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1. The elastic Rayleigh drop

   https://doi.org/10.1039/C9SM01753D  

   Tamim, S. I.; Bostwick, J. B. (November 2019, Soft Matter)

   Bioprinting technologies rely on the formation of soft gel drops for printing tissue scaffolds and the dynamics of these drops can affect the process. A model is developed to describe the oscillations of a spherical gel drop with finite shear modulus, whose interface is held by surface tension. The governing elastodynamic equations are derived and a solution is constructed using displacement potentials decomposed into a spherical harmonic basis. The resulting nonlinear characteristic equation depends upon two dimensionless numbers, elastocapillary and compressibility, and admits two types of solutions, (i) spheroidal (or shape change) modes and (ii) torsional (rotational) modes. The torsional modes are unaffected by capillarity, whereas the frequency of shape oscillations depend upon both the elastocapillary and compressibility numbers. Two asymptotic dispersion relationships are derived and the limiting cases of the inviscid Rayleigh drop and elastic globe are recovered. For a fixed polar wavenumber, there exists an infinity of radial modes that each transition from an elasticity wave to a capillary wave upon increasing the elastocapillary number. At the transition, there is a qualitative change in the deformation field and a set of recirculation vortices develop at the free surface. Two special modes that concern volume oscillations and translational motion are characterized. A new instability is documented that reflects the balance between surface tension and compressibility effects due to the elasticity of the drop. 

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2. Confined Rayleigh-Taylor instability

   https://doi.org/10.1103/PhysRevFluids.7.110504  

   Alqatari, Samar; Videbæk, Thomas E.; Nagel, Sidney R.; Hosoi, Anette; Bischofberger, Irmgard (November 2022, Physical Review Fluids)
3. Exponentiated Strongly Rayleigh Distributions

   Mariet, Zelda; Sra, Suvrit; Jegelka, Stefanie (January 2018, Advances in neural information processing systems)
4. Thermal forcing and ‘classical’ and ‘ultimate’ regimes of Rayleigh–Bénard convection

   https://doi.org/10.1017/jfm.2019.118  

   Doering, Charles R. (June 2019, Journal of Fluid Mechanics)

   The fundamental challenge to characterize and quantify thermal transport in the strongly nonlinear regime of Rayleigh–Bénard convection – the buoyancy-driven flow of a horizontal layer of fluid heated from below – has perplexed the fluid dynamics community for decades. Rayleigh proposed controlling the temperature of thermally conducting boundaries in order to study the onset of convection, in which case vertical heat transport gauges the system response. Conflicting experimental results for ostensibly similar set-ups have confounded efforts to discriminate between two competing theories for how boundary layers and interior flows interact to determine transport through the convecting layer asymptotically far beyond onset. In a conceptually new approach, Bouillaut, Lepot, Aumaître and Gallet ( J. Fluid Mech. , vol. 861, 2019, R5) devised a procedure to radiatively heat a portion of the fluid domain bypassing rigid conductive boundaries and allowing for dissociation of thermal and viscous boundary layers. Their experiments reveal a new level of complexity in the problem suggesting that heat transport scaling predictions of both theories may be realized depending on details of the thermal forcing. 

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5. Linear theory of particulate Rayleigh-Bénard instability

   https://doi.org/10.1103/PhysRevFluids.6.083901  

   Prakhar, Suryansh; Prosperetti, Andrea (August 2021, Physical Review Fluids)