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  • 1
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    Subsurface hydrology of an overdeepened cirque glacier (2011)
    Cambridge University Press
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    Publication Date: 2011-12-28
    Print ISSN: 0022-1430
    Electronic ISSN: 1727-5652
    Topics: Geography , Geosciences
    Published by Cambridge University Press on behalf of The International Glaciological Society (IGS).
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  • 2
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    Mixed mode convection in an inclined slot (1993)
    Cambridge University Press
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    Publication Date: 1993-01-01
    Description: Nonlinear interaction between transverse disturbances and longitudinal rolls has been investigated for flow in an inclined slot with a heated lower wall when both modes of instability occur at nearly the same value of the control parameter. This condition is shown to be possible for a fluid with Prandtl number greater than 0.263897. For slightly supercritical values of the Rayleigh number (R) when the critical Rayleigh number for longitudinal rolls RL C is somewhat less than that for transverse stationary rolls, RS C, and for transverse travelling waves, longitudinal rolls occur first and then remain stable as R is increased beyond RS Cor RT C; no mixed mode state occurs. In contrast, if RS C or RT Cis slightly below RL C, pure transverse modes exist for only a relatively small range of R beyond RS C or RT C. Thereafter, a thee-dimensional mixed mode state occurs well before RL C is reached, i.e. three-dimensionality sets in on a subcritical basis. As R approaches RL C, the contribution of the transverse mode decreases continuously until a pure longitudinal roll state emerges for R slightly greater than RL C Mixed mode convection is also investigated for a special choice of parameters when three modes, namely transverse stationary rolls, transverse travelling waves and longitudinal rolls, become unstable simultaneously. Longitudinal rolls again emerge as the stable supercritical state. © 1993, 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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    Thermocapillary and oscillatory-shear instabilities in a layer of liquid with a deformable surface (1998)
    Cambridge University Press
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    Publication Date: 1998-04-10
    Description: The thermocapillary and shear-induced instabilities of a thin heated layer of liquid bounded from the top by a deformable free surface and at the bottom by a horizontally oscillating plate are studied for both Earth-bound and microgravity conditions. Finite-wavelength thermocapillary convection can be stabilized very significantly by the oscillatory shear, whereas shear-induced instabilities are greatly stabilized if the Marangoni number is negative. For long-wavelength thermocapillary convection, oscillatory shear can stabilize or destabilize the basic state, depending primarily on the imposed forcing frequency. With microgravity, significant stabilization of the dominant long-wavelength convection can be achieved by carefully selecting the imposed frequency.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 4
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    The effects of thermal modulation upon the onset of Marangoni–Bénard convection (2002)
    Cambridge University Press
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    Publication Date: 2002-04-09
    Description: The effects of thermal modulation with time on the thermocapillary instability of a thin horizontal fluid layer with a deformable free surface are investigated on the basis of linear stability theory. First, a sinusoidal heating with a mean component is applied at the lower wall, corresponding to boundary conditions either in the form of prescribed temperature or heat flux. For finite-wavelength convection the thermal modulation exerts a strong effect, giving rise to a family of looped regions of instability corresponding to alternating synchronous or subharmonic responses. In the case of prescribed heat flux, the critical curve consists of significantly fewer loops than in the case of prescribed temperature. Thermal modulation with moderate modulation amplitude tends to stabilize the mean basic state, and optimal values of frequency and amplitude of modulation are determined to yield maximum stabilization. However, large-amplitude modulation can be destabilizing. A basic state with zero mean is then considered and the critical Marangoni number is obtained as a function of frequency. The effects of modulation are also investigated in the long-wavelength limit. For the case of prescribed temperature, the modulation does not affect the onset of the long-wavelength mode associated with the mean basic state and a purely oscillating basic state is always stable with respect to long-wavelength disturbances. For the case of prescribed heat flux both at the wall and free surface, by contrast, thermal modulation exerts a significant effect on the onset of convection from a mean basic state and long-wavelength convection can occur even for a purely oscillating basic state. The modulation can be stabilizing or destabilizing, depending on the frequency.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 5
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    On the resonant interaction of neutral disturbances in two inviscid shear flows (1968)
    Cambridge University Press
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    Publication Date: 1968-03-18
    Description: The second-order resonant interaction of two disturbances which are neutrally stable on a linear basis is investigated for cases when the mean flow is, first, an inviscid, homogeneous jet and, secondly, a stably stratified, antisymmetric shear layer for which the linear eigen-solutions are regular. For the former case, the periodic nature of the neutral disturbances is unaffected by the interaction. For the latter, the interaction can lead to an O(ε½) temporal growth rate of one disturbance, where ε is a characteristic disturbance amplitude.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 6
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    Inviscid instability of an unbounded heterogeneous shear layer (1971)
    Cambridge University Press
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    Publication Date: 1971-07-28
