Floating Thin Sheet in Waves: Drift Force, Drift Velocity and Wave Damping

2002 ◽  
Author(s):  
Choung Mook Lee ◽  
Kwan Hyoung Kang
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Surface Layer ◽  
Free Surface ◽  
Drift Velocity ◽  
Wave Attenuation ◽  
Thin Sheet ◽  
Theoretical Predictions ◽  
Drift Force ◽  
Good Agreement

Wave driven force on a deformable but inextensible thin sheet is investigated analytically by taking into account the boundary layer beneath the sheet. Wave tank experiments are carried out to verify the theoretical predictions. Theoretical prediction of the drift force, drift velocity, and wave attenuation by the sheet are made. It is found that the drift velocity of a contaminated free surface is much greater than that of a clean free surface, and increase in the drift velocity is greater for the greater shear stress on the interface of the viscous surface layer and the water below. The theoretical and experimental results are found in good agreement.

The Mixing Length Derived from Kármán’s Similarity Hypothesis

1973 ◽  
Vol 24 (1) ◽  
pp. 71-76 ◽  
Author(s):  
Michio Nishioka ◽  
Shūsuke Iida
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reasonable Agreement ◽  
Diffusion Constant ◽  
Turbulent Shear ◽  
Appreciable Effect ◽  
Mixing Length ◽  
Similarity Hypothesis ◽  
Turbulent Shear Stress ◽  
Good Agreement

SummaryFrom Kármán’s similarity hypothesis, we derive the equation which describes the mixing length in terms of the turbulent shear stress. For a boundary layer with linear stress distribution, the equation is in reasonable agreement with Bradshaw’s measurements. For a boundary layer with injection, it is shown that injection has an appreciable effect upon the mixing length when (vw/2) /(τ/ρ)1/2becomes comparable to the Kármán constant. Close similarity is also pointed out between the hypotheses due to Kármán and Townsend. Moreover, the diffusion constant in Townsend’s hypothesis is determined to be 0.25, which is in good agreement with the value 0.2 obtained by Townsend from one experiment.

Boundary Layer Measurements at an Internal Free Surface in a Partially Filled Horizontal and Rapidly-Rotating Container

1989 ◽  
Vol 111 (4) ◽  
pp. 457-463 ◽  
Author(s):  
T. J. Singler
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Circular Cylinder ◽  
Steady Flow ◽  
Symmetry Axis ◽  
Azimuthal Velocity ◽  
Free Surfaces ◽  
Horizontal Circular Cylinder ◽  
Good Agreement

Steady flow in a partially filled horizontal circular cylinder rotating rapidly about its symmetry axis is investigated experimentally. Radial boundary layer profiles of the azimuthal velocity in the neighborhood of the internal free surface are reported for a range of inverse Froude numbers and for two types of free surfaces. Results indicate good agreement with an existing theory.

Measurement of sheath characteristics in the presence of convection and ionization

1996 ◽  
Vol 74 (9-10) ◽  
pp. 671-675 ◽  
Author(s):  
R. M. Clements ◽  
J. R. Dawe ◽  
S. A. H. Rizvi ◽  
P. R. Smy
Keyword(s):  
Boundary Layer ◽  
Plasma Electron ◽  
Experimental Results ◽  
Ion Density ◽  
Current Voltage ◽  
Planar Grid ◽  
Theoretical Predictions ◽  
Flame Plasma ◽  
Theoretical Paper ◽  
Good Agreement

A flame plasma whose electron and (or) ion density can be varied over several orders of magnitude is constrained to flow perpendicular to a planar grid Langmuir probe. The probe is biased negative to the plasma, and the current–voltage characteristics and the thickness of the ion sheath formed at the probe are measured. The level of the electron and (or) ion density is set within a range at which the probe current due to thermal ionization throughout the sheath is comparable with the current of ions convected into the sheath. The experimental results are compared with the predictions of a recent theoretical paper that calculates the effect of recombination upon the characteristics of planar, cylindrical, and spherical probes with boundary layer sheaths. The theoretical predictions and experimental results for an idealized planar configuration show good agreement over wide ranges of variation of probe bias and plasma electron and (or) ion density. This verification of the theoretical planar electrode – perpendicular-flow model, which is the basis for all three boundary layer relations, is seen as providing strong backing for these relations, which have application to ionization measurements in various forms of recombinant plasma.

scholarly journals THE DEVELOPMENT OF UNDULAR BORES WITH FRICTION

1970 ◽  
Vol 1 (12) ◽  
pp. 28
Author(s):  
O. Hawaleshka ◽  
S.B. Savage
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Wave Profile ◽  
Wall Friction ◽  
Slight Reduction ◽  
Initial Development ◽  
Theoretical Predictions ◽  
Wall Shear ◽  
Momentum Integral

