VIBRATION OF CIRCULAR PLATES ON A FREE FLUID SURFACE: EFFECT OF SURFACE WAVES

1999 ◽  
Vol 226 (3) ◽  
pp. 407-424 ◽  
Author(s):  
M. AMABILI ◽  
M.K. KWAK
Keyword(s):  
Surface Waves ◽  
Surface Effect ◽  
Free Fluid ◽  
Circular Plates ◽  
Fluid Surface ◽  
Free Fluid Surface ◽  
Effect Of Surface

On Nonlinear Dynamics in a Free Fluid Surface of a Tank Excited by a Non-Ideal Power Source

2011 ◽  
Author(s):  
H. A. Navarro ◽  
J. M. Balthazar ◽  
F. R. Chavarette ◽  
T. S. Krasnopolskaya ◽  
A. Yu. Shvets
Keyword(s):  
Electric Motor ◽  
Nonlinear Oscillations ◽  
Fluid Dynamic ◽  
Equation System ◽  
Power Source ◽  
Free Fluid ◽  
Differential Equation System ◽  
Fluid Surface ◽  
Limited Power ◽  
Free Fluid Surface

We investigate the nonlinear oscillations in a free surface of a fluid in a cylinder tank excited by non-ideal power source, an electric motor with limited power supply. We study the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Additionally, the dynamics of parametrically excited surface waves in the tank can reveal new characteristics of the system. The fluid-dynamic system is modeled in such way as to obtain a nonlinear differential equation system. Numerical experiments are carried out to find the regions of chaotic solutions. Simulation results are presented as phase-portrait diagrams characterizing the resonant vibrations of free fluid surface and the existence of several types of regular and chaotic attractors. We also describe the energy transfer in the interaction process between the hydrodynamic system and the electric motor.

Breakdown of a Discontinuity of the Free Fluid Surface over a Bottom Step in a Channel

2003 ◽  
Vol 38 (6) ◽  
pp. 889-899 ◽  
Author(s):  
V. I. Bukreev ◽  
A. V. Gusev ◽  
V. V. Ostapenko
Keyword(s):  
Free Fluid ◽  
Fluid Surface ◽  
Free Fluid Surface ◽  
Bottom Step

Disturbance of a free fluid surface by a hydrofoil profile

2004 ◽  
Vol 39 (6) ◽  
pp. 972-978
Author(s):  
V. I. Boyarintsev ◽  
A. K. Lednev ◽  
A. S. Prudnikov ◽  
A. S. Savin ◽  
E.O. Savina
Keyword(s):  
Free Fluid ◽  
Fluid Surface ◽  
Free Fluid Surface

Numerical and theoretical solutions for a drop spreading below a free fluid surface

1995 ◽  
Vol 287 ◽  
pp. 251-278 ◽  
Author(s):  
Dorothy M. Koch ◽  
Donald L. Koch
Keyword(s):  
Asymptotic Solution ◽  
Numerical Solutions ◽  
Gravity Currents ◽  
Boundary Integral ◽  
Free Fluid ◽  
Drop Spreading ◽  
Fluid Surface ◽  
Low Viscosity ◽  
Viscosity Contrast ◽  
Free Fluid Surface

Numerical solutions are derived for a viscous, buoyant drop spreading below a free fluid surface. The drop has zero interfacial tension, and we consider viscosity contrasts 0.1 < λ < 10 with the surrounding fluid half-space. The density contrast between the drop and outer fluid is assumed to be small compared with the density contrast at the fluid surface. The numerical solutions for the approach and initial spread of the drop below the fluid surface are obtained using the boundary integral method. To facilitate an investigation over a larger range of viscosity contrasts and for longer time periods, we solve for the motion of gravity currents at the fluid surface. For this geometry we also solve the boundary integral equations for the cases λ = 0 and 1/λ = 0.For extensive drop spreading, the motion is described by asymptotic solutions. Three asymptotic solutions are derived, which apply for different values of the viscosity contrast relative to the aspect ratio ((radial extent R)/(drop thickness a)). For very low-viscosity drops (λ [Lt ] a/R[ln(R/a)]-1), the greatest resistance to spreading occurs at the drop rim, and the asymptotic solution is found using slender body theory. Drops with intermediate viscosity contrast (a/R [Lt ] λ [Lt ] R/a) are slowed primarily by shear stresses at the lower drop surface, and a lubrication solution (Lister & Kerr 1989) applies. The greatest resistance to the spread of very viscous drops (λ [Gt ] R/a) comes from the radial stresses within the drop, and the asymptotic solution is independent of the outer fluid. All drops having 0 [Lt ] λ [Lt ] ∞ will eventually spread according to lubrication theory, when their aspect ratio becomes sufficiently large relative to viscosity contrast.Theoretical results are compared with numerical and experimental results for drops and gravity currents spreading at a fluid surface. The solutions can be applied to aspects of planetary mantle flow where temperature variations cause significant viscosity contrasts. The low-viscosity solution has been applied to study the encounter of a hot, low-viscosity upwelling plume with a planet surface (Koch 1994). Here we apply the high-viscosity asymptotic solution to study how cold downwelling slabs spread at a depth of neutral buoyancy in the Earth's mantle.

Disturbance of a free fluid surface by a hydrofoil profile

2004 ◽  
Vol 39 (6) ◽  
pp. 972-978
Author(s):  
V. I. Boyarintsev ◽  
A. K. Lednev ◽  
A. S. Prudnikov ◽  
A. S. Savin ◽  
E. O. Savina
Keyword(s):  
Free Fluid ◽  
Fluid Surface ◽  
Free Fluid Surface
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