Formation of spiral waves in cylindrical containers under orbital excitation

Abstract

The lowest swirling wave mode arising in upright circular cylinders as a response to circular orbital excitation has been widely studied in the last decade, largely due to its high practical relevance for orbitally shaken bioreactors. Our recent theoretical study (Horstmann et al., J. Fluid Mech., vol. 891, 2020, A22) revealed a damping-induced symmetry breaking mechanism that can cause spiral wave structures manifested in the so far widely disregarded higher rotating wave modes. Building on this work, we develop a linear criterion describing the degree of spiralisation and classify different spiral regimes as a function of the most relevant dimensionless groups. The analysis suggests that high Bond numbers and shallow liquid layers favour the formation of coherent spiral waves. This result paved the way to find the predicted wave structures in our interfacial sloshing experiment. We present two sets of experiments, with different characteristic damping rates, verifying the formation of both coherent and overdamped spiral waves in conformity with the theoretical predictions.

Tidally Forced Planetary Waves in the Tachocline of Solar-like Stars

“…This way, the model can correctly reflect all participating linear damping mechanisms, not only viscous damping. Such empirical approaches have been successfully implemented for simple free-surface wave systems (Horstmann et al 2020(Horstmann et al , 2021. In these controllable mechanical systems, it is, however, easy to determine decay rates, while it seems rather hopeless to extract them from space weather data, especially since solar Rossby waves are constantly and unpredictably excited.…”

Super-harmonically resonant swirling waves in longitudinally forced circular cylinders

“…(2014), among others (see also Hutton 1964; Bouvard, Herreman & Moisy 2017; Moisy, Bouvard & Herreman 2018; Horstmann, Herreman & Weier 2020; Horstmann et al. 2021), experimentally characterized in great detail the hydrodynamics of orbitally shaken circular cylinders, which represent the typical shape of lab-scale bioreactors. In addition to the primary harmonic system response via single-crest (SC) wave dynamics, different multiple-crest wave patterns were observed.…”

“…For these reasons, a strong interest in the gas exchange and mixing processes taking place in these devices has emerged over the last decades (Büchs et al 2000a,b;Büchs 2001;Maier, Losen & Büchs 2004;Muller et al 2005;Micheletti et al 2006;Zhang et al 2009;Tissot et al 2010;Tan, Eberhard & Büchs 2011;Tissot et al 2011;Klöckner & Büchs 2012). Reclari (2013) and Reclari et al (2014), among others (see also Hutton 1964;Bouvard, Herreman & Moisy 2017;Moisy, Bouvard & Herreman 2018;Horstmann, Herreman & Weier 2020;Horstmann et al 2021), experimentally characterized in great detail the hydrodynamics of orbitally shaken circular cylinders, which represent the typical shape of lab-scale bioreactors. In addition to the primary harmonic system response via single-crest (SC) wave dynamics, different multiple-crest wave patterns were observed.…”

An amplitude equation modelling the double-crest swirling in orbital-shaken cylindrical containers

“…These models are often complemented with effective viscous damping rates to incorporate the energy dissipation responsible for the phase shifts between wave and shaker, which was also seen to be sometimes responsible for damping-induced symmetry-breaking linear mechanisms resulting in linear spiral wave patterns (Horstmann et al. 2020, 2021). Previous studies mostly made use of classical existing theories for general linear sloshing dynamics, reviewed for instance in Ibrahim (2005) and Faltinsen & Timokha (2009).…”

“…For these reasons, at a more fundamental level, the hydrodynamics of these orbital shaking devices has received recent attention, from both experimental (Reclari et al 2014;Bouvard, Herreman & Moisy 2017;Moisy, Bouvard & Herreman 2018) and theoretical (Reclari et al 2014;Horstmann, Herreman & Weier 2020) perspectives, predominantly using linear potential flow models. These models are often complemented with effective viscous damping rates to incorporate the energy dissipation responsible for the phase shifts between wave and shaker, which was also seen to be sometimes responsible for damping-induced symmetry-breaking linear mechanisms resulting in linear spiral wave patterns (Horstmann et al 2020(Horstmann et al , 2021. Previous studies mostly made use of classical existing theories for general linear sloshing dynamics, reviewed for instance in Ibrahim (2005) and Faltinsen & Timokha (2009).…”