The damping of surface gravity waves in a bounded liquid

1973 ◽  
Vol 59 (2) ◽  
pp. 239-256 ◽  
Author(s):  
C. C. Mei ◽  
L. F. Liu
Keyword(s):  
Boundary Layer ◽  
Gravity Waves ◽  
Side Wall ◽  
The Other ◽  
Wave Number ◽  
Viscous Damping ◽  
Alternative Derivation ◽  
Surface Gravity Waves ◽  
Damping Rate ◽  
Side Walls

In deducing the viscous damping rate in surface waves confined by side walls, Ursell found in an example that two different calculations, one by energy dissipation within and the other by pressure working on the edge of the side-wall boundary layers, gave different answers. This discrepancy occurs in other examples also and is resolved here by examining the energy transfer in the neighbourhood of the free-surface meniscus. With due care near the meniscus a boundary-layer–Poincaré method is employed to give an alternative derivation for the rate of attenuation and to obtain in addition the frequency (or wave-number) shift due to viscosity. Surface tension is not considered.

scholarly journals Onsager's pancake approximation for the fluid dynamics of a gas centrifuge

1980 ◽  
Vol 101 (1) ◽  
pp. 1-31 ◽  
Author(s):  
Houston G. Wood ◽  
J. B. Morton
Keyword(s):  
Fluid Dynamics ◽  
Boundary Layer ◽  
Side Wall ◽  
Internal Flow ◽  
Ekman Layer ◽  
Linear Temperature ◽  
Gas Centrifuge ◽  
End Caps ◽  
Side Walls ◽  
Special Case

A previously unpublished theory for describing the internal flow in a gas centrifuge is presented. The theory is based on boundary-layer-type arguments on the side walls of the centrifuge with the additional approximation of neglecting radial diffusion of radial momentum. The effects of the top and bottom end caps are incorporated through Ekman-layer solutions. The results are presented in a form amenable to numerical calculations.Some sample calculations are presented for the special case of a centrifuge with a linear temperature profile on the wall and the top and bottom of the centrifuge at the same temperature as the corresponding end of the side wall.

Effect of Side Walls on Natural Convection Between Horizontal Plates Heated From Below

1967 ◽  
Vol 89 (4) ◽  
pp. 295-299 ◽  
Author(s):  
I. Catton ◽  
D. K. Edwards
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
The Other ◽  
Wave Number ◽  
Closed Cell ◽  
Equivalent Wave ◽  
Data Points ◽  
Side Walls

Experimental results are presented giving the Rayleigh number at which convection initiates in a closed cell and the Nusselt number versus Rayleigh number relationship which prevails after convection is initiated. Over 700 data points were obtained for two types of cells heated from below, one a phenolic-fiberglass hexcell of low thermal conductivity and the other aluminum hexcell of high thermal conductivity. Relations based upon the Malkus-Veronis power integral technique and a concept of an equivalent wave number are shown to give good correlation of the experimental data for both the low and high conductivity side walls.

Decreasing the Side Wall Contamination in Wind Tunnels

1983 ◽  
Vol 105 (4) ◽  
pp. 435-438 ◽  
Author(s):  
T. Motohashi ◽  
R. F. Blackwelder
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Laminar Boundary Layer ◽  
Three Dimensional ◽  
Side Wall ◽  
Wind Tunnels ◽  
Turbulent Fluid ◽  
Side Walls ◽  
Suction Slot

To study boundary layers in the transitional Reynolds number regime, the useful spanwise and streamwise extent of wind tunnels is often limited by turbulent fluid emanating from the side walls. Some or all of the turbulent fluid can be removed by sucking fluid out at the corners, as suggested by Amini [1]. It is shown that by optimizing the suction slot width, the side wall contamination can be dramatically decreased without a concomitant three-dimensional distortion of the laminar boundary layer.

