An analytical-based method for studying the nonlinear evolution of localized vortices in planar homogenous shear flows

Cohen, Jacob; Shukhman, I. G.; Karp, Michael; Philip, Jimmy

doi:10.1016/j.jcp.2010.06.035

Cited by 10 publications

(21 citation statements)

References 19 publications

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“…This is an essential difference between calculation and experiment. Analyzed Figure 25 from [20], the authors confirmed the disappearance of the vortex structure at the periphery of the recirculating zone. They note that the vortex structure "loses its spiral shape" at the periphery of the recirculating zone.…”

Section: Rementioning

confidence: 77%

“…At the end of the period, the vortex localized at the periphery of the recirculating zone separates from this zone. The separation of the shed vortex from the recirculating zone is very clearly shown in Figure 40 in [20]. The periphery of the recirculating zone, which is periodically shed from the recirculating zone, rushes downstream and forms a vortex street…”

Section: Rementioning

confidence: 93%

“…x (Figure 7(a,i) in [7]). Because of the absence of the detachment of the recirculating zone in Figure 25 in the ca periphery lculation [20], there is no vortex loop street in the wake behind a sphere. This is an essential difference between calculation and experiment.…”

Section: Rementioning

confidence: 97%

“…Earlier, this point of view was formulated in [25]. An attempt was made [18][19][20][21] [7]). According to Figure 12(c) from [7], the vortex structure appears in the wake suddenly and is fairly well defined starting with the moment of its origination.…”

Section: Rementioning

confidence: 99%

“…x , and x wake behind a sphere after the passage of the Re critical value. A detailed examination of these flow as executed in [2,20]. To summarize, after the arance in the wake behind a sphere, the size of the vortex structure becomes substantial at the surface of the sphere.…”

Section: Rementioning

confidence: 99%

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Lebed¹

2013

OJFD

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The results of the direct numerical integration of the Navier-Stokes equations are evaluated against experimental data for problem on a flow around bluff bodies in an unstable regime. Experiment records several stable medium states for flow past a body. Evolution of each of these states, after losing the stability, inevitably goes by periodic vortex shedding modes. Calculations based on the Navier-Stokes equations satisfactorily reproduced all observed stable medium states. They were, however, incapable of reproducing any of a vortex shedding modes recorded experimentally. The solutions to the classic hydrodynamics equations successfully reach the boundary of instability field. However, classic solutions are unable to cross this boundary. Most likely, the reason for this is the Navier-Stokes equations themselves. The classic hydrodynamics equations directly follow from the Boltzmann equation and naturally contain the error involved in the derivation of classic kinetic equation. Just the Boltzmann hypothesis, which closed kinetic equation, allowed us to construct classic hydrodynamics on only three lower principal hydrodynamic values. The use of the Boltzmann hypothesis excludes higher principal hydrodynamic values from the participation in the formation of classic hydrodynamics equations. The multimoment hydrodynamics equations are constructed using seven lower principal hydrodynamic values. The numerical integration of the multimoment hydrodynamics equations in the problem on flow around a sphere shows that the solutions to these equations cross the boundary and enter the instability field. The boundary crossing is accompanied by appearance of very uncommon acts in scenario of system evolution.

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Section: Rementioning

confidence: 77%

Section: Rementioning

confidence: 93%

Section: Rementioning

confidence: 97%

Section: Rementioning

confidence: 99%

Section: Rementioning

confidence: 99%

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About the Prospects for Passage to Instability

Lebed¹

2013

OJFD

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Numerical investigation on mechanism of multiple vortex rings formation in late boundary-layer transition

2013

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A minimal flow-elements model for the generation of packets of hairpin vortices in shear flows

2014

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Packets of hairpin-shaped vortices and streamwise counter-rotating vortex pairs (CVPs) appear to be key structures during the late stages of the transition process as well as in low-Reynolds-number turbulence in wall-bounded flows. In this work we propose a robust model consisting of minimal flow elements that can produce packets of hairpins. Its three components are: simple shear, a CVP having finite streamwise vorticity magnitude and a two-dimensional (2D) wavy (in the streamwise direction) spanwise vortex sheet. This combination is inherently unstable: the CVP modifies the base flow due to the induced velocity forming an inflection point in the base-flow velocity profile. Consequently, the 2D wavy vortex sheet is amplified, causing undulation of the CVP. The undulation is further enhanced as the wave continues to be amplified and eventually the CVP breaks down into several segments. The induced velocity generates highly localized patches of spanwise vorticity above the regions connecting two consecutive streamwise elements of the CVP. These patches widen with time and join with the streamwise vortical elements situated beneath them forming a packet of hairpins. The results of the unbounded (having no walls) model are compared with pipe and channel flow experiments and with a direct numerical simulation of a transition process in Couette flow. The good agreement in all cases demonstrates the universality and robustness of the model.

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An analytical-based method for studying the nonlinear evolution of localized vortices in planar homogenous shear flows

Cited by 10 publications

References 19 publications

About the Prospects for Passage to Instability

About the Prospects for Passage to Instability

Numerical investigation on mechanism of multiple vortex rings formation in late boundary-layer transition

A minimal flow-elements model for the generation of packets of hairpin vortices in shear flows

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