    Description: Stability curves are computed for both spatially and temporally growing disturbances in a stratified mixing layer between two uniform streams. The low Froude number limit, in which the effects of buoyancy predominate, and the high Froude number limit, in which the effects of density variation are manifested by the inertial terms of the vorticity equation, are considered as limiting cases. For the buoyant case, although the spatial growth rates can be predicted reasonably well by suitable use of the results for temporal growth, spatially growing disturbances appear to have high group velocities near the lower cutoff wave-number. For the inertial case, it is demonstrated that density variations can be destabilizing. More precisely, when the stream with the higher velocity has the lower density, both the wave-number range of unstable disturbances and the maximum spatial growth rate are increased relative to the case of homogeneous flow. Finally, it is shown how the growth rate of the most unstable wave in the inertial case diminishes as buoyancy becomes important. © 1971, 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
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  • 7
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    Control of long-wavelength Marangoni–Bénard convection (1999)
    Cambridge University Press
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    Publication Date: 1999-05-25
    Description: A nonlinear feedback control strategy for delaying the onset and eliminating the subcritical nature of long-wavelength Marangoni-Bénard convection is investigated based on an evolution equation. A control temperature is applied to the lower wall in a gas-liquid layer otherwise heated uniformly from below. It is shown that, if the interface deflection is assumed to be known via sensing as a function of both horizontal coordinates and time, a control temperature with a cubic-order polynomial dependence on the deflection is capable of delaying the onset as well as eliminating the subcritical instability altogether, at least on the basis of a weakly nonlinear analysis. The analytical results are supported by direct numerical simulations. The control coefficients required for stabilization are O(1) for both delaying onset indefinitely and eliminating subcritical instability. In order to discuss the effects of control, a review is made of the dependence of the weakly nonlinear subcritical solutions without control upon the various governing parameters.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 8
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    Spanwise pairing of finite-amplitude longitudinal vortex rolls in inclined free-convection boundary layers (1991)
    Cambridge University Press
    Details
    Publication Date: 1991-10-01
    Description: Buoyancy-driven flow on a heated inclined plate can become unstable to static longitudinal roll instability at a critical distance, measured by Rc, from the leading edge. Experiments in water by Sparrow & HUSAR (1969) indicate that these rolls undergo a second transition further downstream such that adjacent rolls merge and their spanwise wavelength is doubled. We study this secondary bifurcation phenomenon here with a set of model equations by first constructing the full eigenspectrum and eigenfunctions with a Chebyshev-Tau spectral method and then deriving the pertinent amplitude equations. By stipulating that the dimensional cross-stream wavelength of the rolls remains constant beyond Rc which is consistent with experimental observation, we show that the finite-amplitude primary rolls are destabilized by the ⅓ subharmonic mode at another critical distance R1/2 from the edge. This 1/2 mode is shown to have an asymmetric spatial phase shift of 1/2 π relative to the original 1 mode of the primary rolls, thus explaining the unique dislocation of tracer streaks after the rolls coalesce in the experiments. Also consistent with experimental observation is the theoretical result that the merged rolls are annihilated downstream by a saddle-node bifurcation before further wavelength doubling can occur. Simple amplitude criteria and critical distances from the leading edge for the various transitions are derived and compared to experimental values. © 1991, 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
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  • 9
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    The onset of Rayleigh–Bénard convection in non-planar oscillatory flows (1993)
    Cambridge University Press
    Details
    Publication Date: 1993-04-01
    Description: The onset of thermal convection in the presence of an oscillatory, non-planar shear flow is investigated on a linear basis. For the case of planar oscillations, the basic shear has no effect upon the value of the critical Rayleigh number but does act as a pattern selection mechanism. For the non-planar case, when there are two horizontal components of the basic velocity, the same result is true if the components are either in phase or directly out of phase. For the general case, however, stabilization occurs because convection rolls experience the stabilizing effects of shear regardless of their orientation. The results are obtained both by expansion in terms of the amplitude of the oscillating flow and in terms of its frequency, assuming the frequency to be small. The degree of stabilization increases with the Prandtl number. Pattern selection still occurs with non-planar oscillations. © 1993, Cambridge University Press
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 10
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    Degenerate bifurcation in stably stratified plane Poiseuille flow (1997)
    Cambridge University Press
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    Publication Date: 1997-01-25
    Description: Bifurcation characteristics of stably stratified plane Poiseuille flow have been investigated on a weakly nonlinear basis. It is found that the results are sensitive to the value of the Prandtl number, in that subcritical bifurcation persists for most values of the Prandtl number but is replaced by supercritical bifurcation over a range of small values of the Prandtl number. This range includes values characteristic of some liquid metals. The bifurcation becomes degenerate at a particular parameter set where the real part of the cubic nonlinear coefficient in the Stuart-Landau equation vanishes at criticality, and the situation is discussed by including higher-order terms in the manner of Eckhaus & Iooss (1989). An exact hyper-degenerate situation is also found to be possible for which the cubic and the quintic nonlinear coefficients lose their real parts simultaneously; this case is also analysed. For large values of the Prandtl number, stable stratification tends to promote subcritical instability.
    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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