Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Internal waves in sheared flows: Lower bound of the vorticity growth and propagation discontinuities in the parameter space

This study provides sufficient conditions for the temporal monotonic decay of enstrophy for two-dimensional perturbations traveling in the incompressible, viscous, plane Poiseuille, and Couette flows. Extension of Synge's procedure [J. L. Synge, Proc. Fifth Int. Congress Appl. Mech. 2, 326 (1938); Semicentenn. Publ. Am. Math. Soc. 2, 227 (1938)] to the initial-value problem allow us to find the region of the wave-number-Reynolds-number map where the enstrophy of any initial disturbance cannot grow. This region is wider than that of the kinetic energy. We also show that the parameter space is split into two regions with clearly distinct propagation and dispersion properties.

Turbulent superstructures in Rayleigh-Bénard convection

Turbulent Rayleigh-Bénard convection displays a large-scale order in the form of rolls and cells on lengths larger than the layer height once the fluctuations of temperature and velocity are removed. These turbulent superstructures are reminiscent of the patterns close to the onset of convection. Here we report numerical simulations of turbulent convection in fluids at different Prandtl number ranging from 0.005 to 70 and for Rayleigh numbers up to 10⁷. We identify characteristic scales and times that separate the fast, small-scale turbulent fluctuations from the gradually changing large-scale superstructures. The characteristic scales of the large-scale patterns, which change with Prandtl and Rayleigh number, are also correlated with the boundary layer dynamics, and in particular the clustering of thermal plumes at the top and bottom plates. Our analysis suggests a scale separation and thus the existence of a simplified description of the turbulent superstructures in geo- and astrophysical settings.

Heat and momentum transfer for magnetoconvection in a vertical external magnetic field

The scaling theory of Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)JFLSA70022-112010.1017/S0022112099007545] for turbulent heat and momentum transfer is extended to the magnetoconvection case in the presence of a (strong) vertical magnetic field. A comparison with existing laboratory experiments and direct numerical simulations in the quasistatic limit allows us to restrict the parameter space to very low Prandtl and magnetic Prandtl numbers and thus to reduce the number of unknown parameters in the model. Also included is the Chandrasekhar limit, for which the outer magnetic induction field B is large enough such that convective motion is suppressed and heat is transported by diffusion. Our theory identifies four distinct regimes of magnetoconvection that are distinguished by the strength of the outer magnetic field and the level of turbulence in the flow, respectively.