arXiv subjects

Adrian van Kan

Publications and source records attributed to Adrian van Kan.

24 records · Page 2Linked to original sources

arXiv2021

Intermittency of three-dimensional perturbations in a point-vortex model

Three-dimensional (3D) instabilities on a (potentially turbulent) two-dimensional (2D) flow are still incompletely understood, despite recent progress. Here, based on known physical properties of such 3-D instabilities, we propose a simple, energy-conserving model describing this situation. It consists of a 2D point-vortex flow coupled to localized 3D perturbations (ergophages), such that ergophages can gain energy by altering vortex-vortex distances through an induced divergent velocity field, thus decreasing point-vortex energy. We investigate the model in three distinct stages of evolution: (i) The linear regime, where the ergophage amplitude grows or decays exponentially on average, with a randomly fluctuating instantaneous growth rate. The growth rate has a small auto-correlation time, and follows a probability distribution featuring a power-law tail with exponent between -2 and -5/3 (up to a cut-off), depending on the point-vortex base flow. Consequently, the logarithmic ergophage amplitude performs a free Lévy flight. (ii) The passive-nonlinear regime of the model, where the 2D flow evolves independently of the ergophage amplitudes, which saturate by non-linear self-interactions without affecting the 2D flow. In this regime the system exhibits a new type of on-off intermittency that we name Lévy on-off intermittency, and which we study in a companion paper. We compute the bifurcation diagram for the mean and variance of the perturbation amplitude, as well as the probability density of the perturbation amplitude. (iii) Finally, we characterize the the fully nonlinear regime, where ergophages feed back on the 2D flow, and study how the vortex temperature is altered by the interaction with ergophages. It is shown that when the amplitude of the ergophages is sufficiently large, the 2D flow saturates to a zero-temperature state. Given the limitations of existing theories ...

physics.flu-dyn↗

arXiv2020

Critical transition in fast-rotating turbulence within highly elongated domains

We study rapidly rotating turbulent flows in a highly elongated domain using an asymptotic expansion at simultaneously low Rossby number $Ro\ll 1$ and large domain height compared to the energy injection scale, $h=H/\ell_{in}\gg 1$. We solve the resulting equations using an extensive set of direct numerical simulations for different parameter regimes. As the parameter $λ= (h Ro)^{-1}$ is increased beyond a threshold $λ_c$, a transition is observed from a state without an inverse energy cascade to a state with an inverse energy cascade. } For large Reynolds number and large horizontal box size, we provide evidence for criticality of the transition in terms of the large-scale energy dissipation rate.

physics.flu-dyn↗

arXiv2020

Role of the forcing dimensionality in thin-layer turbulent energy cascades

We investigate the transition from forward to inverse energy cascade in turbulent flows in thin layers, varying the functional form of the forcing and the thickness of the layer. We show that, as the forcing function becomes more three-dimensional, the inverse cascade is suppressed and the critical height hc, where the transition occurs, is decreased. We study the dependence of this critical height on a parameter r which measures the dimensionality of the forcing and thus construct a phase space diagram in the parameter space r-h. We discuss the effect of Reynolds number and domain size.

physics.flu-dyn↗

arXiv2019

Rare transitions to thin-layer turbulent condensates

Turbulent flows in a thin layer can develop an inverse energy cascade leading to spectral condensation of energy when the layer height is smaller than a certain threshold. These spectral condensates take the form of large-scale vortices in physical space. Recently, evidence for bistability was found in this system close to the critical height: depending on the initial conditions, the flow is either in a condensate state with most of the energy in the two-dimensional (2-D) large-scale modes, or in a three-dimensional (3-D) flow state with most of the energy in the small-scale modes. This bistable regime is characterised by the statistical properties of random and rare transitions between these two locally stable states. Here, we examine these statistical properties in thin-layer turbulent flows, where the energy is injected by either stochastic or deterministic forcing. To this end, by using a large number of direct numerical simulations (DNS), we measure the decay time $τ_d$ of the 2-D condensate to 3-D flow state and the build-up time $τ_b$ of the 2-D condensate. We show that both of these times $τ_d,τ_b$ follow an exponential distribution with mean values increasing faster than exponentially as the layer height approaches the threshold. We further show that the dynamics of large-scale kinetic energy may be modeled by a stochastic Langevin equation. From time-series analysis of DNS data, we determine the effective potential that shows two minima corresponding to the 2-D and 3-D states when the layer height is close to the threshold.

physics.flu-dyn↗

arXiv2019

Condensates in thin-layer turbulence

We examine the steady state of turbulent flows in thin layers using direct numerical simulations. It is shown that when the layer thickness is smaller than a critical height, an inverse cascade arises which leads to the formation of a steady state condensate where most of the energy is concentrated in the largest scale of the system. For layers of thickness smaller than a second critical height, the flow at steady state becomes exactly two-dimensional. The amplitude of the condensate is studied as a function of layer thickness and Reynolds number. Bi-stability and intermittent bursts are found close to the two critical points. The results are interpreted based on a mean field three-scale model that reproduces some of the basic features of the numerical results.

physics.flu-dyn↗

arXiv2016

Constrained basin stability for studying transient phenomena in dynamical systems

Transient dynamics are of large interest in many areas of science. Here, a generalization of basin stability (BS) is presented: constrained basin stability (CBS) that is sensitive to various different types of transients arising from finite size perturbations. CBS is applied to the paradigmatic Lorenz system for uncovering nonlinear precursory phenomena of a boundary crisis bifurcation. Further, CBS is used in a model of the Earth's carbon cycle as a return time-dependent stability measure of the system's global attractor. Both case studies illustrate how CBS's sensitivity to transients complements BS in its function as an early warning signal and as a stability measure. CBS is broadly applicable in systems where transients matter, from physics and engineering to sustainability science. Thus, CBS complements stability analysis with BS as well as classical linear stability analysis and will be a useful tool for many applications.

nlin.CD↗