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. (2011). Effect of vapor bubbles on velocity fluctuations and dissipation rates in bubbly Rayleigh-Bénard convection. Physical Review E, 84(3), 036312-1/7. [036312]. DOI: 10.1103/PhysRevE.84.036312 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Numerical results for kinetic and thermal energy dissipation rates in bubbly Rayleigh-Bénard convection are reported. Bubbles have a twofold effect on the flow: on the one hand, they absorb or release heat to the surrounding liquid phase, thus tending to decrease the temperature differences responsible for the convective motion; but on the other hand, the absorbed heat causes the bubbles to grow, thus increasing their buoyancy and enhancing turbulence (or, more properly, pseudoturbulence) by generating velocity fluctuations. This enhancement depends on the ratio of the sensible heat to the latent heat of the phase change, given by the Jakob number, which determines the dynamics of the bubble growth.

Previous numerical studies have shown that the "ultimate regime of thermal convection" can be attained in a Rayleigh-Bénard cell when the kinetic and thermal boundary layers are eliminated by replacing the walls with periodic boundary conditions (homogeneous Rayleigh-Bénard convection). Then, the heat transfer scales like Nu ∼ Ra 1/2 and turbulence intensity as Re ∼ Ra 1/2 , where the Rayleigh number Ra indicates the strength of the driving force. However, experiments never operate in unbounded domains and it is important to understand how confinement might alter the approach to this ultimate regime. Here we consider homogeneous Rayleigh-Bénard convection in a laterally confined geometry -a small aspect-ratio vertical cylindrical cell -and show evidence of the ultimate regime as Ra is increased: In spite of the confinement and the resulting kinetic boundary layers, we still find Nu ∼ Re ∼ Ra 1/2 . The system supports exact solutions composed of modes of exponentially growing vertical velocity and temperature fields, with Ra as the critical parameter determining the properties of these modes. Counterintuitively, in the low Ra regime, or for very narrow cylinders, the numerical simulations are susceptible to these solutions which can dominate the dynamics and lead to very high and unsteady heat transfer. As Ra is increased, interaction between modes stabilizes the system, evidenced by the increasing homogeneity and reduced fluctuations in the r.m.s. velocity and temperature fields. We also test that physical results become independent of the periodicity length of the cylinder, a purely numerical parameter, as the aspect ratio is increased.

The axisymmetric collapse of a cylindrical air cavity in water follows a universal power law with logarithmic corrections. Nonetheless, it has been suggested that the introduction of a small azimuthal disturbance induces a long term memory effect, reflecting in oscillations which are no longer universal but remember the initial condition. In this work, we create non-axisymmetric air cavities by driving a metal disc through an initially-quiescent water surface and observe their subsequent gravity-induced collapse. The cavities are characterized by azimuthal harmonic disturbances with a single mode number m and amplitude a m . For small initial distortion amplitude (1 or 2 % of the mean disc radius), the cavity walls oscillate linearly during collapse, with nearly constant amplitude and increasing frequency. As the amplitude is increased, higher harmonics are triggered in the oscillations and we observe more complex pinch-off modes. For small amplitude disturbances we compare our experimental results with the model for the amplitude of the oscillations by Schmidt et al. (2009) and the model for the collapse of an axisymmetric impact-created cavity previously proposed by Bergmann et al. (2009b). By combining these two models we can reconstruct the three-dimensional shape of the cavity at any time before pinch-off. IntroductionThe pinch-off of an axisymmetric air cavity in water is characterized by a finite-time singularity. The kinetic energy of the flow is focused into a vanishing small volume with a velocity whose magnitude diverges as the pinch-off moment is approached. Several experimental and theoretical scenarios have been recently considered in the study of this problem: a bubble rising from a capillary . Depending on the case, the collapse might be initiated by surface tension, external flow, or hydrostatic pressure. However, irrespective of the cause, towards the end it is the inertia of the fluid that takes over in every case, and the collapse is accelerated as the radius of the cavity shrinks.The time it takes each of these systems to reach the inertial collapse regime varies by orders of magnitude . Hence, it was not an easy task to determine whether there was indeed a universal behaviour underlying this phenomenon. The first proposed model was a power law where the radius decreased proportionally to the arXiv:1109.5823v2 [physics.flu-dyn]

In viscous withdrawal, a converging flow imposed in an upper layer of viscous liquid entrains liquid from a lower, stably stratified layer. Using the idea that a thin tendril is entrained by a local straining flow, we propose a scaling law for the volume flux of liquid entrained from miscible liquid layers. A long-wavelength model including only local information about the withdrawal flow is degenerate, with multiple tendril solutions for one withdrawal condition. Including information about the global geometry of the withdrawal flow removes the degeneracy while introducing only a logarithmic dependence on the global flow parameters into the scaling law.Recent experiments on thermal convection with two layers of miscible liquids reveal several distinct regimesan overturn regime with violent mixing of the layers, a doming regime where the interface undulates, and a stratified regime where the convection is largely stable with thin tendrils or sheets of one liquid entrained within the other [1]. Analogous steady-state entrained structures arise in drainage flows [2,3], oil extraction [4], as well as viscous withdrawal of immiscible liquid layers, which occur in microfluidics [5], fiber coating [6] and encapsulation of biological cells [7]. Recent works exploring the connections between thermodynamic phase transitions and the topology transition that takes place at the onset of entrainment have noted that, in order for the entrained structure to be completely isolated from the large-scale flow dynamics, the shape of its base must be a power-law cusp [2,8,9,10]. Intriguingly, experiments [11,12] on miscible entrainment also seem to show a robust cusp-like shape at the base of long-lived tendrils (see Fig. 1). This suggests the entrained tendrils are isolated from the fluctuating, large-scale convection by the cusp-shaped base and are therefore able to remain stable over many convection cycles. If true, this may even explain why hot-spots can persist over many convection cycles in the Earth's mantle [12,13]. Motivated by these observations, we focus on the stratified regime in thermal convection of miscible layers and present a model that tests how the large-scale flow and topography anchor a thin cylindrical tendril.Because the large-scale flow is stabilized in the stratified regime, mixing between the layers is controlled by the volume flux of liquid entrained through the tendrils, Q 0 . Existing estimates of Q 0 assume that the velocity field inside the tendril is uniformly upwards, flowing at a characteristic convection speed [11,12,14]. However, recent particle-image-velocimetry (PIV) measurements within the base of an anchored tendril reveal a stagnation-point velocity field, one more appropriately described by a characteristic strain rate E (s −1 ) instead of a characteristic velocity scale [15]. Viscous withdrawal experiments on immiscible layers suggest how an interior stagnation point can arise [8]. When the effect of the entrainment penetrates deeply into the lower layer, a broad tendril forms with the int...