Free-surface breakdown in a rapidly rotating liquid

1978 ◽  
Vol 86 (3) ◽  
pp. 457-463 ◽  
Author(s):  
W. E. Scott
Keyword(s):  
Free Surface ◽  
Capillary Waves ◽  
Mode Frequency ◽  
Wave Form ◽  
Inertial Waves ◽  
Rotating Liquid ◽  
Surface Breakdown ◽  
Beat Phenomenon ◽  
Inertial Wave ◽  
Wave Modes

It is shown that the wavelets which appear on the inertial wave form of the inner free surface of a fully spun-up cylindrical mass of liquid contained in a vertical, rapidly rotating and gyrating gyrostat are capillary waves. It is further shown that the interaction between these capillary waves and the excited inertial waves is not the mechanism which effects an observed two-period collapse (‘breakdown’) and reappearance of the free-surface inertial wave form. Rather, the two-period breakdown can be explained by the conjecture that it is a beat phenomenon arising from the interaction of two differently structured inertial wave modes, which have the same frequency at small amplitudes of oscillation of the gyrostat but which, owing to the dependence of the inertial mode frequency on the amplitude of the gyrostatic motion, have slightly different frequencies at larger amplitudes of oscillation of the gyrostat.

The large amplitude motion of a liquid-filled gyroscope and the non-interaction of inertial and Rossby waves

1975 ◽  
Vol 72 (4) ◽  
pp. 649-660 ◽  
Author(s):  
W. E. Scott
Keyword(s):  
Growth Rate ◽  
Free Surface ◽  
Rossby Waves ◽  
Experimental Fact ◽  
Wave Form ◽  
Resonant Amplitude ◽  
Axis Of Rotation ◽  
Surface Breakdown ◽  
Inertial Wave ◽  
Amplitude Growth

An attempt is made to explain theoretically two curious phenomena involving the motion of the liquid in a spinning, gyrating, liquid-filled gyroscope. One of the phenomena is the periodic breakdown of the free-surface wave form of the spinning liquid in the gyroscope when it gyrates at angles larger than about 1°. The other is the resonant amplitude growth rate of the liquid-filled gyroscope at these angles, for then the small angle stability theory of Stewartson (1959) fails to make the correct predictions.The analysis exploits the experimental fact that the axis of rotation of liquid in the rotor of a spinning gyrating gyroscope does not remain coincident with the axis of rotation of the rotor when the gyroscope gyrates at amplitudes greater than the above-mentioned 1°. It is shown that this lack of coincidence generates Rossby waves and modifies the inertial wave frequencies that would ordinarily occur in a right circular cylinder. There is no nonlinear interaction between these Rossby and inertial waves; hence the free-surface breakdown remains unexplained. However, the modification of the inertial wave frequencies does seem to account for the curious amplitude growth rate.

Inertial wave dynamics in a rotating liquid metal

2014 ◽  
Vol 753 ◽  
pp. 472-498 ◽  
Author(s):  
Tobias Vogt ◽  
Dirk Räbiger ◽  
Sven Eckert
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Swirling Flow ◽  
Harmonic Wave ◽  
Wave Mode ◽  
Rotating Magnetic Field ◽  
Inertial Waves ◽  
Aspect Ratios ◽  
Inertial Wave ◽  
Wave Modes

AbstractThe dynamics of free and forced inertial waves inside cylinders of different aspect ratios ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}A=H_0/2R_0$) were investigated experimentally in this study. The liquid metal GaInSn was chosen as the fluid in order to enable a contactless stimulation of the flow by means of alternating electromagnetic fields. A rotating magnetic field generates the rotating motion of the liquid, whereas periodic modulations of the field strength and short pulses excite specific wave modes. Ultrasound Doppler velocimetry was used to record the flow structure and to identify inertial waves in the set-up. Our experiments demonstrate selective excitation of different inertial wave modes by deliberate variation of the magnetic field parameters. Furthermore, it was found that turbulent perturbations in the boundary layers of the swirling flow are able to induce an inertial wave mode that survives over a long time. Experiments at the fundamental resonance have shown that multiple harmonic wave modes appeared simultaneously. The measured inertial wave frequencies were compared to the predictions of the linear inviscid theory.

