Philip Yecko | Searcharxiv

arXiv2011

Set-based corral control in stochastic dynamical systems: Making almost invariant sets more invariant

We consider the problem of stochastic prediction and control in a time-dependent stochastic environment, such as the ocean, where escape from an almost invariant region occurs due to random fluctuations. We determine high-probability control-actuation sets by computing regions of uncertainty, almost invariant sets, and Lagrangian Coherent Structures. The combination of geometric and probabilistic methods allows us to design regions of control that provide an increase in loitering time while minimizing the amount of control actuation. We show how the loitering time in almost invariant sets scales exponentially with respect to the control actuation, causing an exponential increase in loitering times with only small changes in actuation force. The result is that the control actuation makes almost invariant sets more invariant.

nlin.AO↗

arXiv2004

Transient growth and instability in rotating boundary layers

The three-dimensional temporal instability of rotating boundary layer flows is investigated by computing classical normal modes as well as by evaluating the transient growth of optimal disturbances. The flows examined are the rotating Blasius (RB) and the rotating asymptotic suction layers (RAS), with the rotation axis normal to the basic flow plane. In agreement with an inviscid criterion, streamwise unstable modes are found in both flow cases for anti-cyclonic rotation: at high Reynolds numbers, one obtains the Rossby number unstable range 0<1/Ro<0.57 for RB, or 0<1/Ro<1 for RAS. Critical Reynolds and Rossby numbers are also determined in both instances. Moreover the dependence of transient growth with respect to wavenumbers, Rossby and Reynolds numbers is presented for both cyclonic and anti-cyclonic régimes. In particular, the {\it peak} transient growth is computed for a wide range of parameter values within the cyclonic regime and is shown to be reduced by rotation. A scaling analysis with respect to the Reynolds number is performed showing that the standard Re^2 scaling is recovered only at very weak rotation. Optimal disturbances resemble oblique vortices. At weak rotation, they are almost streamwise vortices though their structure departs from the classical non-rotating case. Strong rotation imposes two-dimensionality and the optimal disturbances vary weakly in the spanwise direction and exhibit growth by the Orr mechanism.

physics.flu-dyn↗

arXiv1999

Turbulent Convection in Pulsating Stars

We review recent results of stellar pulsation modelling that show that even very simple one-dimensional models for time dependent turbulent energy diffusion and convection provide a substantial improvement over purely radiative models.

astro-ph↗