A theoretical and experimental study of the initial development of undular bores in two-dimensional, rectangular channels with and without boundary friction was performed Equations similar to those of Boussmesq, but including higher order and wall friction terms are presented and solved numerically by an implicit finite difference method A Pohlhausentype boundary layer momentum integral method is used to obtain the wall shear stress distribution under a developing long wave from the consideration of the boundary layer underneath it The solution is performed in a quasi-iterative manner proceeding from the friction coefficient calculation for an initially assumed wave profile to the inclusion of this coefficient in the calculation of a new wave profile at an advanced time Comparisons of theoretical and experimental results are given For the initial development of the undular bore with which the present work is concerned, the measurements are found to be m reasonable agreement with the theoretical predictions The effect of the wall shear stress manifests itself mainly in a slight reduction of the wave amplitudes.

Turbulent shear flow over slowly moving waves

1993 ◽  
Vol 251 ◽  
pp. 109-148 ◽  
Author(s):  
S. E. Belcher ◽  
J. C. R. Hunt
Keyword(s):  
Boundary Layer ◽  
Growth Rate ◽  
Shear Stress ◽  
Surface Layer ◽  
Reynolds Shear Stress ◽  
Surface Velocity ◽  
Wave Crest ◽  
Turbulent Shear ◽  
Effective Roughness ◽  
Inner Surface

We investigate the changes to a fully developed turbulent boundary layer caused by the presence of a two-dimensional moving wave of wavelength L = 2π/k and amplitude a. Attention is focused on small slopes, ak, and small wave speeds, c, so that the linear perturbations are calculated as asymptotic sequences in the limit (u* + c)/UB(L) → 0 (u* is the unperturbed friction velocity and UB(L) is the approach-flow mean velocity at height L). The perturbations can then be described by an extension of the four-layer asymptotic structure developed by Hunt, Leibovich & Richards (1988) to calculate the changes to a boundary layer passing over a low hill.When (u* + c)/UB(L) is small, the matched height, zm (the height where UB equals c), lies within an inner surface layer, where the perturbation Reynolds shear stress varies only slowly. Solutions across the matched height are then constructed by considering an equation for the shear stress. The importance of the shear-stress perturbation at the matched height implies that the inviscid theory of Miles (1957) is inappropriate in this parameter range. The perturbations above the inner surface layer are not directly influenced by the matched height and the region of reversed flow below zm: they are similar to the perturbations due to a static undulation, but the ‘effective roughness length’ that determines the shape of the unperturbed velocity profile is modified to zm = z0 exp (kc/u*).The solutions for the perturbations to the boundary layer are used to calculate the growth rate of waves, which is determined at leading order by the asymmetric pressure perturbation induced by the thickening of the perturbed boundary layer on the leeside of the wave crest. At first order in (u* + c)/UB(L), however, there are three new effects which, numerically, contribute significantly to the growth rate, namely: the asymmetries in both the normal and shear Reynolds stresses associated with the leeside thickening of the boundary layer, and asymmetric perturbations induced by the varying surface velocity associated with the fluid motion in the wave; further asymmetries induced by the variation in the surface roughness along the wave may also be important.

Laminar Free Convection From a Downward-Projecting Fin

1968 ◽  
Vol 90 (1) ◽  
pp. 63-70 ◽  
Author(s):  
G. S. H. Lock ◽  
J. C. Gunn
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Prandtl Number ◽  
Experimental Program ◽  
Boundary Layer Problem ◽  
Theoretical Predictions ◽  
Theoretical Results ◽  
Good Agreement ◽  
Quiescent Fluid

A theoretical analysis of conduction through and free convection from a tapered, downward-projecting fin immersed in an isothermal quiescent fluid is presented. The problem is solved by assuming quasi-one-dimensional heat conduction in the fin and matching the solution to that of the convection system, which is treated as a boundary layer problem. For an infinite Prandtl number, solutions are derived which take the form of a power law temperature distribution along the fin. The effect of this power (n) on heat transfer, drag, and the corresponding boundary layer profiles is discussed. It is shown that n is independent of the fin profile and dependent on a single nondimensional group χ. The theoretical results for infinite Prandtl number are compared with corresponding results derived from previous work using a Prandtl number of unity. The effect of Prandtl number on the determination of n and consequently the fin effectiveness is found to be extremely small. The results of an experimental program are also presented. These consist of temperature profiles and the n — χ relation for different fin geometries and surrounding fluids. Comparison with the theoretical predictions reveals good agreement.

scholarly journals Experimental study of the turbulent boundary layer in acceleration-skewed oscillatory flow

2011 ◽  
Vol 684 ◽  
pp. 251-283 ◽  
Author(s):  
Dominic A. van der A ◽  
Tom O’Donoghue ◽  
Alan G. Davies ◽  
Jan S. Ribberink
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Oscillatory Flow ◽  
Bed Shear Stress ◽  
Flow Conditions ◽  
Oscillatory Boundary Layer ◽  
Layer Flow ◽  
Momentum Integral ◽  
Good Agreement

