Transitional regimes of penetrative convection in a plain layer

Kuznetsova, Daria; Sibgatullin, Ilias

doi:10.1134/s102833581105003x

Cited by 2 publications

(3 citation statements)

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“…In particular, the presence of a heat source or sink may give rise to the idea of penetrative convection where part of the layer has a tendency to move whereas the remainder of the layer will remain motionless until a certain point when movement in the rest of the layer "penetrates" into the stable layer and a resultant motion then ensues, cf. Altawallbeh et al [1], van den Berg et al [3], Berlengiero et al [4], Capone et al [5,6,7], Capone 1 & de Luca [8], Capone et al [9], Capone & Rionero [10], Carr [11], Chasnov & Tse [13], Hetsroni et al [19], Hill [20,21], Imamura et al [23], Kirillov et al [26], Krishnamurti [27], Kuznetsova & Sibgatullin [28], Larson [29,30], Machado et al [32], Mharzi et al [33], Papanicolaou et al [36], Prudhomme & Jasmin [37], Saravan & Nayaki [47], Shalbaf et al [49], Siddheshwar & Titus [51], Storesletten & Titus [52], Straughan [53,55,54,60,62], and Straughan & Walker [64]. Straughan [54], section 17.2, pp.…”

Section: Introductionmentioning

confidence: 99%

Resonant Penetrative Convection with an Internal Heat Source/Sink

Straughan

2014

Acta Appl Math

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We develop a detailed linear instability and nonlinear stability analysis for the situation of convection in a horizontal plane layer of fluid when there is a heat sink / source which is linear in the vertical coordinate which is in the opposite direction to gravity. This can give rise to a scenario where the layer effectively splits into three sublayers. In the lowest one the fluid has a tendency to be convectively unstable while in the intermediate layer it will be gravitationally stable. In the top layer there is again the possibility for the layer to be unstable. This results in a problem where convection may initiate in either the lowest layer, the upmost layer, or perhaps in both sublayers simultaneously. In the last case there is the possibility of resonance between the upmost and lowest layers. In all cases penetrative convection may occur where convective movement in one layer induces motion in an adjacent sublayer. In certain cases the critical Rayleigh number for thermal convection may display a very rapid increase which is much greater than normal. Such behaviour may have application in energy research such as in thermal insulation. * Research supported by a "Tipping Points, Mathematics, Metaphors and Meanings" grant of the Leverhulme Trust. I should like to thank an anonymous referee for pointing out some errors and for several helpful remarks.

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Section: Introductionmentioning

confidence: 99%

Resonant Penetrative Convection with an Internal Heat Source/Sink

Straughan

2014

Acta Appl Math

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“…At R = R qp ≡ 21176 ( T = 1.38) there is a transition from periodic-2 to quasiperiodic motion (Kuznetsova and Sibgatullin 2011)…”

Section: Loss Of Stability Of Periodic Solutions: Period Doubling And...mentioning

confidence: 99%

“…In Kuznetsova and Sibgatullin (2011) the preliminary results are given for the evolution of the 2D solution with equal heights of stable and unstable sublayers in the initial state. The horizontal scales of steady and periodic solutions, the phenomenon of hysteresis and quasiperiodic solutions are described.…”

Section: Introductionmentioning

confidence: 99%

Transitional regimes of penetrative convection in a plane layer

Kuznetsova¹,

Sibgatullin²

2012

Fluid Dyn. Res.

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Hydrodynamical regimes are described for penetrative convection in a twodimensional bounded plane layer of water at the temperature range close to the point of maximum density. Stress-free conditions on the horizontal and vertical boundaries of the domain are assumed. The point of maximum density is supposed to be located in the middle plane of the layer in conductive state. Steady and time-periodic solutions are found on large horizontal scales and the lengths of a spatial periodicity inside the layer are determined. Hydrodynamical peculiarities of time-periodic solution are described. In the domain equal to the periodicity cell corresponding to time-periodic solution, the sequence of hydrodynamical regimes with the increase of supercriticality is analyzed and the full sequence of bifurcations from conductive state to chaotic motion is described. The time-periodic solution loses the stability through the subcritical Neimark-Sacker bifurcation. First, the closed invariant curve has one stable period-2 cycle, so the bifurcation looks like period doubling. With a further increase of supercriticality the period-2 cycle transforms to a torus through the saddle-node bifurcation for maps. Then, loss of stability of quasiperiodic motion occurs through intermittency and chaotic mixing on the background of quasiperiodic solution. The window of quasiperiodicity was obtained in the interval of supercriticality corresponding to intermittent regimes, after which intermittency on the background of another quasiperiodic mode appears.

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Transitional regimes of penetrative convection in a plain layer

Cited by 2 publications

References 6 publications

Resonant Penetrative Convection with an Internal Heat Source/Sink

Resonant Penetrative Convection with an Internal Heat Source/Sink

Transitional regimes of penetrative convection in a plane layer

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