It is known that the pitchfork bifurcation of Kelvin-Helmholtz instability occurring at minimum gradient Richardson number Ri(m) similar or equal to 1/4 in viscous stratified shear flows can be subcritical or supercritical depending on the value of the Pra ...
Close to a saddle-node bifurcation, when two invariant solutions collide and disappear, the behavior of a dynamical system can closely resemble that of a solution which is no longer present at the chosen parameter value. For bifurcating equilibria in low-d ...
The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoidal time dependence. For a limited number of dynamical systems, it is possible ...
It has recently been speculated that long-time average quantities of hyperchaotic dissipative systems may be approximated by weighted sums over unstable invariant tori embedded in the attractor, analogous to equivalent sums over periodic orbits, which are ...
One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's chaotic attractor. The significance of zero-dimensional unstable fixed points ...
Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier-Stokes equations, bas ...
In dynamical systems governed by differential equations, a guarantee that trajectories emanating from a given set of initial conditions do not enter another given set can be obtained by constructing a barrier function that satisfies certain inequalities on ...
The breaking of internal gravity waves in the abyssal ocean is thought to be responsible for much of the mixing necessary to close oceanic buoyancy budgets. The exact mechanism by which these waves break down into turbulence remains an active area of resea ...
A Koopman decomposition of a complex system leads to a representation in which nonlinear dynamics appear to be linear. The existence of a linear framework with which to analyze nonlinear dynamical systems brings new strategies for prediction and control, w ...
