Torricelli's Curtain: Morphology of Horizontal Laminar Jets Under Gravity

• Main Authors: Tramis, O, Merlin-Anglade, E, Paternoster, G, Rabaud, M, Ribe, N. M
• Format: Journal Article
• Language: English
• Published: 04-06-2021
• Subjects: Physics - Fluid Dynamics; Physics - Geophysics
• DOI: 10.48550/arxiv.2106.02296

Viscous fluid exiting a long horizontal circular pipe develops a complex
structure comprising a primary jet above and a smaller secondary jet below with
a thin fluid curtain connecting them. We present here a combined experimental,
theoretical and numerical study of this 'Torricelli's curtain' phenomenon,
focusing on the factors that control its morphology. We propose a theoretical
model for the curtain in which particle trajectories result from the
composition of two motions: a horizontal component corresponding to the
evolving axial velocity profile of an axisymmetric viscous jet, and a vertical
component due to free fall under gravity. The model predicts well the
trajectory of the primary jet, but somewhat less well that of the secondary
jet. We suggest that the remaining discrepancy may be explained by surface
tension-driven (Taylor-Culick) retraction of the secondary jet. Finally, direct
numerical simulation reveals recirculating 'Dean' vortices in vertical sections
of the primary jet, placing Torricelli's curtain firmly within the context of
flow in curved pipes.