Stationary gravity waves on non-uniform free streams: jet-like streams

1975 ◽  
Vol 77 (2) ◽  
pp. 415-438 ◽  
Author(s):  
D. H. Peregrine ◽  
Ronald Smith
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Small Amplitude ◽  
Wave Number ◽  
Explicit Solutions ◽  
Stationary Waves ◽  
Two Dimensional ◽  
Large Wave ◽  
Surface Gravity Waves ◽  
Large Wave Number

AbstractThe basic state considered in this paper is a parallel flow of a jet-like character with the centre of the jet being at or near a free surface which is horizontal. Stationary surface gravity waves may exist on such a flow, and a number of examples are looked at for small amplitude waves. Explicit solutions are given for ‘top-hat’ profile jets and for two-dimensional flows. Asymptotic solutions are developed for stationary waves of large wave-number.

Array measurements of atmospheric pressure fluctuations above surface gravity waves

1981 ◽  
Vol 102 ◽  
pp. 1-59 ◽  
Author(s):  
R. L. Snyder ◽  
F. W. Dobson ◽  
J. A. Elliott ◽  
R. B. Long
Keyword(s):  
Gravity Waves ◽  
Atmospheric Pressure ◽  
Pressure Sensors ◽  
Phase Speed ◽  
Limited Range ◽  
Surface Gravity ◽  
Wave Number ◽  
Surface Gravity Waves ◽  
Array Measurements ◽  
Wave Induced

A joint experiment to study microscale fluctuations of atmospheric pressure above surface gravity waves was conducted in the Bight of Abaco, Bahamas, during November and December 1974. Field hardware included a three-dimensional array of six wave sensors and seven air-pressure sensors, one of which was mounted on a wave follower. The primary objectives of the study were to resolve differences in previous field measurements by Dobson (1971), Elliott (1972b) and Snyder (1974), and to estimate the vertical profile of wave-induced pressure and the corresponding input of energy and momentum to the wave field.Analysis of a pre-experiment intercalibration of instruments and of 30 h of field data partially removes the discrepancy between the previous measurements of the wave-induced component of the pressure and gives a consistent picture of the profile of this pressure over a limited range of dimensionless height and wind speed. Over this range the pressure decays approximately exponentially without change of phase; the decay is slightly less steep than predicted by potential theory. The corresponding momentum transfer is positive for wind speeds exceeding the phase speed. Extrapolation of present results to higher frequencies suggests that the total transfer is a significant fraction of the wind stress (0·1 to 1·0, depending on dimensionless fetch).Analysis of the turbulent component of the atmospheric pressure shows that the ‘intrinsic’ downwind coherence scale is typically an order-of-magnitude greater than the crosswind scale, consistent with a ‘frozen’ turbulence hypothesis. These and earlier data of Priestley (1965) and Elliott (1972c) suggest a horizontally isotropic ‘intrinsic’ turbulent pressure spectrum which decays ask−νwherekis the (horizontal) wave-number and ν is typically −2 to −3; estimates of this spectrum are computed for the present data. The implications of these findings for Phillips’ (1957) theory of wave growth are examined.

Perturbation theory for metal pad roll instability in cylindrical reduction cells

2019 ◽  
Vol 878 ◽  
pp. 598-646 ◽  
Author(s):  
W. Herreman ◽  
C. Nore ◽  
J.-L. Guermond ◽  
L. Cappanera ◽  
N. Weber ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Gravity Waves ◽  
Experimental Measurements ◽  
Viscous Damping ◽  
Joule Dissipation ◽  
Explicit Formulas ◽  
Capillary Effects ◽  
Fluid Layers ◽  
Damping Rate ◽  
Two Fluid

We propose a new theoretical model for metal pad roll instability in idealized cylindrical reduction cells. In addition to the usual destabilizing effects, we model viscous and Joule dissipation and some capillary effects. The resulting explicit formulas are used as theoretical benchmarks for two multiphase magnetohydrodynamic solvers, OpenFOAM and SFEMaNS. Our explicit formula for the viscous damping rate of gravity waves in cylinders with two fluid layers compares excellently to experimental measurements. We use our model to locate the viscously controlled instability threshold in cylindrical shallow reduction cells but also in Mg–Sb liquid metal batteries with decoupled interfaces.

