The irrotational motion generated by two planar stirrers in inviscid fluid

2007 ◽  
Vol 19 (1) ◽  
pp. 018103 ◽  
Author(s):  
D. G. Crowdy ◽  
A. Surana ◽  
K-Y. Yick
Keyword(s):  
Inviscid Fluid ◽  
Irrotational Motion

A note on the unsteady motion under gravity of a corner point on a free surface: a generalization of Stokes' theory

2008 ◽  
Vol 465 (2101) ◽  
pp. 165-173 ◽  
Author(s):  
D.J Needham ◽  
J Billingham
Keyword(s):  
Free Surface ◽  
Corner Point ◽  
Constant Pressure ◽  
Unsteady Motion ◽  
Constant Speed ◽  
Inviscid Fluid ◽  
Irrotational Motion

In this paper, we develop a theory based on local asymptotic coordinate expansions for the unsteady propagation of a corner point on the constant-pressure free surface bounding an incompressible inviscid fluid in irrotational motion under the action of gravity. This generalizes the result of Stokes and Michell relating to the horizontal propagation of a corner at constant speed.

scholarly journals On the vortex theory of screw propellers

1929 ◽  
Vol 123 (792) ◽  
pp. 440-465 ◽  
Keyword(s):  
Exact Solution ◽  
Unit Length ◽  
Inviscid Fluid ◽  
Vortex System ◽  
Vortex Theory ◽  
Trailing Vortices ◽  
Screw Surface ◽  
Blade Section ◽  
Flow Round ◽  
Irrotational Motion

The vortex-theory of screw propellers develops along similar lines to aerofoil theory. There is circulation of flow round each blade; this circulation vanishes at the tip and the root. The blade may be replaced by a bound vortex system, which, for the sake of simplicity, may be taken, as a first approximation, to be a bound vortex line. The strength of the vortex at any point is equal to Γ, the circulation round the corresponding blade section. From every point of this bound vortex spring free, trailing vortices, whose strength per unit length is —∂Γ/∂ r , where r is distance from the axis of the screw. When the interference flow of this vortex system is small compared with the velocity of the blades, the trailing vortices are approximately helices, and together build a helical or screw surface. Part of the work supplied by the motor is lost in producing the trailing vortex system. When the distribution of Γ along the blade is such that, for a given thrust, the energy so lost per unit time is a minimum, then the flow far behind the screw is the same as if the screw surface formed by the trailing vortices was rigid, and moved backwards in the direction of its axis with a constant velocity, the flow being that of classical hydro dynamics in an inviscid fluid, continuous, irrotational, and without circulation. The circulation round any blade section is then equal to the discontinuity in the velocity potential at the corresponding point of the screw surface. Further, for symmetrical screws, the interference flow at the blade is half that at the corresponding point of the screw surface far behind the propeller. An approximate solution for the irrotational motion of a screw surface in an inviscid fluid was given by Prandtl. The accuracy of the approximation increases with the number of blades and with the ratio of the tip speed to the velocity of advance, but for given values of these numbers we have no means of estimating the error, since the exact solution of the problem has not yet been found. It is the main object of this work to find the exact solution.

scholarly journals Stokes drift through corals

2021 ◽  
Author(s):  
Joseph J. Webber ◽  
Herbert E. Huppert
Keyword(s):  
Coral Reef ◽  
Coral Reefs ◽  
Porous Layer ◽  
Large Scale ◽  
Fluid Layer ◽  
Ocean Waves ◽  
Stokes Drift ◽  
Inviscid Fluid ◽  
Porous Bed ◽  
Vertical Drift

AbstractMotivated by shallow ocean waves propagating over coral reefs, we investigate the drift velocities due to surface wave motion in an effectively inviscid fluid that overlies a saturated porous bed of finite depth. Previous work in this area either neglects the large-scale flow between layers (Phillips in Flow and reactions in permeable rocks, Cambridge University Press, Cambridge, 1991) or only considers the drift above the porous layer (Monismith in Ann Rev Fluid Mech 39:37–55, 2007). Overcoming these limitations, we propose a model where flow is described by a velocity potential above the porous layer and by Darcy’s law in the porous bed, with derived matching conditions at the interface between the two layers. Both a horizontal and a novel vertical drift effect arise from the damping of the porous bed, which requires the use of a complex wavenumber k. This is in contrast to the purely horizontal second-order drift first derived by Stokes (Trans Camb Philos Soc 8:441–455, 1847) when working with solely a pure fluid layer. Our work provides a physical model for coral reefs in shallow seas, where fluid drift both above and within the reef is vitally important for maintaining a healthy reef ecosystem (Koehl et al. In: Proceedings of the 8th International Coral Reef Symposium, vol 2, pp 1087–1092, 1997; Monismith in Ann Rev Fluid Mech 39:37–55, 2007). We compare our model with field measurements by Koehl and Hadfield (J Mar Syst 49:75–88, 2004) and also explain the vertical drift effects as documented by Koehl et al. (Mar Ecol Prog Ser 335:1–18, 2007), who measured the exchange between a coral reef layer and the (relatively shallow) sea above.

scholarly journals New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170220 ◽  
Author(s):  
Didier Clamond
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Water Waves ◽  
Two Dimensional ◽  
Physical Plane ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Dimensional Gravity ◽  
Irrotational Motion ◽  
Exact Relations

Steady two-dimensional surface capillary–gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained. This article is part of the theme issue ‘Nonlinear water waves’.

scholarly journals The approach of a vortex pair to a plane surface in inviscid fluid

1979 ◽  
Vol 92 (3) ◽  
pp. 497-503 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Approximate Calculation ◽  
Plane Surface ◽  
Vortex Pair ◽  
Plane Wall ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Axis Ratio ◽  
Local Rate

It is shown that a symmetrical vortex pair consisting of equal and opposite vortices approaching a plane wall at right angles must approach the wall monotonically in the absence of viscous effects. An approximate calculation is carried out for uniform vortices in which the vortices are assumed to be deformed into ellipses whose axis ratio is determined by the local rate of strain according to the results of Moore & Saffman (1971).

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