We use direct numerical simulations to study convection in rotating Rayleigh-B & eacute;nard convection in horizontally confined geometries of a given aspect ratio, with the walls held at fixed temperatures. We show that this arrangement is unconditionally unstable to flow that takes the form of wall-adjacent convection rolls. For wall temperatures close to the temperatures of the upper or lower boundaries, we show that the base state undergoes a Hopf bifurcation to a state comprised of spatiotemporal oscillations - 'wall modes' - precessing in a retrograde direction. We study the saturated nonlinear state of these modes, and show that the velocity boundary conditions at the upper and lower boundaries are crucial to the formation and propagation of the wall modes: asymmetric velocity boundary conditions at the upper and lower boundaries can lead to prograde wall modes, while stress-free boundary conditions at both walls can lead to wall modes that have no preferred direction of propagation.

We study the orientation dynamics of two-dimensional concavo-convex solid bodies that are denser than the fluid through which they fall under gravity. We show that the orientation dynamics of the body, quantified in terms of the angle phi relative to the hori-zontal, undergoes a transcritical bifurcation at a Reynolds number Re(1c) and a subcritical pitchfork bifurcation at a Reynolds number Re(2) c . For Re < Re(1) c , the concave-downwards orientation of phi = 0 is unstable and bodies overturn into the phi = pi orientation. For Re(1) c < Re < Re(2) c , the falling body has two stable equilibria at phi = 0 and phi = pi for steady descent. For Re > Re(2) c , the concave-downwards orientation of phi = 0 is again unstable and bodies that start concave-downwards exhibit overstable oscillations about the unstable fixed point, eventually tumbling into the stable phi = pi orientation. The Re(2) c approximate to 15 at which the subcritical pitchfork bifurcation occurs is distinct from the Re for the onset of vortex shedding, which causes the phi = pi equilibrium to also become unstable, with bodies fluttering about phi = pi. The complex orientation dynamics of irregularly shaped bodies evidenced here are relevant in a wide range of settings, from the tumbling of hydrometeors to the settling of mollusk shells.

We study entrainment in dry thermals in neutrally and unstably stratified ambients, and moist thermals in dry-neutrally stratified ambients using direct numerical simulations. We find, in agreement with results of Lecoanet and Jeevanjee [J. Atmos. Sci. 76, 3785 (2019)], that turbulence plays a minor role in entrainment in dry thermals in a neutral ambient for Reynolds numbers Re < 104. We then show that the net entrainment rate increases when the buoyancy of the thermals increases, either by condensation heating or because of an unstably stratified ambient. This is in contrast with the findings of Morrison et al. [J. Atmos. Sci. 78, 797 (2021)]. We also show that the role of turbulence is greater in these cases than in dry thermals and, significantly, that the combined action of condensation heating and turbulence creates intense small-scale vorticity, destroying the coherent vortex ring that is seen in dry and moist laminar thermals. These findings suggest that fully resolved simulations at Reynolds numbers significantly larger than the mixing transition Reynolds number Re = 104 are necessary to understand the role of turbulence in the entrainment in growing cumulus clouds, which consist of a series of thermals rising and decaying in succession.

We study, by direct numerical simulations in two and three dimensions, the instability caused by the settling and evaporation of water droplets out of a cloudy layer saturated with vapor into a dry subcloud ambient under conditions where mammatus clouds were shown to form but with the addition of background shear. We show that shear changes the type of cloud formation qualitatively from mammatus-like to a newly identified cloud type called asperitas. Intermediate levels of shear are shown to be needed. Shear suppresses the growth of small-scale perturbations, giving rise to smooth, long-lasting structures and smaller rates of mixing. Three-dimensionality is shown to make a qualitative difference, unlike in mammatus clouds. We also show that under non-cloud-like conditions, the instability can be very different.

