I-7 Theorem of Schwarz-Christoffel, free streamlines and applications

2013 ◽  
pp. 195-234
Keyword(s):  
Free Streamlines

scholarly journals Free-streamlines

1998 ◽  
Vol 36 (1) ◽  
pp. 69-129 ◽  
Author(s):  
W.C. Hassenpelug
Keyword(s):  
Free Streamlines

Ageostrophic instability of ocean currents

1982 ◽  
Vol 117 ◽  
pp. 343-377 ◽  
Author(s):  
R. W. Griffiths ◽  
Peter D. Killworth ◽  
Melvin E. Stern
Keyword(s):  
Potential Vorticity ◽  
Lower Layer ◽  
Rotation Period ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Inertial Effects ◽  
Mean Flow ◽  
Special Cases ◽  
Free Streamlines ◽  
A Current

We investigate the stability of gravity currents, in a rotating system, that are infinitely long and uniform in the direction of flow and for which the current depth vanishes on both sides of the flow. Thus, owing to the role of the Earth's rotation in restraining horizontal motions, the currents are bounded on both sides by free streamlines, or sharp density fronts. A model is used in which only one layer of fluid is dynamically important, with a second layer being infinitely deep and passive. The analysis includes the influence of vanishing layer depth and large inertial effects near the edges of the current, and shows that such currents are always unstable to linearized perturbations (except possibly in very special cases), even when there is no extremum (or gradient) in the potential vorticity profile. Hence the established Rayleigh condition for instability in quasi-geostrophic models, where inertial effects are assumed to be vanishingly small relative to Coriolis effects, does not apply. The instability does not depend upon the vorticity profile but instead relies upon a coupling of the two free streamlines. The waves permit the release of both kinetic and potential energy from the mean flow. They can have rapid growth rates, the e-folding time for waves on a current with zero potential vorticity, for example, being close to one-half of a rotation period. Though they are not discussed here, there are other unstable solutions to this same model when the potential vorticity varies monotonically across the stream, verifying that flows involving a sharp density front are much more likely to be unstable than flows with a small ratio of inertial to Coriolis forces.Experiments with a current of buoyant fluid at the free surface of a lower layer are described, and the observations are compared with the computed mode of maximum growth rate for a flow with a uniform potential vorticity. The current is observed to be always unstable, but, contrary to the predicted behaviour of the one-layer coupled mode, the dominant length scale of growing disturbances is independent of current width. On the other hand, the structure of the observed disturbances does vary: when the current is sufficiently narrow compared with the Rossby deformation radius (and the lower layer is deep) disturbances have the structure predicted by our one-layer model. The flow then breaks up into a chain of anticyclonic eddies. When the current is wide, unstable waves appear to grow independently on each edge of the current and, at large amplitude, form both anticyclonic and cyclonic eddies in the two-layer fluid. This behaviour is attributed to another unstable mode.

A Zone-Interaction Method for the Outer Flow Analysis of a Separated Airfoil

1980 ◽  
Vol 24 (02) ◽  
pp. 123-127
Author(s):  
James W. White
Keyword(s):  
Solution Method ◽  
Pressure Field ◽  
Flow Analysis ◽  
Separated Flow ◽  
Outer Flow ◽  
Free Streamlines ◽  
Principal Value ◽  
Airfoil Flow ◽  
Parallel Strips ◽  
Massive Separation

The pressure distribution over a subsonic airfoil experiencing massive separation is analyzed by a zonal modeling approach. Important physics are included in the mathematical description of each zone, and the zones are allowed to interact until convergence of the overall flow is obtained. The separated region is modeled as a zone of uniform pressure, the magnitude of which is determined by the solution method. The elliptic effect of the separated flow on the pressure field over the airfoil is included by bounding the stalled zone by two free streamlines which are iteratively located. Influence of the wake on the airfoil flow is modeled by two parallel strips which allow the subambient pressure in the stalled zone to adjust continuously black to freestream conditions. A Cauchy principal-value integral equation is used to compute the potential flow with no restrictions on the airfoil contour. Unlike most complex-variable methods, no mappings are required and the numerical solution is obtained entirely in the physical (Z) plane.

scholarly journals ALMA discovery of a rotating SO/SO2 flow in HH212

2017 ◽  
Vol 607 ◽  
pp. L6 ◽  
Author(s):  
B. Tabone ◽  
S. Cabrit ◽  
E. Bianchi ◽  
J. Ferreira ◽  
G. Pineau des Forêts ◽  
...  
Keyword(s):  
Rotating Flow ◽  
Wide Angle ◽  
Disk Wind ◽  
The Core ◽  
Lever Arm ◽  
Free Streamlines

We wish to constrain the possible contribution of a magnetohydrodynamic disk wind (DW) to the HH212 molecular jet. We mapped the flow base with ALMA Cycle 4 at 0.̋13 ~ 60 au resolution and compared these observations with synthetic DW predictions. We identified, in SO/SO2, a rotating flow that is wider and slower than the axial SiO jet. The broad outflow cavity seen in C34S is not carved by a fast wide-angle wind but by this slower agent. Rotation signatures may be fitted by a DW of a moderate lever arm launched out to ~40 au with SiO tracing dust-free streamlines from 0.05−0.3 au. Such a DW could limit the core-to-star efficiency to ≤50%.

On two-dimensional inviscid flow in a waterfall

1965 ◽  
Vol 22 (2) ◽  
pp. 359-369 ◽  
Author(s):  
N. S. Clarke
Keyword(s):  
Asymptotic Expansion ◽  
Flow Field ◽  
Froude Number ◽  
Inviscid Flow ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Free Streamlines ◽  
Two Dimensional Flow ◽  
Boundary Geometry

This paper is concerned with the two-dimensional flow in a free waterfall, falling under the influence of gravity, the fluid being considered to be incompressible and inviscid. A parameter ε, such that 2/ε is the Froude number based on conditions far upstream, is defined and considered to be small. A flowline co-ordinate system is used to overcome the difficulty that the boundary geometry is not known in advance. An asymptotic expansion based on ε is constructed as an approximation valid upstream and near the edge, but singular far downstream. Another asymptotic expansion, based upon the thinness of the fall, is constructed as an approximation valid far downstream, but failing to satisfy the conditions upstream. The two expansions are then matched to give a solution covering the whole flow field. The shapes of the free streamlines are shown for a number of values of ε for which the solutions are seemingly valid.

The two-dimensional jet

1966 ◽  
Vol 62 (3) ◽  
pp. 519-521
Author(s):  
William E. Conway
Keyword(s):  
Steady Flow ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Body Forces ◽  
Free Streamlines ◽  
Lower Plane ◽  
Made In

Consider the two-dimensional steady flow of an incompressible inviscid fluid under no body forces between two infinite horizontal planes. When an aperture is made in the lower plane, the fluid will issue as a jet bounded by free streamlines along which the pressure is constant. At infinity the flow in the jet will be uniform and parallel.

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