Surface waves and stability of free surface of a magnetizable liquid

1976 ◽  
Vol 15 (4) ◽  
pp. 465-469 ◽  
Author(s):  
I. E. Tarapov
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Magnetizable Liquid

scholarly journals Experiments on generation of surface waves by an underwater moving bottom

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150069 ◽  
Author(s):  
Timothée Jamin ◽  
Leonardo Gordillo ◽  
Gerardo Ruiz-Chavarría ◽  
Michael Berhanu ◽  
Eric Falcon
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Surface Deformation ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Spatio Temporal ◽  
Experimental Findings

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

Study on vibration of dragon wash basin and free surface waves inside

2018 ◽  
Vol 35 (1) ◽  
pp. 15-23
Author(s):  
Zi-Yu Guo ◽  
Xiao-Peng Chen ◽  
Lai-Bing Jia ◽  
Bin Xu
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Wash Basin ◽  
Free Surface Waves

Pseudo-three-timescale approximation of exponentially modulated free-surface waves

2009 ◽  
Vol 625 ◽  
pp. 435-443 ◽  
Author(s):  
MARK A. KELMANSON
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Test Problem ◽  
Evolution Equations ◽  
Film Coating ◽  
Rotating Cylinder ◽  
New Method ◽  
Free Surface Waves ◽  
Numerical Integrations ◽  
Order Of Magnitude

A novel pseudo-three-timescale asymptotic procedure is developed and implemented for obtaining accurate approximations to solutions of an evolution equation arising in thin-film free-surface viscous flow. The new procedure, which employs strained fast and slow timescales, requires considerably fewer calculations than its standard three-timescale counterpart employing fast, slow and slower timescales and may readily be applied to other evolution equations of fluid mechanics possessing wave-like solutions exhibiting exponential decay in amplitude and variations in phase over disparate timescales. The new method is validated on the evolution of free-surface waves on a thin, viscous film coating the exterior of a horizontal rotating cylinder and is shown to yield accurate solutions up to non-dimensional times exceeding by an order of magnitude those of previous related studies. Results of the new method applied to this test problem are demonstrated to be in excellent agreement, over large timescales, with those of corroborative spectrally accurate numerical integrations.

Large amplitude progressive interfacial waves

1979 ◽  
Vol 93 (3) ◽  
pp. 433-448 ◽  
Author(s):  
Judith Y. Holyer
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Surface Waves ◽  
Large Amplitude ◽  
Phase Speed ◽  
Maximum Height ◽  
Interfacial Waves ◽  
Free Surface Waves ◽  
Lower Fluid ◽  
Over The Top

This paper contains a study of large amplitude, progressive interfacial waves moving between two infinite fluids of different densities. The highest wave has been calculated using the criterion that it has zero horizontal fluid velocity at the interface in a frame moving at the phase speed of the waves. For free surface waves this criterion is identical to the criterion due to Stokes, namely that there is a stagnation point at the crest of each wave. I t is found that as the density of the upper fluid increases relative to the density of the lower fluid the maximum height of the wave, for fixed wavelength, increases. The maximum height of a Boussinesq wave, which has the density almost the same above and below the interface, is 2·5 times the maximum height of a surface wave of the same wavelength. A wave with air over the top of it can be about 2% higher than the highest free surface wave. The point at which the limiting criterion is first satisfied moves from the crest for free surface waves to the point half-way between the crest and the trough for Boussinesq waves. The phase speed, momentum, energy and other wave properties are calculated for waves up to the highest using Padé approximants. For free surface waves and waves with air above the interface the maximum value of these properties occurs for waves which are lower than the highest. For Boussinesq waves and waves with the density of the upper fluid onetenth of the density of the lower fluid these properties each increase monotonically with the wave height.

scholarly journals Heat transfer in the seabed boundary layer

2021 ◽  
Vol 928 ◽  
Author(s):  
S. Michele ◽  
R. Stuhlmeier ◽  
A.G.L. Borthwick
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Surface ◽  
Surface Waves ◽  
Multiple Scales ◽  
Perturbation Expansion ◽  
Phase Speed ◽  
Maximum Heat ◽  
Practical Applications ◽  
Free Surface Waves

We present a theoretical model of the temperature distribution in the boundary layer region close to the seabed. Using a perturbation expansion, multiple scales and similarity variables, we show how free-surface waves enhance heat transfer between seawater and a seabed with a solid, horizontal, smooth surface. Maximum heat exchange occurs at a fixed frequency depending on ocean depth, and does not increase monotonically with the length and phase speed of propagating free-surface waves. Close agreement is found between predictions by the analytical model and a finite-difference scheme. It is found that free-surface waves can substantially affect the spatial evolution of temperature in the seabed boundary layer. This suggests a need to extend existing models that neglect the effects of a wave field, especially in view of practical applications in engineering and oceanography.

Non-Boussinesq gravity currents and surface waves generated by lock release in a circular-section channel: theoretical and experimental investigation

2019 ◽  
Vol 869 ◽  
pp. 610-633 ◽  
Author(s):  
L. Chiapponi ◽  
M. Ungarish ◽  
D. Petrolo ◽  
V. Di Federico ◽  
S. Longo
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Cross Section ◽  
Cross Sections ◽  
Density Ratio ◽  
Circular Cross Section ◽  
Gravity Currents ◽  
Numerical Code ◽  
Long Distance ◽  
Front Speed

We present a combined theoretical and experimental study of lock-release inertial gravity currents (GCs) propagating in a horizontal channel of circular cross-section with open-top surface in the non-Boussinesq regime. A two-layer shallow-water (SW) model is developed for a generic shape of the cross-section with open top, and then implemented in a finite difference numerical code for the solution in a circular-cross-section channel of the type used in the experiments. The model predicts propagation with (almost) constant speed for a fairly long distance, accompanied by a depression of the ambient free open-top surface behind the front of the current. Sixteen experiments were conducted with a density ratio $r=0.587{-}0.939$ in full-depth and part-depth release conditions, measuring the front speed and the free-surface time series at four cross-sections. The channel was a circular tube 409 cm long, with a radius of 9.5 cm; the lengths of the locks were 52 and 103.5 cm. Density contrast was obtained by adding sodium chloride and dipotassium phosphate to fresh water. The theoretical values of the front speed and of the depression overestimate the experimental values, but they predict correctly their trend for varying parameters and provide reliable insights into the underlying mechanisms. In particular, we demonstrate that the circular cross-section increases the speed of propagation as compared to the standard rectangular cross-section case (for the same initial height and density ratio). The discrepancies between the SW predictions and the present experiments are of the same order of magnitude as those of previously published results for simpler systems (Boussinesq, rectangular). In addition to the depression, which is a wave bound to, and following the front of, the GC, the system also displays two kinds of free-surface waves, namely the initial bump (its amplitude is of the same order as the depression) and some short-length and low-amplitude waves in the tail of the bump. These free waves propagate with a celerity well predicted by the ‘fast’ eigenvalues of the mathematical model. Comparison is provided with the celerity of a solitary wave. It is expected that discrepancies between theory and experiments can be partly attributed to the presence of these waves. The reported insights and SW prediction method can be applied to a variety of cross-sections of practical interest (triangles, trapezoids, etc.).

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