We use well-resolved numerical simulations to study the combined effects of buoyancy, pressure-driven shear and rotation on the melt rate and morphology of a layer of pure solid overlying its liquid phase in three dimensions at a Rayleigh number Ra = 1.25 x 10(5) . During thermal convection, we find that the rate of melting of the solid phase varies non-monotonically with the strength of the imposed shear flow. In the absence of rotation, depending on whether buoyancy or shear dominates the flow, we observe either domes or ridges aligned in the direction of the shear flow, respectively. Furthermore, we show that the geometry of the phase boundary has important effects on the magnitude and evolution of the heat flux in the liquid layer. In the presence of rotation, the strength of which is characterized by the Rossby number, Ro, we observe that for Ro = O(1), the mean flow in the interior is perpendicular to the direction of the constant horizontal applied pressure gradient. As the magnitude of this pressure gradient increases, the geometry of solid-liquid interface evolves from the voids characteristic of melting by rotating convection, to grooves oriented perpendicular or obliquely to the direction of the pressure gradient.

We study the role of phase change and thermal noise in particle transport in turbulent flows. We employ a toy model to extract the main physics: Condensing droplets are modelled as heavy particles which grow in size, the ambient flow is modelled as a two-dimensional Taylor-Green flow consisting of an array of vortices delineated by separatrices, and thermal noise are modelled as uncorrelated Gaussian white noise. In general, heavy inertial particles are centrifuged out of regions of high vorticity and into regions of high strain. In cellular flows, we find, in agreement with earlier results, that droplets with Stokes numbers smaller than a critical value, St < St(cr) remain trapped in the vortices in which they are initialized, while larger droplets move ballistically away from their initial positions by crossing separatrices. We independently vary the Peclet number Pe characterizing the amplitude of thermal noise and the condensation rate 11 to study their effects on the critical Stokes number for droplet trapping, as well as on the final states of motion of the droplets. We find that the imposition of thermal noise, or of a finite condensation rate, allows droplets of St < St(cr). to leave their initial vortices. We find that the effects of thermal noise become negligible for growing droplets and that growing droplets achieve ballistic motion when their Stokes numbers become O(1). We also find an intermediate regime prior to attaining the ballistic state, in which droplets move diffusively away from their initial vortices in the presence of thermal noise.

This article describes the dynamics of small inertial particles centrifuging out of a single vortex. It shows the importance of caustics formation in the vicinity of a single vortex: both for particle collisions and void formation. From these single-vortex studies we provide estimates of the role of caustics in high Reynolds number turbulence, and in the case of clouds, estimate how they may help in rain initiation by bridging the droplet-growth bottleneck. We briefly describe how the Basset-Boussinesq history force may be calculated by a method which does not involve huge memory costs, and we provide arguments for its possible importance for droplets in turbulence. We discuss how phase change could render cloud turbulence fundamentally different from turbulence in other situations.

We study numerically the melting of a horizontal layer of a pure solid above a convecting layer of its fluid rotating about the vertical axis. In the rotating regime studied here, with Rayleigh numbers of order , convection takes the form of columnar vortices, the number and size of which depend upon the Ekman and Prandtl numbers, as well as the geometry - periodic or confined. As the Ekman and Rayleigh numbers vary, the number and average area of vortices vary in inverse proportion, becoming thinner and more numerous with decreasing Ekman number. The vortices transport heat to the phase boundary, thereby controlling its morphology characterized by the number and size of the voids formed in the solid, and the overall melt rate, which increases when the lower boundary is governed by a no-slip rather than a stress-free velocity boundary condition. Moreover, the number and size of voids formed are relatively insensitive to the Stefan number, here inversely proportional to the latent heat of fusion. For small values of the Stefan number, the convection in the fluid reaches a slowly evolving geostrophic state wherein columnar vortices transport nearly all the heat from the lower boundary to melt the solid at an approximately constant rate. In this quasi-steady state, we find that the Nusselt number, characterizing the heat flux, co-varies with the interfacial roughness, for all the flow parameters and Stefan numbers considered here. This confluence of processes should influence the treatment of moving boundary problems, particularly those in astrophysical and geophysical problems where rotational effects are important.