Unidirectional Modes Induced by Nontraditional Coriolis Force in Stratified Fluids.

Using topology, we unveil the existence of new unidirectional modes in compressible rotating stratified fluids. We relate their emergence to the breaking of time-reversal symmetry by rotation and vertical mirror symmetry by stratification and gravity. We stress the role of the Coriolis force's nontraditional part, induced by a rotation field tangent to the surface. In contrast with horizontally trapped equatorial waves induced by the traditional component of the Coriolis force perpendicular to the surface, we find vertically trapped modes that propagate along interfaces between regions with distinct stratification properties. We show that such modes are generalized atmospheric Lamb waves whose direction of propagation can be selected by the nontraditional component of the Coriolis force.

Periodicity Disruption of a Model Quasibiennial Oscillation of Equatorial Winds.

The quasibiennial oscillation (QBO) of equatorial winds on Earth is the clearest example of the spontaneous emergence of a periodic phenomenon in geophysical fluids. In recent years, observations have revealed intriguing disruptions of this regular behavior, and different QBO-like regimes have been reported in a variety of systems. Here, we show that part of the variability in mean-flow reversals can be attributed to the intrinsic dynamics of wave-mean-flow interactions in stratified fluids. Using a constant-in-time monochromatic wave forcing, bifurcation diagrams are mapped for a hierarchy of simplified models of the QBO, ranging from a quasilinear model to fully nonlinear simulations. The existence of new bifurcations associated with faster and shallower flow reversals, as well as a quasiperiodic route to chaos are reported in these models. The possibility for periodicity disruptions is investigated by probing the resilience of regular wind reversals to external perturbations.

Topological origin of equatorial waves.

Topology sheds new light on the emergence of unidirectional edge waves in a variety of physical systems, from condensed matter to artificial lattices. Waves observed in geophysical flows are also robust to perturbations, which suggests a role for topology. We show a topological origin for two well-known equatorially trapped waves, the Kelvin and Yanai modes, owing to the breaking of time-reversal symmetry by Earth's rotation. The nontrivial structure of the bulk Poincaré wave modes encoded through the first Chern number of value 2 guarantees the existence of these waves. This invariant demonstrates that ocean and atmospheric waves share fundamental properties with topological insulators and that topology plays an unexpected role in Earth's climate system.

Statistical ensemble inequivalence and bicritical points for two-dimensional flows and geophysical flows.

A theoretical description for the equilibrium states of a large class of models of two-dimensional and geophysical flows is presented. A statistical ensemble equivalence is found to exist generically in these models, related to the occurrence of peculiar phase transitions in the flow topology. The first example of a bicritical point (a bifurcation from a first toward two second order phase transitions) in the context of systems with long-range interactions is reported. Academic ocean models, the Fofonoff flows, are studied in the perspective of these results.

Is turbulent mixing a self-convolution process?

Experimental results for the evolution of the probability distribution function (PDF) of a scalar mixed by a turbulent flow in a channel are presented. The sequence of PDF from an initial skewed distribution to a sharp Gaussian is found to be nonuniversal. The route toward homogeneization depends on the ratio between the cross sections of the dye injector and the channel. In connection with this observation, advantages, shortcomings, and applicability of models for the PDF evolution based on a self-convolution mechanism are discussed.

Synchronization and coordination of sequences in two neural ensembles.

There are many types of neural networks involved in the sequential motor behavior of animals. For high species, the control and coordination of the network dynamics is a function of the higher levels of the central nervous system, in particular the cerebellum. However, in many cases, especially for invertebrates, such coordination is the result of direct synaptic connections between small circuits. We show here that even the chaotic sequential activity of small model networks can be coordinated by electrotonic synapses connecting one or several pairs of neurons that belong to two different networks. As an example, we analyzed the coordination and synchronization of the sequential activity of two statocyst model networks of the marine mollusk Clione. The statocysts are gravity sensory organs that play a key role in postural control of the animal and the generation of a complex hunting motor program. Each statocyst network was modeled by a small ensemble of neurons with Lotka-Volterra type dynamics and nonsymmetric inhibitory interactions. We studied how two such networks were synchronized by electrical coupling in the presence of an external signal which lead to winnerless competition among the neurons. We found that as a function of the number and the strength of connections between the two networks, it is possible to coordinate and synchronize the sequences that each network generates with its own chaotic dynamics. In spite of the chaoticity, the coordination of the signals is established through an activation sequence lock for those neurons that are active at a particular instant of time.