The geometry of passive tracer trajectories is studied in two different types of rotating turbulent flows; rotating Rayleigh-Bénard convection (RBC; experiments and direct numerical simulations) and rotating electromagnetically forced turbulence (EFT; experiments). This geometry is fully described by the curvature and torsion of trajectories and from these geometrical quantities we can subtract information on the typical flow structures at different rotation rates. Previous studies, focusing on non-rotating homogeneous isotropic turbulence (HIT), show that the probability density functions (PDFs) of curvature and torsion reveal pronounced power laws. However, the set-ups studied here involve inhomogeneous turbulence and in RBC the flow near the horizontal plates is definitely anisotropic. We want to investigate how the typical shapes of the curvature and torsion PDFs, including the pronounced scaling laws, are influenced by this level of anisotropy and inhomogeneity and how this effect changes with rotation. A first effect of rotation is observed as a shift of the curvature and torsion PDFs towards higher values in the case of RBC and towards lower values in the case of EFT. This shift is related to the length scale of typical vortical structures that decreases with rotation in RBC, but increases with rotation in EFT, explaining the opposite shifts of the curvature (and torsion) PDFs. A second remarkable observation is that in RBC the HIT scaling laws are always recovered, as long as the boundary layer (BL) is excluded. This suggests that these scaling laws are very robust and hold as long as we measure in the turbulent bulk. In the BL of the RBC cell, however, the scaling deviates from the HIT prediction for lower rotation rates. This scaling behavior is found to be consistent with the coupling between the boundary layer dynamics and the bulk flow, that changes under rotation. In particular, it is found that the active coupling of the Ekman-type boundary layer with the bulk flow suppresses anisotropy in the BL region for increasing rotation rates.

The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary dynamics during such a range expansion is little understood. Here, we investigate the evolutionary dynamics of populations consisting of many selectively neutral genotypes expanding on curved surfaces. Using a combination of individual-based off-lattice simulations, geometrical arguments, and lattice-based stepping-stone simulations, we characterise the effect of individual bumps on an otherwise flat surface. Compared to the case of a range expansion on a flat surface, we observe a transient relative increase, followed by a decrease, in neutral genetic diversity at the population front. In addition, we find that individuals at the sides of the bump have a dramatically increased expected number of descendants, while their neighbours closer to the bump's centre are far less lucky. Both observations can be explained using an analytical description of straight paths (geodesics) on the curved surface. Complementing previous studies of heterogeneous flat environments, the findings here build our understanding of how complex environments shape the evolutionary dynamics of expanding populations.

Background rotation causes different flow structures and heat transfer efficiencies in Rayleigh–Bénard convection (RBC). Three main regimes are known: rotation-unaffected, rotation-affected and rotation-dominated. It has been shown that the transition between rotation-unaffected and rotation-affected regimes is driven by the boundary layers. However, the physics behind the transition between rotation-affected and rotation-dominated regimes are still unresolved. In this study, we employ the experimentally obtained Lagrangian velocity and acceleration statistics of neutrally buoyant immersed particles to study the rotation-affected and rotation-dominated regimes and the transition between them. We have found that the transition to the rotation-dominated regime coincides with three phenomena; suppressed vertical motions, strong penetration of vortical plumes deep into the bulk and reduced interaction of vortical plumes with their surroundings. The first two phenomena are used as confirmations for the available hypotheses on the transition to the rotation-dominated regime while the last phenomenon is a new argument to describe the regime transition. These findings allow us to better understand the rotation-dominated regime and the transition to this regime.

In Rayleigh-Bénard convection (RBC) for fluids with Prandtl number P r 1, rotation beyond a critical (small) rotation rate is known to cause a sudden enhancement of heat transfer which can be explained by a change in the character of the boundary layer (BL) dynamics near the top and bottom plates of the convection cell. Namely, with increasing rotation rate, the BL signature suddenly changes from Prandtl-Blasius type to Ekman type. The transition from a constant heat transfer to an almost linearly increasing heat transfer with increasing rotation rate is known to be sharp and the critical Rossby number Roc occurs typically in the range 2.3 Roc 2.9 (for Rayleigh number Ra = 1.3 × 10 9 , P r = 6.7, and a convection cell with aspect ratio Γ = D H = 1, with D the diameter and H the height of the cell). The explanation of the sharp transition in the heat transfer points to the change in the dominant flow structure. At 1/Ro 1/Roc (slow rotation), the well-known large-scale circulation (LSC) is found: a single domain-filling convection roll made up of many individual thermal plumes. At 1/Ro 1/Roc (rapid rotation), the LSC vanishes and is replaced with a collection of swirling plumes that align with the rotation axis. In this paper, by numerically studying Lagrangian acceleration statistics, related to the small-scale properties of the flow structures, we reveal that this transition between these different dominant flow structures happens at a second critical Rossby number, Roc 2 ≈ 2.25 (different from Roc 1 ≈ 2.7 for the sharp transition in the Nusselt number N u; both values for the parameter settings of our present numerical study). When statistical data of Lagrangian tracers near the top plate are collected, it is found that the root-mean-square (rms) values and the kurtosis of the horizontal acceleration of these tracers show a sudden increase at Roc 2 . To better understand the nature of this transition we compute joint statistics of the Lagrangian velocity and acceleration of fluid particles and vertical vorticity near the top plate. It is found that for Ro 2.25 there is hardly any correlation between the vertical vorticity and extreme acceleration events of fluid particles. For Ro 2.25, on the other hand, vortical regions are much more prominent and extreme horizontal acceleration events are now correlated to large values of positive (cyclonic) vorticity. This suggests that the observed sudden transition in the acceleration statistics is related to thermal plumes with cyclonic vorticity developing in the Ekman BL and subsequently becoming mature and entering the bulk of the flow for Ro 2.25.

The dynamics of a population expanding into unoccupied habitat has been primarily studied for situations in which growth and dispersal parameters are uniform in space or vary in one dimension. Here, we study the influence of finite-sized individual inhomogeneities and their collective effect on front speed if randomly placed in a two-dimensional habitat. We use an individual-based model to investigate the front dynamics for a region in which dispersal or growth of individuals is reduced to zero (obstacles) or increased above the background (hotspots), respectively. In a regime where front dynamics is determined by a local front speed only, a principle of least time can be employed to predict front speed and shape. The resulting analytical solutions motivate an event-based algorithm illustrating the effects of several obstacles or hotspots. We finally apply the principle of least time to large heterogeneous environments by solving the Eikonal equation numerically. Obstacles lead to a slow-down that is dominated by the number density and width of obstacles, but not by their precise shape. Hotspots result in a speed-up, which we characterize as function of hotspot strength and density. Our findings emphasize the importance of taking the dimensionality of the environment into account.