The collective effect of finite-sized inhomogeneities on the spatial spread of populations in two dimensions.

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.

Statistical properties of thermally expandable particles in soft-turbulence Rayleigh-Bénard convection.

The dynamics of inertial particles in Rayleigh-Bénard convection, where both particles and fluid exhibit thermal expansion, is studied using direct numerical simulations (DNS) in the soft-turbulence regime. We consider the effect of particles with a thermal expansion coefficient larger than that of the fluid, causing particles to become lighter than the fluid near the hot bottom plate and heavier than the fluid near the cold top plate. Because of the opposite directions of the net Archimedes' force on particles and fluid, particles deposited at the plate now experience a relative force towards the bulk. The characteristic time for this motion towards the bulk to happen, quantified as the time particles spend inside the thermal boundary layers (BLs) at the plates, is shown to depend on the thermal response time, [Formula: see text], and the thermal expansion coefficient of particles relative to that of the fluid, [Formula: see text]. In particular, the residence time is constant for small thermal response times, [Formula: see text], and increasing with [Formula: see text] for larger thermal response times, [Formula: see text]. Also, the thermal BL residence time is increasing with decreasing K. A one-dimensional (1D) model is developed, where particles experience thermal inertia and their motion is purely dependent on the buoyancy force. Although the values do not match one-to-one, this highly simplified 1D model does predict a regime of a constant thermal BL residence time for smaller thermal response times and a regime of increasing residence time with [Formula: see text] for larger response times, thus explaining the trends in the DNS data well.

Velocity and acceleration statistics in rapidly rotating Rayleigh-Bénard convection.

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.

Directional change of tracer trajectories in rotating Rayleigh-Bénard convection.

The angle of directional change of tracer trajectories in rotating Rayleigh-Bénard convection is studied as a function of the time increment τ between two instants of time along the trajectories, both experimentally and with direct numerical simulations. Our aim is to explore the geometrical characterization of flow structures in turbulent convection in a wide range of timescales and how it is affected by background rotation. We find that probability density functions (PDFs) of the angle of directional change θ(t,τ) show similar behavior as found in homogeneous isotropic turbulence, up to the timescale of the large-scale coherent flow structures. The scaling of the averaged (over particles and time) angle of directional change Θ(τ)=〈|θ(t,τ)|〉 with τ shows a transition from the ballistic regime [Θ(τ)∼τ^{c} with c=1] for τ≲τ_{η}, with τ_{η} the Kolmogorov timescale, to a scaling with smaller exponent c for τ_{η}≲τ≲T_{L}, with T_{L} the Lagrangian integral timescale. This scaling exponent is approximately constant in the weakly rotating regime (Rossby number Ro≳2.5) and is decreasing for increasing rotation rates when Ro≲2.5. We show that this trend in the scaling exponent is related with the large-scale coherent structures in the flow; the large-scale circulation for Ro≳2.5 and vertically aligned vortices emerging from the boundary layers (BLs) near the top and bottom plates and penetrating into the bulk for Ro≲2.5. In the viscous BLs, the PDFs of θ(t,τ) and scaling properties of Θ(τ) are in general different from those measured in the bulk and depend on the type of boundary layer, in particular whether the BL is of Prandtl-Blasius type (Ro≳2.5) or of Ekman type (Ro≲2.5). When it is of Ekman type, a stronger dynamic coupling exists between the BL and the bulk of the flow, resulting in similar scaling exponents in BL and bulk.

Transitions in turbulent rotating convection: A Lagrangian perspective.

Using measurements of Lagrangian acceleration in turbulent rotating convection and accompanying direct numerical simulations, we show that the transition between turbulent states reported earlier [e.g., S. Weiss et al., Phys. Rev. Lett. 105, 224501 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.224501] is a boundary-layer transition between the Prandtl-Blasius type (typical of nonrotating convection) and Ekman type.