
Masayuki Kawagoe ◽  
Koji Fukagata
Keyword(s):  
Numerical Simulation ◽  
Mixing Layer ◽  
Mixing Enhancement ◽  
Computational Domain ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Control Effect ◽  
Chemical Product ◽  
Vortex Pairing ◽  
Time Periodic

Direct numerical simulation of two-dimensional mixing layer with time-periodic forcing mimicking the input of piezofilm actuator is performed. Three different forcing frequencies (i.e., the natural frequency, its first subharmonic and second subharmonic frequencies) are examined. Simplified chemical reactions are also taken into account. We investigate whether mixing is promoted or suppressed using two indices: the momentum thickness and the concentration of chemical product. The momentum thickness indicates that the forcing enhances the development of mixing layer near the inlet and suppresses it in the region right downstream. Instantaneous vorticity fields show that the location where the vortex pairing starts depend on the forcing frequency. The effect of forcing on the mixing layer development strongly depends on its frequency: in particular, the forcing at the second subharmonic frequency is found to suppress the development of mixing layer in a wide region. On the other hand, from the chemical product concentration, mixing is found to be promoted regardless of the forcing frequency. We also investigate how far the control effect lasts. It is revealed that in the downstream region the mixing layer thickness develops linearly regardless of the forcing frequency, which in turn suggests that the present numerical simulation is performed in a computational domain large enough to examine the control effect.

A spatial analogue of transient growth in plane Couette flow

1999 ◽  
Vol 397 ◽  
pp. 317-330 ◽  
Author(s):  
JACQUES VANNESTE
Keyword(s):  
Couette Flow ◽  
Linear Response ◽  
The Self ◽  
Transient Growth ◽  
Plane Couette Flow ◽  
Periodic Forcing ◽  
Straight Line ◽  
Growth Phenomenon ◽  
Time Periodic ◽  
Self Consistency

The linear response of an inviscid two-dimensional Couette flow disturbed by a time-periodic forcing is studied under the assumption that the forcing is distributed along a straight line. When the forcing is tilted against the shear, the disturbance streamfunction and energy are shown to be locally amplified downstream of the source before decaying at large distance. This spatially localized amplification is interpreted as an analogue of the transient growth phenomenon studied in the context of unforced intial-value problems. The self-consistency of the linear approximation and the instability of the disturbance are also examined.

scholarly journals Stochastic parametric resonance in shear flows

2005 ◽  
Vol 12 (6) ◽  
pp. 871-876 ◽  
Author(s):  
F. J. Poulin ◽  
M. Scott
Keyword(s):  
Shear Flow ◽  
Shear Flows ◽  
Parametric Instability ◽  
Mathieu Equation ◽  
Cape Cod ◽  
Transient Growth ◽  
Constant Frequency ◽  
Cape Cod Bay ◽  
Linearized System ◽  
Time Periodic

Abstract. Time-periodic shear flows can give rise to Parametric Instability (PI), as in the case of the Mathieu equation (Stoker, 1950; Nayfeh and Mook, 1995). This mechanism results from a resonance between the oscillatory basic state and waves that are superimposed on it. Farrell and Ioannou (1996a, b) explain that PI occurs because the snap-shots of the velocity profile are subject to transient growth. If the flows were purely steady the transient growth would subside and not have any long lasting effect. However, the coupling between transient growth and the time variation of the basic state create PI. Mathematically, transient growth, and therefore PI, are due to the nonorthogonal eigenspace in the linearized system. Poulin et al. (2003) studied a time-periodic barotropic shear flow that exhibited PI, and thereby produced mixing at the interface between Potential Vorticity (PV) fronts. The instability led to the formation of vortices that were stretched. A later study of an oscillatory current in the Cape Cod Bay illustrated that PI can occur in realistic shear flows (Poulin and Flierl, 2005). These studies assumed that the basic state was periodic with a constant frequency and amplitude. In this work we study a shear flow similar to that found in Poulin et al. (2003), but now where the magnitude of vorticity is a stochastic variable. We determine that in the case of stochastic shear flows the transient growth of perturbations of the snapshots of the basic state still generate PI.

scholarly journals Measurement of Flow Fluctuation in the Flow Standard Facility Based on Singular Value Decomposition

Sensors ◽  
2021 ◽  
Vol 21 (20) ◽  
pp. 6850
Author(s):  
Tao Meng ◽  
Huanchang Wei ◽  
Feng Gao ◽  
Huichao Shi
Keyword(s):  
Singular Value Decomposition ◽  
Measuring Method ◽  
Flow Stability ◽  
Singular Value ◽  
Single Frequency ◽  
Standard Facility ◽  
Flow Fluctuation ◽  
Set Up ◽  
Value Decomposition ◽  
The Impact

In order to accurately evaluate the flow stability of the flow standard facility, the flow fluctuation in the standard facility needs to be accurately measured. However, the flow fluctuation signal is always superimposed with the fluctuation signal of the measuring flowmeter or measurement system (mainly noise), which leads to inaccurate measurement of the flow fluctuation and even an unreliable evaluation result of the flow stability. In addition, when there are multiple fluctuation sources, flow fluctuations with different frequencies are superimposed together, which is extremely unfavorable for evaluating the impact of flow fluctuation with different single frequencies. In this paper, a new measuring method was proposed to obtain the fluctuation signal and the flow fluctuation based on singular value decomposition (SVD). Simulation experiments on the fluctuation signal (single frequency and multiple frequencies) under different levels of noise were conducted, and simulation results showed that the proposed method could accurately obtain the fluctuation signal and the flow fluctuation, even under high noise. Finally, an experimental platform was set-up based on a water flow standard facility and a flow fluctuation generator, and experiments on the output signal of a venturi flowmeter were carried out. The experiment results showed that the proposed method could effectively obtain the fluctuation signal and accurately measure the flow fluctuation.

Quiescence and transient growth dynamics in chemostat models

1994 ◽  
Vol 119 (2) ◽  
pp. 225-239 ◽  
Author(s):  
Willi Jäger ◽  
Susanne Krömker ◽  
Betty Tang
Keyword(s):  
Growth Dynamics ◽  
Transient Growth

Instability and transient growth for two trailing-vortex pairs

1997 ◽  
Vol 350 ◽  
pp. 311-330 ◽  
Author(s):  
J. D. CROUCH
Keyword(s):  
Transient Growth ◽  
Vortex System ◽  
Long Wavelength ◽  
Vortex Pairs ◽  
Temporal Differentiation ◽  
Trailing Vortices ◽  
The Stability ◽  
Time Required ◽  
Crow Instability ◽  
Time Periodic

The stability of two vortex pairs is analysed as a model for the vortex system generated by an aircraft in flaps-down configuration. The co-rotating vortices on the starboard and port sides tumble about one another as they propagate downward. This results in a time-periodic basic state for the stability analysis. The dynamics and instability of the trailing vortices are modelled using thin vortex filaments. Stability equations are derived by matching the induced velocities from Biot–Savart integrals with kinematic equations obtained by temporal differentiation of the vortex position vectors. The stability equations are solved analytically as an eigenvalue problem, using Floquet theory, and numerically as an initial value problem. The instabilities are periodic along the axes of the vortices with wavelengths that are large compared to the size of the vortex cores. The results show symmetric instabilities that are linked to the long-wavelength Crow instability. In addition, new symmetric and antisymmetric instabilities are observed at shorter wavelengths. These instabilities have growth rates 60–100% greater than the Crow instability. The system of two vortex pairs also exhibits transient growth which can lead to growth factors of 10 or 15 in one-fifth of the time required for the same growth due to instability.

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