Experimental Investigation of Lagrangian Coherent Structures and Lobe Dynamics in Perturbed Rayleigh-Benard Convection

It is well known that Rayleigh-Benard convection with perturbations yields Lagrangian chaotic transport, and the mechanism of inducing chaotic transport has been numerically clarified by lobe dynamics [2]. On the other hand, the mechanism of such Lagrangian transport has not been enough studied by experiments. In our previous work [16], we made an experimental study to investigate the Lagrangian transport appeared in the two-dimensional Rayleigh-Benard convection by giving oscillation on the velocity fields and showed that there exist Lagrangian Coherent Structures (LCSs) which correspond to invariant manifolds of non-autonomous systems. We also showed that the LCSs entangle with each other around cell boundaries. In this paper, we further explore the global invariant structures of the perturbed Rayleigh-Benard convection by clarifying the details on the LCSs and explain how the fluid transport obeys lobe dynamics. Finally, we propose a novel Hamiltonian model for the two-dimensional perturbed Rayleigh-Benard convection that enables to elucidate the global structures detected by experiments.

Study on Mass Transports in Evolution of Separation Bubbles Using LCSs and Lobe Dynamics

The lobe dynamics andmass transport between separation bubble and main flow in flow over airfoil are studied in detail, using Lagrangian coherent structures (LCSs), in order to understand the nature of evolution of the separation bubble. For this problem, the transient flow over NACA0012 airfoil with low Reynolds number is simulated numerically by characteristic based split (CBS) scheme, in combination with dual time stepping. Then, LCSs and lobe dynamics are introduced and developed to investigate themass transport between separation bubble and main flow, from viewpoint of nonlinear dynamics. The results show that stable manifolds and unstable manifolds could be tangled with each other as time evolution, and the lobes are formed periodically to induce mass transport between main flow and separation bubble, with dynamic behaviors. Moreover, the evolution of the separation bubble depends essentially on the mass transport which is induced by lobes, ensuing energy and momentum transfers. As the results, it can be drawn that the dynamics of flow separation could be studied using LCSs and lobe dynamics, and could be controlled feasibly if an appropriate control is applied to the upstream boundary layer with high momentum.

Routes of Transport across the Antarctic Polar Vortex in the Southern Spring

Transport in the lower stratosphere over Antarctica has been studied in the past by means of several approaches, such as contour dynamics or Lyapunov exponents. This paper examines the problem by means of a new Lagrangian descriptor, which is referred to as the function M. The focus is on the southern spring of 2005, which allows for a comparison with previous analyses based on Lyapunov exponents. With the methodology based on the function M, a much sharper depiction of key Lagrangian features is achieved and routes of large-scale horizontal transport across the vortex edge are captured. These results highlight the importance of lobe dynamics as a transport mechanism across the Antarctic polar vortex.

Lagrangian Transport through an Ocean Front in the Northwestern Mediterranean Sea

With the tools of lobe dynamics, the authors analyze the structures present in the velocity field obtained from a numerical simulation of the surface circulation in the northwestern Mediterranean Sea. In particular, focus is placed on the North Balearic Front, the westernmost part of the transition zone between saltier and fresher waters in the western Mediterranean, which is here interpreted in terms of the presence of a semipermanent “Lagrangian barrier,” across which little transport occurs. Identified are relevant hyperbolic trajectories and their manifolds, and it is shown that the transport mechanism known as the turnstile, previously identified in abstract dynamical systems and simplified model flows, is also at work in this complex and realistic ocean flow. In addition, nonlinear dynamics techniques are shown to be powerful enough to identify the key geometric structures in this part of the Mediterranean. The construction also reveals the spatiotemporal routes along which this transport happens. Topological changes in that picture, which are associated with the crossing by eddies and may be interpreted as the breakdown of the front, are also observed during the simulation.