Numerical calculations of steady gravity-capillary waves using an integro-differential formulation

1979 ◽  
Vol 94 (4) ◽  
pp. 777-793 ◽  
Author(s):  
James W. Rottman ◽  
D. B. Olfe
Keyword(s):  
Gravity Waves ◽  
Small Amplitude ◽  
Numerical Solutions ◽  
Capillary Wave ◽  
Capillary Waves ◽  
The Other ◽  
Wave Number ◽  
Infinite Depth ◽  
Free Surface Waves ◽  
Differential Formulation

A new integro-differential equation is derived for steady free-surface waves. Numerical solutions of this equation for periodic gravity-capillary waves on a fluid of infinite depth are presented. For the two limiting cases of gravity waves and capillary waves, our results are in excellent agreement with previous calculations. For gravity-capillary waves, detailed calculations are performed near the wave-number at which the classical second-order perturbation solution breaks down. Our calculations yield two solutions in this region, which in the limit of small amplitudes agree with the results obtained by Wilton in 1915; one solution has the small amplitude behaviour of a gravity wave and the other that of a capillary wave, but the numerical results show that at large amplitudes both waves have the characteristics of capillary waves. The calculations also show that the wavenumber range in which two solutions exist increases with increasing wave height.

The axisymmetric convective regime for a rigidly bounded rotating annulus

1968 ◽  
Vol 32 (4) ◽  
pp. 625-655 ◽  
Author(s):  
Michael E. Mcintyre
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Axisymmetric Flow ◽  
Side Wall ◽  
Boundary Layer Equations ◽  
Wall Boundary Layer ◽  
Ekman Layers ◽  
Interior Flow ◽  
Side Walls ◽  
Annular Container

The axisymmetric flow of liquid in a rigidly bounded annular container of heightH, rotating with angular velocity Ω and subjected to a temperature difference ΔTbetween its vertical cylindrical perfectly conducting side walls, whose distance apart isL, is analysed in the boundary-layer approximation for small Ekman numberv/2ΩL2, withgαΔTHv/4Ω2L2K∼ 1. The heat transfer across the annulus is then convection-dominated, as is characteristic of the experimentally observed ‘upper symmetric regime’. The Prandtl numberv/kis assumed large, andHis restricted to be less than about 2L. The side wall boundary-layer equations are the same as in (non-rotating) convection in a rectangular cavity. The horizontal boundary layers are Ekman layers and the four boundary layers, together with certain spatialaveragesin the interior, are determined independently of the interior flow details. The determination of the latter comprises a ‘secondary’ problem in which viscosity and heat conduction are important throughout the interior; the meridional streamlines are not necessarily parallel to the isotherms. The secondary problem is discussed qualitatively but not solved. The theory agrees fairly well with an available numerical experiment in the upper symmetric regime, forv/k[bumpe ] 7, after finite-Ekmannumber effects such as finite boundary-layer thickness are allowed for heuris-tically.

scholarly journals Boundary layer models for calving marine outlet glaciers

2017 ◽  
Author(s):  
Christian Schoof ◽  
Andrew D. Davis ◽  
Tiberiu V. Popa
Keyword(s):  
Boundary Layer ◽  
Ice Sheets ◽  
The Other ◽  
Ice Shelf ◽  
Bedrock Channel ◽  
Extensional Stress ◽  
Grounding Line ◽  
Direct Numerical Solution ◽  
Glacier Ice ◽  
Side Walls

Abstract. We consider the flow of marine-terminating outlet glaciers that are laterally confined in a channel of prescribed width. In that case, the drag exerted by the channel side walls on the glacier affects extensional stress at the grounding line, and as a result, the flux through the grounding line. Lateral drag in turn is affected by the length of the floating ice shelf when the latter is present, and therefore by calving. Using two calving laws, one due to Nick et al based on a model for crevasse propagation due to hydrofracture, and the other simply asserting that calving occurs where the glacier ice becomes afloat, we pose and analyse a flowline model by two methods: direct numerical solution and matched asymptotic expansions. The latter leads to a boundary layer formulation that predicts flux through the grounding line as a function of depth to bedrock, channel width, basal drag coefficient, and a calving parameter. By contrast with unbuttressed marine ice sheets, we find that flux can decrease with increasing depth to bedrock at the grounding line, reversing the usual stability criterion for steady grounding line location. We show how this anomalous behaviour relates to the strength of lateral versus basal drag on the grounded portion of the glacier, and to the specifics of the calving law used.

Sign in / Sign up

Export Citation Format

Share Document