<div class="csl-bib-body">
<div class="csl-entry">Scheichl, B., Bowles, R. I., & Pasias, G. (2023, November 20). <i>Viscous–inviscid interaction of a just detached planar liquid film near the Taylor–Culick speed: waves, blow-up, reversed-flow breakdown</i> [Conference Presentation]. 76th Annual Meeting of the Division of Fluid Dynamics (2024), Washington, DC, United States of America (the). https://doi.org/10.34726/6363</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/197714
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dc.identifier.uri
https://doi.org/10.34726/6363
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dc.description.abstract
We consider a stationary developed thin liquid film having just passed a trailing edge of a horizontal plate under the action of gravity and surface tension. In the associated limit of large Reynolds and Froude numbers and long waves, the classical, double-deck type of viscous-inviscid interaction accounts for the rigorous treatment of the flow around the edge. The resultant asymptotic flow description is then solely parametrised by the reciprocal Weber number, T, suitably formed with the momentum flow of the just detaching film, and a rescaled, reciprocal Froude number of O(1), G. Correspondingly, our focus lies on the numerical and analytical treatment of the fully nonlinear interaction problem. Most interestingly, the capillary influence on the jet-type pressure-displacement (interaction) law reveals an unprecedented kind of choking of a capillary wave if T equals 1/2; a value disclosing that the momentum-based averaged speed of the detaching flow is given by the associated Taylor-Culick speed. Specifically, the asymptotic analysis in the least-degenerate, self-similar limit of vanishingly small values of ε given by T–1/2 and small ones of G discovers a surprising richness of phenomena. This condenses the various flow manifestations for all values of T smaller than 1 (a second critical threshold representing another type of choking) and all non-negative ones of G. For negative values of ε, the theory predicts nonlinear Squire modes of the flapping kind; for positive ones, no waves are found but the interacting-flow description terminates in strikingly different manner in dependence of the deviation of G from a unique critical threshold: for smaller values of G, the free jet undegoes massive flow reversal far downstream (compressive interaction); for larger ones, however, a blow-up singularity is encountered (expansive interaction, regularized on an Euler stage). Both types of breakdowns resemble those found in originally wall-bounded interaction. In all other cases, a WKBJ analysis predicts a Goldstein wake far downstream. This also quantifies how the wavelength diverges when T approaches 1/2 from below and how gravity increases the amplitude of the waves, pointing to inviscid cnoidal waves for sufficiently large values G. Viscous dissipation concentrated around their troughs attenuates them periodically.
