Oscillating wake

At Re > 65, the vorticity region in the rear area ceases to be stable and becomes unsteady. At 65 < Re < 200, a long oscillating wake is formed behind the particle, which gradually becomes turbulent for 200 < Re < 1.5 x 105. Simultaneously, the separation point moves upstream according to the law [94]... 

Theoretical solution of the Navier-Stokes equation for prediction of the collision efficiency, E(Dp,dp), for the general raindrop-aerosol interaction case is a difficult undertaking. Complications arise because the aerosol size varies over orders of magnitude, and also because the large raindrop size results in complicated flow patterns (drop oscillations, wake creation, eddy shedding, etc.) Pruppacher and Klett (1997) present a critical overview of the theoretical attempts for the solution of the problem. A detailed discussion of these efforts is outside our scope. However, it is important to understand at least qualitatively the various processes involved. 

As the Reynolds number rises above about 40, the wake begins to display periodic instabiUties, and the standing eddies themselves begin to oscillate laterally and to shed some rotating fluid every half cycle. These still laminar vortices are convected downstream as a vortex street. The frequency at which they are shed is normally expressed as a dimensionless Strouhal number which, for Reynolds numbers in excess of 300, is roughly constant ... 

One of us examined the timely use of three factors (melatonin treatment, exposure to light, physical exercise) to hasten the resynchronization of the sleep-wake cycle in a group of elite sports competitors after a transmeridian flight across 12 time zones (Cardinali et al. 2002). Outdoor light exposure and physical exercise were used to cover symmetrically the phase delay and the phase advance portions of the phase-response curve. Melatonin taken at local bedtime helped to resynchronize the circadian oscillator to the new time. Individual actograms taken from sleep log data showed that all subjects became synchronized in their sleep to the local time in 24-48 h, well in advance of what would be expected in the absence of any treatment (Cardinali et al. 2002). More recently, a retrospective analysis of the data obtained from 134 normal volunteers flying the Buenos Aires - Sydney transpolar route in the past 9 years was published this further supports such a role for exogenous melatonin in resynchronization of sleep cycles (Cardinal et al. 2006). 

Mieda, M., Williams, S. C., Sinton, C. M. et al. (2004a). Orexin neurons function in an efferent pathway of a food-entrainable circadian oscillator in eliciting food-anticipatory activity and wakefulness. J. Neurosci. 24, 10493-501. 

Fig. 3a indicates that the bubble-rise velocity measured based on the displacement of the top surface of the bubble ( C/bt) quickly increases and approaches the terminal bubble rise velocity in 0.02 s. The small fluctuation of Ubt is caused by numerical instability. The bubble-rise velocity measured based on the displacement of the bottom surface of the bubble (Ubb) fluctuates significantly with time initially and converges to Ubt after 0.25 s. The overshooting of Ubb can reach 45-50 cm/s in Fig. 3a. The fluctuation of Ubb reflects the unsteady oscillation of the bubble due to the wake flow and shedding at the base of the bubble. Although the relative deviation between the simulation results of the 40 X 40 x 80 mesh and 100 x 100 x 200 mesh is notable, the deviation is insignificant between the results of the 80 x 80 x 160 mesh and those of the 100 X 100 x 200 mesh. The agreement with experiments at all resolutions is generally reasonable, although the simulated terminal bubble rise velocities ( 20 cm/s) are slightly lower than the experimental results (21 25 cm/s). A lower bubble-rise velocity obtained from the simulation is expected due to the no-slip condition imposed at the gas-liquid interface, and the finite thickness for the gas-liquid interface employed in the computational scheme.

Ret < 300 Unsteady laminar inertial flow in which laminar wake oscillations appear in the pores and vortices form at around Ret — 250 ... 

Circadian clock-controlled rhythms provide most organisms with an orchestrated temporal programme that allows for appropriate timing of physiology (i.e. blood pressure, hormonal levels) and behaviour (i.e. alertness, sleep-wake cycle). The mammalian central circadian pacemaker resides in the suprachiasmatic nucleus (SCN) of the brain (Weaver 1998). At the molecular level, the core oscillator driving the mammahan clock consists of interconnected autoregulatory... 

At Re = 130, a weak long-period oscillation appears in the tip of the wake (T2). Its amplitude increases with Re, but the flow behind the attached wake remains laminar to Re above 200. The amplitude of oscillation at the tip reaches 10% of the sphere diameter at Re = 270 (GIO). At about this Re, large vortices, associated with pulsations of the fluid circulating in the wake, periodically form and move downstream (S6). Vortex shedding appears to result from flow instability, originating in the free surface layer and moving downstream to affect the position of the wake tip (Rll, R12, S6). 

While other explanations have been proposed [e.g. (B6, El, H6)], secondary motions are most plausibly related to wake shedding. The onset of oscillations coincides with the onset of vortex shedding from the wake (El, E2, S5, W8). For high k or contaminated drops and bubbles, the onset of oscillations... 

Fig. 7.11 Wake configurations for drops in water (highly purified systems), reproduced from Winnikow and Chao (W8) with permission, (a) nonoscillating nitrobenzene drop = 0.280 cm, Re = 515 steady thread-like laminar wake (b) nonoscillating m-nitrotoluene drop 4 = 0.380 cm. Re = 688 steady thread accompanied by attached toroidal vortex wake (c) oscillating nitrobenzene drop 4 = 0.380 cm. Re = 686 central thread plus axisymmetric outer vortex sheet rolled inward to give inverted bottle shape of wake (d) oscillating nitrobenzene drop = 0.454 cm. Re = 775 vortex sheet in c has broken down to form vortex rings (e) oscillating nitrobenzene drop d = 0.490 cm. Re = 804 vortex rings in d now shed asymmetrically and the drop exhibits a rocking motion.

In practice, this model is oversimplified since the exciting wake shedding is by no means harmonic and is itself coupled with the shape oscillations and since Eq. (7-30) is strictly valid only for small oscillations and stationary fluid particles. However, this simple model provides a conceptual basis to explain certain features of the oscillatory motion. For example, the period of oscillation, after an initial transient (El), becomes quite regular while the amplitude is highly irregular (E3, S4, S5). Beats have also been observed in drop oscillations (D4). If /w and are of equal magnitude, one would expect resonance to occur, and this is one proposed mechanism for breakage of drops and bubbles (Chapter 12). 

The validity of the various simplifications has been the subject of considerable discussion [e.g. (A3, B2, H3, T4)]. Schoneborn (S4) showed that in the range where periodic wake shedding normally occurs (Re > 200 see Chapter 5), the effect of fluid oscillations depends on the relationship between the forced fluid frequency and the natural wake frequency ... 

Collection of cells in the anterior hypothalamus acting as a biological clock or oscillator that maintains the circadian rhythm of the sleep-wake cycle. 

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