We present a numerical study of the reversals and reorientations of the large scale circulation (LSC) of convective fluid in a cylindrical container of aspect ratio one. We take Prandtl number to be 0.7 and Rayleigh numbers in the range from 6 × 10 5 to 3 × 10 7 . It is observed that the reversals of the LSC are induced by its reorientation along the azimuthal direction, which are quantified using the phases of the first Fourier mode of the vertical velocity measured near the lateral surface in the mid plane. During a "complete reversal", the above phase changes by around 180 0 leading to reversals of the vertical velocity at all the probes. On the contrary, the vertical velocity reverses only at some of the probes during a "partial reversal" with phase change other than 180 0 . Numerically we observe rotation-led and cessation-led reorientations, in agreement with earlier experimental results. The ratio of the amplitude of the second Fourier mode and the first Fourier mode rises sharply during the cessation-led reorientations. This observation is consistent with the quadrupolar dominant temperature profile observed during the cessations. We also observe reorientations involving double cessation.

SUMMARYThis paper reports simulation results for free-stream flow past an oscillating square cylinder at Re = 100 and 150, for oscillating-to-natural-shedding frequency ratios of 0.5 f r 3.0 at a fixed oscillation amplitude of 0.2 of the cylinder width. The transformed governing equations are solved in a non-inertial frame of reference using the finite volume technique. The 'lock-in' phenomena, where the vortex shedding becomes one with the oscillation frequency, is observed near the natural shedding frequency ( f r ≈ 1). Beyond the synchronization band, downstream recovery of the wake to its stationary (natural) state (frequency) is observed in cross-stream velocity spectra. At higher forcing frequencies, a phase lag between the immediate and the far wake results in a shear layer having multi-polar vortices. A 'Vortex-switch' accompanied by a change in the direction of energy transfer is identified at the 'lock-in' boundaries. The variation of aerodynamic forces is noticed to be different in the lock-in regime. The velocity phase portrait in the far wake revealed a chaotic state of flow at higher excitation though a single (natural) frequency appears in the spectra.

No abstract

No abstract

No abstract

No abstract

No abstract

This paper introduces certain generalizations of the notions of approximate limit, continuity and derivative and of absolute continuity, of real functions, leading to generalized integrals of Perron and Denjoy types comprising the /(/"-integral of Burkill (1931) and Sonouchi and Utagawa (1949) and the AD-inlegral of Kubota (1963)