The Frequency of Inertial Waves in a Rotating, Sectored Cylinder

1976 ◽  
Vol 43 (4) ◽  
pp. 571-574 ◽  
Author(s):  
W. E. Scott
Keyword(s):  
Cross Section ◽  
Inertial Waves ◽  
Fundamental Frequencies ◽  
Cylinder Diameter ◽  
Rotating Liquid ◽  
Order Of Magnitude ◽  
Inertial Wave

An analysis of the inertial wave eigenfrequencies of a rapidly rotating liquid in a cylinder whose cross section is divided into four 90 deg sectors reveals that only if the cylinder height is less than the cylinder diameter can the fundamental frequencies be of the order of magnitude of the frequencies of spin-stablilized projectiles. Hence, sectoring the usual long cavities in liquid-filled, spin-stabilized projectiles will preclude the occurrence of a “Stewartson” resonance.

Experimental Investigation of Boundary Layer Instabilities on the Free Surface of Non-Turbulent Jet

2012 ◽  
Author(s):  
Matthieu A. Andre ◽  
Philippe M. Bardet
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
High Speed ◽  
Particle Tracking Velocimetry ◽  
Capillary Waves ◽  
Wave Growth ◽  
Image Velocimetry ◽  
Planar Laser ◽  
Surface Visualization ◽  
The Waves

Shear instabilities induced by the relaxation of laminar boundary layer at the free surface of a high speed liquid jet are investigated experimentally. Physical insights into these instabilities and the resulting capillary wave growth are gained by performing non-intrusive measurements of flow structure in the direct vicinity of the surface. The experimental results are a combination of surface visualization, planar laser induced fluorescence (PLIF), particle image velocimetry (PIV), and particle tracking velocimetry (PTV). They suggest that 2D spanwise vortices in the shear layer play a major role in these instabilities by triggering 2D waves on the free surface as predicted by linear stability analysis. These vortices, however, are found to travel at a different speed than the capillary waves they initially created resulting in interference with the waves and wave growth. A new experimental facility was built; it consists of a 20.3 × 146.mm rectangular water wall jet with Reynolds number based on channel depth between 3.13 × 104 to 1.65 × 105 and 115. to 264. based on boundary layer momentum thickness.

scholarly journals Energy intensity of inertial waves in a sphere

1983 ◽  
Vol 25 (2) ◽  
pp. 145-160
Author(s):  
W. W. Wood
Keyword(s):  
Energy Density ◽  
General Theory ◽  
Energy Intensity ◽  
Initial Disturbance ◽  
Inertial Waves ◽  
Inertial Wave

AbstractThe decay at large wavenumbers of the energy density in an inertial wave generated in a sphere by an arbitrary initial disturbance is determined as a first step to a comparison with the general theory of Phillips [17] for a statistically steady field of random inertial waves in an arbitrary cavity.

Vibration-induced drop atomization and bursting

2003 ◽  
Vol 476 ◽  
pp. 1-28 ◽  
Author(s):  
A. J. JAMES ◽  
B. VUKASINOVIC ◽  
MARC K. SMITH ◽  
A. GLEZER
Keyword(s):  
Free Surface ◽  
Resonance Frequency ◽  
Capillary Waves ◽  
Dynamical Process ◽  
Entire Volume ◽  
Droplet Ejection ◽  
Basic Physics ◽  
Free Surface Wave ◽  
Secondary Droplets ◽  
Diaphragm System

A liquid drop placed on a vibrating diaphragm will burst into a fine spray of smaller secondary droplets if it is driven at the proper frequency and amplitude. The process begins when capillary waves appear on the free surface of the drop and then grow in amplitude and complexity as the acceleration amplitude of the diaphragm is slowly increased from zero. When the acceleration of the diaphragm rises above a well-defined critical value, small secondary droplets begin to be ejected from the free-surface wave crests. Then, quite suddenly, the entire volume of the drop is ejected from the vibrating diaphragm in the form of a spray. This event is the result of an interaction between the fluid dynamical process of droplet ejection and the vibrational dynamics of the diaphragm. During droplet ejection, the effective mass of the drop–diaphragm system decreases and the resonance frequency of the system increases. If the initial forcing frequency is above the resonance frequency of the system, droplet ejection causes the system to move closer to resonance, which in turn causes more vigorous vibration and faster droplet ejection. This ultimately leads to drop bursting. In this paper, the basic phenomenon of vibration-induced drop atomization and drop bursting will be introduced, demonstrated, and characterized. Experimental results and a simple mathematical model of the process will be presented and used to explain the basic physics of the system.

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