scholarly journals Boundary layer study for an ocean related system with a small viscosity parameter

2019 ◽  
Vol 96 ◽  
pp. 108-114
Author(s):  
Wenshu Zhou ◽  
Xulong Qin ◽  
Xiaodan Wei ◽  
Xu Zhao
Keyword(s):  
Boundary Layer ◽  
Related System ◽  
Viscosity Parameter ◽  
Small Viscosity

The boundary layer on a flat plate in a stream with uniform shear

1961 ◽  
Vol 11 (2) ◽  
pp. 309-316 ◽  
Author(s):  
J. D. Murray
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Flat Plate ◽  
Pressure Field ◽  
Free Stream ◽  
Main Stream ◽  
Uniform Shear ◽  
Small Viscosity ◽  
Boundary Layer Region ◽  
Layer Region

The incompressible laminar boundary layer on a semi-infinite flat plate is considered, when the main stream has uniform shear. A solution is obtained for the first two terms of an asymptotic solution for small viscosity. It is shown that one of the principal effects of free-stream vorticity is to introduce a modified pressure field outside the boundary-layer region.

The velocity of rise of distorted gas bubbles in a liquid of small viscosity

1965 ◽  
Vol 23 (4) ◽  
pp. 749-766 ◽  
Author(s):  
D. W. Moore
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Gas Bubbles ◽  
Quantitative Agreement ◽  
Terminal Velocity ◽  
Dimensionless Group ◽  
Gas Bubble ◽  
Numerical Accuracy ◽  
Small Viscosity ◽  
Acceleration Of Gravity

The terminal velocity of rise of small, distorted gas bubbles in a liquid of small viscosity is calculated. Small viscosity means that the dimensionless group gμ4/ρT3 where g is the acceleration of gravity, μ the viscosity, ρ the density and T the surface tension, is less than 10−8. It is assumed—and the numerical accuracy of the assumption is discussed—that the distorted bubbles are oblate ellipsoids of revolution. The drag coefficient is found by extending the theory given recently (Moore 1963) for the boundary layer on a spherical gas bubble. The results are in reasonable quantitative agreement with the experimental data.

Vortex decay above a stationary boundary

1967 ◽  
Vol 27 (1) ◽  
pp. 155-175 ◽  
Author(s):  
Albert I. Barcilon
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Plate Boundary ◽  
Swirling Flows ◽  
Rigid Boundary ◽  
Free Vortex ◽  
Stationary Boundary ◽  
Small Viscosity

An attempt is made to understand the decay of a free vortex normal to a stationary, infinite boundary. For rapidly swirling flows in fluids of small viscosity, thin boundary layers develop along the rigid boundary and along the axis, the axial boundary layer being strongly influenced by the behaviour of the plate boundary. An over-all picture of the flow is sought, with only moderate success in the region far from the origin. Near the origin, the eruption of the plate boundary layer into the axial boundary layer is studied.

Asymptotic solution for the perturbed Stokes problem in a bounded domain in two and three dimensions

1999 ◽  
Vol 129 (4) ◽  
pp. 811-824
Author(s):  
Dialla Konate
Keyword(s):  
Boundary Layer ◽  
Bounded Domain ◽  
Stokes Equation ◽  
Stokes Problem ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Potential Vector ◽  
Small Viscosity ◽  
The Given ◽  
Natural Way

We consider the Stokes problem with a small viscosity. When the viscosity goes to zero, the boundary-layer phenomenon can appear. In this case, the solution of the given perturbed Stokes equation cannot be properly approximated by the solution of its limiting equation ‘near’ the boundary Γ of the domain of study, say Ω To overcome this problem, we need to construct a corrector term in the neighbourhood of Γ Lions has studied this problem and has constructed a corrector for the case where Ω is a half space in ℝ2. The case where Ω is an open and bounded domain of ℝ2 or ℝ3, which remained unsolved, is the concern of this paper. The construction of the corrector to the perturbed Stokes equation depends heavily on the geometry of Ω In two dimensions, we construct the corrector in the form of a stream function, while in ℝ3 we construct it in the form of a potential vector. The corrector acts effectively in a neighbourhood of Γ that is the boundary layer. Using similar methods to those of Baranger and Tartar, we define the thickness of the boundary layer in a natural way. In addition, in this paper we study the behaviour of the corrected solution in some Hölder spaces.

Note on the velocity distribution in the wake behind a flat plate placed along the stream

1936 ◽  
Vol 32 (3) ◽  
pp. 385-391 ◽  
Author(s):  
L. Rosenhead ◽  
J. H. Simpson
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Distribution ◽  
Flat Plate ◽  
Great Distance ◽  
Large Reynolds Number ◽  
Small Viscosity ◽  
First Approximation ◽  
Image Position ◽  
Forward Edge

1. The velocity distribution in fluid of small viscosity, or at large Reynolds number, in the laminar boundary layer associated with a thin flat plate along the main direction of flow, has been worked out by Blasius on the basis of the Prandtl theory. These original investigations covered the region from the forward edge of the plate to the downstream edge. In a recent paper Goldstein investigated the velocity distribution in the wake immediately behind the downstream edge over a region within about 0·5lfrom it,lbeing the length of the plate. LaterTollmien obtained a first approximation to the flow at a great distance down-stream. Goldstein § extended Tollmien's solution by finding a second approximation and by joining it up with his previous work on the flow very near the plate.

The boundary layer on a spherical gas bubble

1963 ◽  
Vol 16 (2) ◽  
pp. 161-176 ◽  
Author(s):  
D. W. Moore
Keyword(s):  
Boundary Layer ◽  
Potential Flow ◽  
Bubble Radius ◽  
Terminal Velocity ◽  
Gas Bubble ◽  
Fractional Powers ◽  
Small Viscosity ◽  
Flow Round ◽  
Bubble Rising ◽  
Rear Stagnation Point

The equations governing the boundary layer on a spherical gas bubble rising steadily through liquid of small viscosity are derived. These equations are linear are linear and are solved in closed form. The boundary layer separates at the rear stagnation point of the bubble to form a thin wake, whose structure is determined. Thus the drag force can be calculated from the momentum defect. The value obtained is 12πaaUμ, where a is the bubble radius and U the terminal velocity, and this agrees with the result of Levich (1949) who argued from the viscous dissipation in the potential flow round the bubble. The next term in an expansion of the drag in descending fractional powers of R is found and the results compared with experiment.

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