Shear Flow in Cylindrical Open Channel Under Precession

TL;DR

This paper investigates shear flow effects in a cylindrical open channel under precession, combining theoretical analysis and numerical simulations to understand stability, wave behavior, and the influence of shear on flow dynamics.

Contribution

It introduces a new model incorporating shear effects into the analysis of precessing cylindrical channels, including a modified KdV equation and numerical solutions.

Findings

Shear has no significant impact on wave form.

Derived a new version of the KdV equation for shear flow.

Experimental velocity distribution is sinusoidal with depth.

Abstract

The study of forced oscillations in open cylindrical channel under precession is extended to include the shear effect, that is induced by inertial waves in such systems. The linear part of the problem led to two equations for stability one for the viscous part similar to Orr- Sommerfeld equation and one for the inviscid part similar to Rayleigh equation, the second was solved and discussed depending on the stream function observation. The linear part also led to relationship that connects between the stream velocity and the disturbance one is derived in a form similar to Burns conditions for open flows under normal conditions. Experimentally measuring the horizontal velocity distribution with depth showed that this distribution is sinusoidal one. Burns condition was solved based on this assumption. The nonlinear part of the problem led to a new version of Koteweg De-Vries (KdV) equation that is solved numerically by applying the leapfrog method for time discretization, Fourier transformation for the space one, and the trapezoidal rule for solving the integrals with depth, the results showed that the shear has no specific impact on the wave form which is similar to the classical results obtained by the theories under normal conditions.