Formation of nonlinear waves in decelerated centrifuges of noncircular cross-section

TL;DR

This paper investigates the formation of nonlinear waves in noncircular, decelerated centrifuges using a numerical method for ideal fluid flows, revealing wave breaking and overturning depending on angular acceleration.

Contribution

It introduces a numerical approach for modeling free boundary flows in noncircular centrifuges with constant vorticity, highlighting nonlinear wave formation during decelerated rotation.

Findings

Decelerated rotation induces nonlinear breaking waves.

Wave overturning occurs in or against rotation direction depending on angular acceleration.

Sharp crests form in the nonlinear wave structures.

Abstract

Planar flows with a free boundary in a partially filled and nonuniformly rotating container, with a strongly noncircular shape of the cross-section, are investigated numerically within the ideal fluid approximation. Vorticity is assumed constant across the fluid, thus allowing us to apply the recently developed, highly efficient numerical method based upon exact equations of motion of the free boundary in terms of conformal variables and on the fast Fourier transform algorithms. It is shown that decelerated rotation of such centrifuge leads to formation of strongly nonlinear breaking waves with sharp crests, and the wave overturning occurs either in the rotation direction or against it, depending on value of the (negative) angular acceleration.