Thickness of a boundary layer attributed to the wave motion on the charged free surface of a viscous liquid

2008 ◽  
Vol 53 (3) ◽  
pp. 306-313
Author(s):  
D. F. Belonozhko ◽  
A. I. Grigor’ev
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Viscous Liquid ◽  
Wave Motion

Flow along a horizontal plate near a free surface

1993 ◽  
Vol 252 ◽  
pp. 399-418
Author(s):  
Milan Hofman
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Flat Plate ◽  
Viscous Liquid ◽  
Gravity Waves ◽  
Asymptotic Expansions ◽  
Small Amplitude ◽  
Surface Effect ◽  
Matched Asymptotic Expansions ◽  
Horizontal Plate

The problem of flow along a horizontal semi-infinite flat plate moving in its own plane through a viscous liquid just below the free surface is considered. The method of matched asymptotic expansions is used to analyse the interaction between the free surface and the boundary layer formed on the plate. It is found that, due to viscosity, small-amplitude gravity waves on the free surface can be formed. The formulae for the resistance of the plate containing the free-surface effect and for the lift, appearing as a new phenomenon, are derived.

On the theory of a boundary layer associated with wave motion on the free surface of a liquid

2007 ◽  
Vol 52 (8) ◽  
pp. 981-990
Author(s):  
D. F. Belonozhko ◽  
A. I. Grigor’ev
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Wave Motion

On the thickness of a boundary layer related to the oscillating free surface of a charged drop of a viscous liquid

2010 ◽  
Vol 55 (10) ◽  
pp. 1419-1425
Author(s):  
S. O. Shiryaeva ◽  
A. I. Grigor’ev ◽  
A. R. Paranin
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Viscous Liquid ◽  
Charged Drop

scholarly journals Development of Depth-Limited Wave Boundary Layers over a Smooth Bottom

2020 ◽  
Vol 9 (1) ◽  
pp. 27
Author(s):  
Hitoshi Tanaka ◽  
Nguyen Xuan Tinh ◽  
Xiping Yu ◽  
Guangwei Liu
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Wave Motion ◽  
Numerical Study ◽  
Experiment Data ◽  
Tidal Motion ◽  
Long Period ◽  
Simulation Results ◽  
Wave Boundary

A theoretical and numerical study is carried out to investigate the transformation of the wave boundary layer from non-depth-limited (wave-like boundary layer) to depth-limited one (current-like boundary layer) over a smooth bottom. A long period of wave motion is not sufficient to induce depth-limited properties, although it has simply been assumed in various situations under long waves, such as tsunami and tidal currents. Four criteria are obtained theoretically for recognizing the inception of the depth-limited condition under waves. To validate the theoretical criteria, numerical simulation results using a turbulence model as well as laboratory experiment data are employed. In addition, typical field situations induced by tidal motion and tsunami are discussed to show the usefulness of the proposed criteria.

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 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.

Jet Impingement of a Non-Newtonian Fluid

2006 ◽  
Author(s):  
Jiangang Zhao ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Hydraulic Jump ◽  
Similarity Solutions ◽  
Surface Velocity ◽  
Free Surface Velocity ◽  
Viscous Boundary Layer ◽  
Boundary Layer Region ◽  
Layer Region ◽  
Viscous Boundary

The similarity solutions are presented for the wall flow which is formed when a smooth planar jet of power-law fluids impinges vertically on to a horizontal plate, and spreads out in a thin layer bounded by a hydraulic jump. This problem is formulated analogous to radial jet flow problem and the solution procedure is accounted for by means of similarity solution of the boundary-layer equation [1] for Newtonian fluids. For the convenience of analysis, the flow may be divided into three regions, namely a developing boundary-layer region, a fully viscous boundary-layer region, and a hydraulic jump region. The similarity solutions of the film thickness and free surface velocity in fully viscous boundary-layer region include unknown constant L, which is solved numerically and approximately in the developing boundary-layer flow region. Comparison between the numerical and approximate solutions leads generally to good agreement, except for severely shear-thinning fluids. The boundary-layer solution depends on two parameters: power-law index n and α, the dimensionless flow parameters. The effect of α on film thickness and free surface velocity is investigated. The relations between the position of the hydraulic jump and dimensionless flow parameter are obtained and the effect of α on the position of the jump is presented.

scholarly journals Deceleration of droplets that glide along the free surface of a bath

2016 ◽  
Vol 803 ◽  
pp. 313-331 ◽  
Author(s):  
Jacob Hale ◽  
Caleb Akers
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Droplet Diameter ◽  
Reynolds Numbers ◽  
Viscous Drag ◽  
Bath Surface ◽  
Exponential Rate ◽  
Viscous Coupling ◽  
Air Film ◽  
O 10

A droplet obliquely impacting a bath surface of the same fluid can traverse along the interface while slowing at an exponential rate. The droplet rests on a thin film of air, deforms the bath surface creating a dimple and travels along the surface similarly to a wave pulse. Viscous coupling of the droplet and bath surfaces through the air film leads to viscous drag on the bath and perturbs the wave motion of the otherwise free surface. Even though the Reynolds numbers are greater than unity ($\mathit{Re}\,O(10{-}100)$), we show that the droplet’s deceleration is only due to viscous coupling through the air gap. The rate of deceleration is found to increase linearly with droplet diameter.

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