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.
Highlights
Most of the waves theories focus on the cases where the flow is irrotational one, from which the effect of stream vorticity is negligible
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 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
Summary
Most of the waves theories focus on the cases where the flow is irrotational one, from which the effect of stream vorticity is negligible. Drazin and Howard [9] presented as well many schemes for the stream velocity distribution including the sinusoidal form, which is similar to the case in the present flume under study, they discussed the rectangular jet form, plane Couette flow Their starting point was the modified version of NavierStokes equations that takes the perturbation effects, from which they discussed boundary layer formation for inertial waves, and different cases of instability and the corresponding solutions. To add the proper distribution of velocity with depth measurements were carried out using Vectrino Profiler (ADV) at specific point in the channel with depth, it turned out that the form vertically is sinusoidal one This function was inserted into the new version of Burns condition that was derived for the linear case and solved similar to the normal flows the wave velocity relative to the bottom has two values negative and positive.
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