The motion of inviscid and Newtonian jets issuing from elliptical orifices is analyzed. The analysis is not confined to small departures of the jet free surface from a circular cylindrical mean surface, but rather is fully nonlinear. Two types of behavior are predicted: (1) In the presence of surface tension the major axis of the elliptical jet cross-section alternates between perpendicular directions with distance down the jet. In this case the system is described as a single-degree-of-freedom nonlinear oscillator, conservative for the inviscid elliptical jet in the absence of gravity, and nonconservative for the Newtonian jet. (2) When surface tension is neglected, the transformation occurs only once, after which the jet flattens into a sheet perpendicular to the major axis of the orifice. The effect of gravity is discussed both for downward flowing jets and fountains.
The Oscillation of Slender Elliptical Inviscid and Newtonian Jets: Effects of Surface Tension, Inertia, Viscosity, and Gravity
Bechtel, S. E. (December 1, 1989). "The Oscillation of Slender Elliptical Inviscid and Newtonian Jets: Effects of Surface Tension, Inertia, Viscosity, and Gravity." ASME. J. Appl. Mech. December 1989; 56(4): 968–974. https://doi.org/10.1115/1.3176198
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