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  • Cambridge University Press  (3)
  • 1
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    Transitions in time-dependent thermal convection in fluid-saturated porous media (1982)
    Cambridge University Press
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    Publication Date: 1982-08-01
    Description: Numerical simulations of single-cell, two-dimensional, time-dependent thermal convection in a square cross-section of fluid-saturated porous material heated uniformly from below reveal a series of transitions between distinct oscillatory dynamical regimes. With increasing Rayleigh number R, the flow first evolves from steady-state behaviour into periodic motion with a single frequency/which depends on R approximately according to f ∞ Ri; the transition Rayleigh number lies between about 380 and 400. At a value of R between about 480 and 500 the flow transforms into a fluctuating state characterized by two frequencies. Soon thereafter, for R between about 500 and 520, it reverts back to single-frequency periodic behaviour with/approximately proportional to R$. The two frequencies in the narrow transition regime may be locked to a rational ratio, in which case the flow is periodic, or they may be commensurate, in which case the flow is quasi-periodic. The spectral characteristics of numerical realizations of unsteady convection and the occurrences of transitions therein are highly dependent on truncation level in Galerkin schemes or resolution in finite-difference approaches. © 1982, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 2
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    Route to chaos in porous-medium thermal convection (1986)
    Cambridge University Press
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    Publication Date: 1986-05-01
    Description: A pseudo-spectral numerical scheme is used to study two-dimensional, single-cell, time-dependent convection in a square cross-section of fluid saturated porous material heated from below. With increasing Rayleigh number R convection evolves from steady S to chaotic NP through the sequence of bifurcations S→ P(1) → QP2→ p(2) → NP, where P(1) and P(2) are simply periodic regimes and QP2 is a quasi-periodic state with two basic frequencies. The transitions (from onset of convection to chaos) occur at Rayleigh numbers of 4π2380–400, 500–520, 560–570, and 850–1000. In the first simply periodic regime the fundamental frequency f1 varies as R7/8and the average Nusselt number Nu is proportional to R2/3; in P(2)f1varies as R3/2 and Nu oc R11/10. Convection in QP2 exhibits hysteresis, i.e. if the QP2 state is reached from P(1)(P(2)) by increasing (decreasing) R then the frequency with the largest spectral power is the one consistent with the extrapolation of f1 according to R7/8(R3/2). The chaotic states are characterized by spectral peaks with at least 3 fundamental frequencies superimposed on a broadband background noise. The time dependence of these states arises from the random generation of tongue-like disturbances within the horizontal thermal boundary layers. Transition to the chaotic regime is accompanied by the growth of spectral components that destroy the centre-symmetry of convection in the other states. Over-truncation can lead to spurious transitions and bifurcation sequences; in general it produces overly complex flows. © 1986, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 3
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    Time-dependent convection in a fluid-saturated porous cube heated from below (1989)
    Cambridge University Press
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    Publication Date: 1989-10-01
    Description: A numerical scheme based on the pseudospectral method has been implemented in order to study three-dimensional convection in a fluid-saturated cube of porous material. With increasing Rayleigh number R, convection first evolves from a symmetric steady state (S) to a partially non-symmetric steady state (S‘, physical symmetry in the vertical direction is preserved). The transition Rayleigh number is about 550. At a Rayleigh number of 575 the flow becomes oscillatory P(1) with a single frequency that increases with R. At a value of R between 650 and 680 the oscillation becomes quasi-periodic with at least two fundamental frequencies. It returns to a simply periodic state in a narrow range about R = 725. A further increase of R transforms the simply periodic state again to a quasi-periodic state. The sequence of three-dimensional time-dependent states resembles previously studied two-dimensional cases in that evolution from more complex states to less complex states occurs with increasing R. The partial symmetry breaking prior to the onset of time dependence is unique to the three-dimensional flows, but a dependence of the S-〉 S’ transition on the step size in R suggests the possibility that S-〉 S’ might not occur prior to S→P(1) for sufficiently small steps in R. The quasi-periodic flows sometimes exhibit intermittency, causing difficulty in exactly defining their spectral characteristics. © 1989, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
    Location Call Number Expected Availability
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