Abstract
In this letter some experimental and theoretical results from the flow in open cylindrical channel under precession conditions are reported. This includes the linear solutions of velocity field based on real experimental observations, and the nonlinear solution where a new weakly nonlinear KdV model equation is derived and solved numerically, this was compared with the real single Kelvin mode of the problem that appears in a symmetrical form with constant speed. The paper also shades the light on the instability features, mainly the wave breaking of single Kelvin mode, that is considered the resonance case of the problem, a new instability diagram in terms of Strouhal and Reynolds numbers is presented for the different cases reported from the experiment. The measurements of the mean azimuthal flow have been carried out using particle tracking procedure that enabled us finally to extract equation fit connects between the control parameters of the problem (which are the water volume, the angle of tilt and rotation rate) and the drift velocity the results pours in favor of the ADV measurements extracted in the previous work, and show that the mean flow increases by increasing both the tilt and the rotation rate where the instability features in the system appear at earlier levels, while increasing the water volume needs more energy to get the flow instability.
Highlights
When precession effect exists in the background of the flow, inertial oscillations are excited and appeared as natural results in such systems, the detuning Coriolis force effect adds additional momentum into the water body that causes those inertial oscillations as long as the forcing frequency smaller than twice the base rotation rate [1]
Similar to the waves studied in closed containers, the investigation of open flows focused on a cylinder that is filled partially under precession conditions [12, 13], or lately a new case study in open channel by the present author [3], where the cavity is replaced with two concentric cylinders with radii
As stated that those instability features are signs of resonance which is cannot be predicted theoretically using the linear Eq (7), and the nonlinear effect should be included in addition to the viscous effects if possible, here we focus on the nonlinear effect only, precisely the weakly nonlinear case where the scaling of potential Bernoulli Eq (2) and Laplace Eq (1) in terms of the shallowness and the amplitude parameters will give a new version of KdV equation that includes the effect of rotation in its coefficients, and it has forcing term that includes the tilt, the full explanation on the mathematical derivation can be found in the previous work [16]
Summary
When precession effect exists in the background of the flow, inertial oscillations are excited and appeared as natural results in such systems, the detuning Coriolis force effect adds additional momentum into the water body that causes those inertial oscillations as long as the forcing frequency smaller than twice the base rotation rate [1]. This will lead to ill-posed hyperbolic boundary value problem that gives a dense set of eigenmodes that were first introduced in the previous study [3], each mode accords with eigenfrequency. The cylinders are filled with water of different volumes, the inner cylinder has higher height than the outer one
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
