Skip navigation
Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01c534fs32g
Title: The Dynamics of the Viscous Catenary
Authors: Tang, Alex
Advisors: Stone, Howard
Department: Mechanical and Aerospace Engineering
Class Year: 2024
Abstract: The viscous catenary is the fluid mechanics extension of the classic catenary problem. This extension to fluid mechanics, however, significantly complicates the problem's physics — and thus, the mathematical description thereof as well. Prior works approaching this problem from a mathematical perspective have focused mostly on the linearised early-time behaviour of a viscous catenary with negligible cross-sectional area and experiencing only small deformations. In this work, we derive a model for the intermediate- and late-time behaviour of the quasi-parabolic viscous catenary, taking into account changing cross-sectional area and eliminating the need for an analysis by asymptotic boundary layers at the wall endpoints. We evaluate this model against existing experimental works on the viscous catenary. We then use this model to understand the effects of surface tension, varying nonuniform initial cross-sectional area profiles, and the relationship between the time evolution of cross-sectional area and the eventual detachment of the catenary from its wall endpoint supports. We find that surface tension is of significant importance to the problem and must not be neglected, as well as that the detachment time is set by the catenary's initial cross-sectional area at the wall. Finally, we elucidate scaling laws for the evolution of the catenary, which hold for all cases of initial cross-sectional area nonuniformities. These scaling laws characterise the universal dynamics of the quasi-parabolic viscous catenary in the intermediate- and late-time limits.
URI: http://arks.princeton.edu/ark:/88435/dsp01c534fs32g
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Mechanical and Aerospace Engineering, 1924-2024

Files in This Item:
File Description SizeFormat 
TANG-ALEX-THESIS.pdf29.61 MBAdobe PDF    Request a copy


Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.