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Nonlinear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure

Journal Paper
Wienkers, Aaron F. & Ogilvie, G. I.
Monthly Notices of the Royal Astronomical Society, Volume 477, Issue 4, July 2018, Pages 4838–4855
Publication year: 2018

Abstract

Non-linear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce exponentially growing eccentricities at certain mean-motion resonances. However, the details of an efficient saturation mechanism balancing this growth still are not fully understood. This paper develops a local numerical model for an eccentric quasi-axisymmetric shearing box which generalizes the often-used Cartesian shearing box model. The numerical method is an overall second-order well-balanced finite volume method which maintains the stratified and oscillatory steady-state solution by construction. This implementation is employed to study the non-linear outcome of the parametric instability in eccentric discs with vertical structure. Stratification is found to constrain the perturbation energy near the mid-plane and localize the effective region of inertial wave breaking that sources turbulence. A saturated marginally sonic turbulent state results from the non-linear breaking of inertial waves and is subsequently unstable to large-scale axisymmetric zonal flow structures. This resulting limit-cycle behaviour reduces access to the eccentric energy source and prevents substantial transport of angular momentum radially through the disc. Still, the saturation of this parametric instability of inertial waves is shown to damp eccentricity on a time-scale of a thousand orbital periods. It may thus be a promising mechanism for intermittently regaining balance with the exponential growth of eccentricity from the eccentric Lindblad resonances and may also help explain the occurrence of ‘bursty’ dynamics such as the superhump phenomenon.

Keywords

  • Accretion discs;
  • Hydrodynamics;
  • Instabilities;
  • Turbulence;
  • Waves

3D printed microfluidic circuitry via multijet-based additive manufacturing

Journal Paper
Sochol, R. D., Wienkers, Aaron F., & Lin, L. et al.
Lab on a Chip, Volume 16, 2016, Pages 668-678
Publication year: 2016

Abstract

The miniaturization of integrated fluidic processors affords extensive benefits for chemical and biological fields, yet traditional, monolithic methods of microfabrication present numerous obstacles for the scaling of fluidic operators. Recently, researchers have investigated the use of additive manufacturing or “three-dimensional (3D) printing” technologies – predominantly stereolithography – as a promising alternative for the construction of submillimeter-scale fluidic components. One challenge, however, is that current stereolithography methods lack the ability to simultaneously print sacrificial support materials, which limits the geometric versatility of such approaches. In this work, we investigate the use of multijet modelling (alternatively, polyjet printing) – a layer-by-layer, multi-material inkjetting process – for 3D printing geometrically complex, yet functionally advantageous fluidic components comprised of both static and dynamic physical elements. We examine a fundamental class of 3D printed microfluidic operators, including fluidic capacitors, fluidic diodes, and fluidic transistors. In addition, we evaluate the potential to advance on-chip automation of integrated fluidic systems via geometric modification of component parameters. Theoretical and experimental results for 3D fluidic capacitors demonstrated that transitioning from planar to non-planar diaphragm architectures improved component performance. Flow rectification experiments for 3D printed fluidic diodes revealed a diodicity of 80.6 ± 1.8. Geometry-based gain enhancement for 3D printed fluidic transistors yielded pressure gain of 3.01 ± 0.78. Consistent with additional additive manufacturing methodologies, the use of digitally-transferrable 3D models of fluidic components combined with commercially-available 3D printers could extend the fluidic routing capabilities presented here to researchers in fields beyond the core engineering community.