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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 ...
Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatiotemporal systems including fluid turbulence is supported by nonchaotic, exactly recurring time-periodic solutions of the governing equations ...
Predicting particle transport in turbulent flows has a plethora of applications, some of which are: the transport of atmospheric aerosols, the deposition of blood cells in the arteries of human bodies and the atomization of fuel droplets in combustion cham ...
Multiscale phenomena are involved in countless problems in fluid mechanics. Coating flows are known to exhibit a broad variety of patterns, such as wine tears in a glass and dripping of fresh paint applied on a wall. Coating flows are typically modeled und ...
Thermal convection in an inclined layer between two parallel walls kept at different fixed temperatures is studied for fixed Prandtl number . Depending on the angle of inclination and the imposed temperature difference, the flow exhibits a large variety of ...
Spatiotemporally chaotic dynamics of transitional plane Couette flow may give rise to regular turbulent-laminar stripe patterns with a large-scale pattern wavelength and an oblique orientation relative to the laminar flow direction. A recent dynamical syst ...
Flows of gases and liquids interacting with solid objects are often turbulent within a thin boundary layer. As energy dissipation and momentum transfer are dominated by the boundary layer dynamics, many engineering applications can benefit from an improved ...
The use of low-dimensional dynamical systems as reduced models for plasma dynamics is useful as solving an initial value problem requires much less computational resources than fluid simulations. We utilize a data-driven modeling approach to identify a red ...
When laminar shear flows in large wall-bounded domains transition to turbulence, the flow exhibits spatio-temporally chaotic dynamics. Despite its chaotic dynamics, the flow may self-organize into characteristic spatially periodic patterns of unknown origi ...
Steep mountain streams exhibit shallow waters with roughness elements such as stones and pebbles that are comparable in size to flow depth. Owing to the difficulty in measuring fluid velocities at the interface, i.e., from the rough permeable bed to the fr ...