The motion and the action of microbubbles in homogeneous and isotropic turbulence are investigated through (three-dimensional) direct numerical simulations of the NavierStokes equations and applying the Lagrangian approach to track the bubble trajectories. The forces acting on the bubbles are added mass, drag, lift, and gravity. The bubbles are found to accumulate in vortices, preferably on the side with downward velocity. This effect, mainly caused by the lift force, leads to a reduced average bubble rise velocity. Once the reaction of the bubbles on the carrier flow is embodied using a point-force approximation, an attenuation of the turbulence on large scales and an extra forcing on small scales is found.
The ultimate regime of thermal convection, the so called Kraichnan regime (R. H. Kraichnan, Phys. Fluids 5, 1374 (1962)), hitherto has been elusive. Here, numerical evidence for that regime is presented by performing simulations of the bulk of turbulence only, eliminating the thermal and kinetic boundary layers and replacing them by periodic boundary conditions.
In this paper we analyze the numerical solution by a collocation method of a hypersingular
integral equation resulting from the boundary value problem related to an infinite strip containing an edge crack perpendicular
to its boundaries. Moreover, we show convergence results as well as numerical tests in a case of interest in fracture mechanics
