arXiv subjects

Marina Pausch

Publications and source records attributed to Marina Pausch.

2 recordsLinked to original sources

arXiv2015

Direct and noisy transitions in a model shear flow

The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. "Optimal" perturbations are distinguished as extrema of certain functionals, and different functionals give different optima. We here discuss the phase space structure of a 2-d simplified model of the transition to turbulence and discuss optimal perturbations with respect to three criteria: energy of the initial condition, energy dissipation of the initial condition and amplitude of noise in a stochastic transition. We find that the states that trigger the transition are different in the three cases, but show the same scaling with Reynolds number.

physics.flu-dyn↗

arXiv2014

Groebner basis methods for stationary solutions of a low-dimensional model for a shear flow

We use Groebner basis methods to extract all stationary solutions for the 9-mode shear flow model that is described in Moehlis et al, New J. Phys. 6, 54 (2004). Using rational approximations to irrational wave numbers and algebraic manipulation techniques we reduce the problem of determining all stationary states to finding roots of a polynomial of order 30. The coefficients differ by 30 powers of 10 so that algorithms for extended precision are needed to extract the roots reliably. We find that there are eight stationary solutions consisting of two distinct states that each appear in four symmetry-related phases. We discuss extensions of these results for other flows.

physics.flu-dyn↗