AbstractExperiments have been conducted in a large oscillatory flow tunnel to investigate the effects of acceleration skewness on oscillatory boundary layer flow over fixed beds. As well as enabling experimental investigation of the effects of acceleration skewness, the new experiments add substantially to the relatively few existing detailed experimental datasets for oscillatory boundary layer flow conditions that correspond to full-scale sea wave conditions. Two types of bed roughness and a range of high-Reynolds-number, $\mathit{Re}\ensuremath{\sim} O(1{0}^{6} )$, oscillatory flow conditions, varying from sinusoidal to highly acceleration-skewed, are considered. Results show the structure of the intra-wave velocity profile, the time-averaged residual flow and boundary layer thickness for varying degrees of acceleration skewness, $\ensuremath{\beta} $. Turbulence intensity measurements from particle image velocimetry (PIV) and laser Doppler anemometry (LDA) show very good agreement. Turbulence intensity and Reynolds stress increase as the flow accelerates after flow reversal, are maximum at around maximum free-stream velocity and decay as the flow decelerates. The intra-wave turbulence depends strongly on $\ensuremath{\beta} $ but period-averaged turbulent quantities are largely independent of $\ensuremath{\beta} $. There is generally good agreement between bed shear stress estimates obtained using the log-law and using the momentum integral equation, and flow acceleration skewness leads to high bed shear stress asymmetry between flow half-cycles. Turbulent Reynolds stress is much less than the shear stress obtained from the momentum integral; analysis of the stress contributors shows that significant phase-averaged vertical velocities exist near the bed throughout the flow cycle, which lead to an additional shear stress, $\ensuremath{-} \rho \tilde {u} \tilde {w} $; near the bed this stress is at least as large as the turbulent Reynolds stress.

Hypersonic Laminar Heat Transfer and Boundary Layer Transition on Blunted Cones

1968 ◽  
Vol 19 (4) ◽  
pp. 301-316 ◽  
Author(s):  
N. B. Wood
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Transition ◽  
Flow Visualisation ◽  
Vertex Angle ◽  
Layer Transition ◽  
Pressure Distributions ◽  
Theoretical Predictions ◽  
Good Agreement

SummaryMeasurements have been made of laminar and transitional heat transfer rate distribution on a 15° semi-vertex angle, spherically blunted, cone at Mach numbers 8·6, 10·6 and 13·0. The laminar results are compared with theoretical predictions and good agreement is obtained with a modified form of the analysis due to Lees. Using a development of the correlation of pressure distributions previously obtained by the author, a new correlation of experimental and theoretical heat transfer results is suggested. The effect of nose bluntness on boundary layer transition has been observed both from flow visualisation and heat transfer results. It is suggested that the main factor causing nose bluntness to influence transition is the adverse pressure gradient which is induced.

Calculation of Interacting Turbulent Shear Layers: Duct Flow

1973 ◽  
Vol 95 (2) ◽  
pp. 214-219 ◽  
Author(s):  
P. Bradshaw ◽  
R. B. Dean ◽  
D. M. McEligot
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Calculation Method ◽  
Shear Layers ◽  
Turbulent Shear ◽  
Jet Flows ◽  
Duct Flow ◽  
Free Jet ◽  
Good Agreement

The boundary-layer calculation method of Bradshaw, Ferriss, and Atwell has been adapted to deal with the interaction between two shear layers with a change of sign of shear stress. Good agreement with experiments in symmetrical duct flow is found, using the same empirical input as in a boundary layer and assuming that the turbulence fields on either side of the duct can be superposed. The restriction to symmetrical flow is temporary and is a numerical rather than a physical simplification. In free jet flows, which have higher turbulence levels than ducts, small changes in empirical input are required to treat the interaction.

An Analysis of Jet Stripping of Liquid Coatings

1984 ◽  
Vol 106 (4) ◽  
pp. 399-404 ◽  
Author(s):  
C. H. Ellen ◽  
C. V. Tu
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Gradient Effect ◽  
Theoretical Predictions ◽  
Coating Mass ◽  
Stress Term ◽  
Good Agreement

This paper presents a new analysis of the jet stripping process, as used to control coating thicknesses in the paper, photographic and galvanizing industries, and demonstrates that the inclusion of a surface shear stress term, acting in conjunction with the pressure gradient on the coating, gives theoretical predictions of coating behavior quite different from those based on stripping which allows only for pressure gradient effect. An illustration is given of how jets operating close to, and further from, the strip during hot dip galvanizing have different effects on the molten coating even though the final coating mass might be the same. Measurements of coating mass, taken from galvanizing line trials, have shown good agreement with the revised theory.

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