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.
Highlights
Ranging from galaxy-scale accretion discs (Boffin 2001) via atmospheric cyclones (Nolan & Zhang 2017) down to the human heart (Gray & Jalife 1996), rotating spiral waves are a common phenomenon in nature, which may occur in very diverse and physically different environments
It came as a slight surprise to us that our recently published formulation of interfacial waves in upright circular cylinders (Horstmann, Herreman & Weier 2020) predicted the formation of non-propagating spiral wave patterns under the influence of viscous damping as a linear response to orbital excitation
In two- and three-layer stratifications, the interfacial wave motion is subject to considerably stronger damping forces as compared to free-surface waves, rendering it impossible to apply existing inviscid sloshing models. We addressed this issue recently in Horstmann et al (2020), where we presented a hybrid model on orbital sloshing of both free-surface and two-layer interfacial waves under the impact of viscous damping
Summary
Ranging from galaxy-scale accretion discs (Boffin 2001) via atmospheric cyclones (Nolan & Zhang 2017) down to the human heart (Gray & Jalife 1996), rotating spiral waves are a common phenomenon in nature, which may occur in very diverse and physically different environments. It came as a slight surprise to us that our recently published formulation of interfacial waves in upright circular cylinders (Horstmann, Herreman & Weier 2020) predicted the formation of non-propagating spiral wave patterns under the influence of viscous damping as a linear response to orbital excitation. Orbitally shaken bioreactors (Klöckner & Büchs 2012) were identified as an important application in the last decade, where gas transfer, mixing dynamics and shear stresses are essentially imposed by the wave motion. In two- and three-layer stratifications, the interfacial wave motion is subject to considerably stronger damping forces as compared to free-surface waves, rendering it impossible to apply existing inviscid sloshing models. The formation of similar rotating spiral patterns is known only from physically different Faraday experiments (Kiyashko et al 1996).
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