To explore the physics of large-scale flows in solar-like stars, we perform 3D anelastic simulations of rotating convection for global models with stratification resembling the solar interior. The numerical method is based on an implicit large-eddy simulation approach designed to capture effects from non-resolved small scales. We obtain two regimes of differential rotation, with equatorial zonal flows accelerated either in the direction of rotation (solar-like) or in the opposite direction (anti-solar). While the models with the solar-like differential rotation tend to produce multiple cells of meridional circulation, the models with anti-solar differential rotation result in only one or two meridional cells. Our simulations indicate that the rotation and large-scale flow patterns critically depend on the ratio between buoyancy and Coriolis forces. By including a subadiabatic layer at the bottom of the domain, corresponding to the stratification of a radiative zone, we reproduce a layer of strong radial shear similar to the solar tachocline.Similarly, enhanced superadiabaticity at the top results in a near-surface shear layer located mainly at lower latitudes. The models reveal a latitudinal entropy gradient localized at the base of the convection zone and in the stable region, which however does not propagate across the convection zone. In consequence, baroclinicity effects remain small and the rotation iso-contours align in cylinders along the rotation axis. Our results confirm the alignment of large convective cells along the rotation axis in the deep convection zone, and suggest that such "banana-cell" pattern can be hidden beneath the supergranulation layer.

We report the use of focused acoustic beams to eject discrete droplets of controlled diameter and velocity from a free-liquid surface. No nozzles are involved. Droplet formation has been experimentally demonstrated over the frequency range of 5–300 MHz, with corresponding droplet diameters from 300 to 5 μm. The physics of droplet formation is essentially unchanged over this frequency range. For acoustic focusing elements having similar geometries, droplet diameter has been found to scale inversely with the acoustic frequency. A simple model is used to obtain analytical expressions for the key parameters of droplet formation and their scaling with acoustic frequency. Also reported is a more detailed theory which includes the linear propagation of the focused acoustic wave, the coupling of the acoustic fields to the initial surface velocity potential, and the subsequent dynamics of droplet formation. This latter phase is modeled numerically as an incompressible, irrotational process using a boundary integral vortex method. For simulations at 5 MHz, this numerical model is very successful in predicting the key features of droplet formation.

Nonlinear oscillations and other motions of large axially symmetric liquid drops in zero gravity are studied numerically by a boundary-integral method. The effect of small viscosity is included in the computations by retaining first-order viscous terms in the normal stress boundary condition. This is accomplished by making use of a partial solution of the boundary-layer equations which describe the weak vortical surface layer. Small viscosity is found to have a relatively large effect on resonant-mode coupling phenomena.

A microburst can be modelled by releasing a volume of fluid that is slightly heavier than the ambient fluid, allowing it to fall onto a horizontal surface. Vorticity develops on the sides of this parcel as it descends and causes it to roll up into a turbulent vortex ring which impinges on the ground. Such a model exhibits many of the features of naturally occurring microbursts which are a hazard to aviation. In this paper this model is achieved experimentally by releasing a volume of salt water into fresh water from a cylindrical dispenser. When care is taken with the release the spreading rate of the surface outflow is measurable and quite repeatable despite the fact that the flow is turbulent. An elementary numerical approximation to this model, based on inviscid vortex dynamics, has also been developed. A scaling law is proposed which allows experiments with different fluid densities to be compared with each other and with the numerical results. More importantly the scaling law allows us to compare the model results with real microbursts.

Computations of finite-amplitude, spatially periodic wave growth on a cylindrical jet have been carried out using a boundary integral method. The initial wave growth is in agreement with Rayleigh’s linear theory. When followed to completion these waves pinch off large drops separated by smaller satellite drops (spherules) that decrease in size with decreasing wavelength. The computed sizes of both drops and satellites agree with experiment. It is found that satellites will form for all unstable wave numbers. The small satellites that are computed at wave numbers near the critical wave number were not predicted by near-linear analysis but are observed in experimental photographs of jet breakup. Computation of the collapse of elongated satellites shows short waves propagating on their surfaces.