On the low-Rossby-number flow of a rotating fluid past a circular cylinder

Page, Michael A.

doi:10.1017/s0022112085002051

Cited by 18 publications

(35 citation statements)

References 24 publications

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“…More details of the derivation are given by Page. 34 Also introducing a scaled time tϭ2U*t*/l*, we obtain the boundary-layer equations…”

Section: Formulationmentioning

confidence: 99%

“…Note that here ͑3͒ has been scaled slightly differently from that given in Page 34 and Page and Cowley, 31 using an additional factor of N 1/2 in both the radial coordinate and the normal velocity, in order to avoid rescaling the equations in the limit N→0. The initial conditions we consider for the problem correspond to the cylinder starting impulsively from rest, at time tϭ0, to a constant velocity.…”

Section: Formulationmentioning

confidence: 99%

“…The above condition will be satisfied for a range of values of 0ϽxϽ, if Nр1 but flow reversal in the usual sense cannot occur for NϾ1. Leibovich In summary, noting that Nϭ0 corresponds to the nonrotating case, as N increases the flow field for the steady case passes through the following regimes 0рNϽ1: Similar to the non-rotating case, with separation occurring away from the rear stagnation point, e.g., Page, 35 Becker, 36 Page and Duck;37 1рNϽ2: The solution becomes singular at the rear stagnation point and forms three asymptotic regions, e.g., Page, 34 Page and Cowley;31 2рNϽ3: The displacement thickness becomes infinite at the rear stagnation point and forms two asymptotic regions, e.g., Page and Cowley;31 Nу3: There exists a steady non-singular solution in the boundary layer, e.g., Leibovich,28 Buckmaster. 29,30 Little attention has been paid to the parameter regime 2ϽNр3.…”

Section: Introductionmentioning

confidence: 96%

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On the unsteady low-Rossby number flow of a rotating fluid past a circular cylinder

1997

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The unsteady flow of a homogeneous viscous fluid past a straight circular cylinder (radius l*) confined between two infinite parallel plates (a distance d* apart) relative to a rapidly rotating frame is considered. The cylinder is impulsively started from rest to a uniform velocity. The unsteady form of the boundary-layer equations for a rotating fluid is used to examine the flow Rossby number Ro∼O(E1/2), where E≪1 is the Ekman number. A range of values of the non-dimensional parameter N=lE1/2/Ro (where l=l*/d*) is considered. For 0⩽N<1, the flow pattern resembles that of the non-rotating case (N=0). Initially, the wall shear around the cylinder is positive everywhere. After a time, flow reversal begins at the rear stagnation point and then the position of zero wall shear moves upstream, towards the front stagnation point. The boundary-layer thickness in the region of reversed flow grows with time until a singularity/eruption at a point in the flow occurs. The boundary-layer equations are written in terms of Lagrangian coordinates in order to numerically investigate the finite-time singularity for 0⩽N<1. The flow close to the rear stagnation point is also examined in detail for a range of values of N and results are compared with the large-time asymptotic forms for the growth of the displacement thickness. The analysis suggests the displacement thickness in this region grows exponentially with time, for certain ranges of N. For 0<N<1, the displacement thickness grows exponentially with time in a manner similar to the non-rotating case. For N>1, the wall shear remains positive for all time. However, for 1⩽N<2, the displacement thickness of the boundary layer close to the rear stagnation point again grows exponentially with time. For 2<N<3 the flow close to the rear stagnation point also grows exponentially with time, although the form of solution differs from that for 0⩽N<2. For N>3, the solution tends to a truly steady limit, consistent with previous studies on the steady problem.

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“…More details of the derivation are given by Page. 34 Also introducing a scaled time tϭ2U*t*/l*, we obtain the boundary-layer equations…”

Section: Formulationmentioning

confidence: 99%

Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

See 1 more Smart Citation

On the unsteady low-Rossby number flow of a rotating fluid past a circular cylinder

1997

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“…3 for sech 2 profiles. In particular, the decrease in the velocities in the jet in proportion to ( -x) and the increase in the thickness of the layer are reminiscent of features of the flow near the rear stagnation point of a circular cylinder, described in Page [18] and Page and Cowley [19], suggesting that the flow in the vicinity of 7s may be predominantly inviscid. As a result, a similar technique to that used in Page and Cowley [19] is used again here, transforming the inviscid form of (2.14) into Von Mises coordinates (, 5q) so that the flow near ix satisfies…”

Section: Approach To the Singularitymentioning

confidence: 83%

“…1. In that case it can be expected that there will be an additional viscous layer close to y7= 0 on the approach to the singularity, rather like the viscous layer in Page [18] and Page and Cowley [19].…”

Section: Discussionmentioning

confidence: 99%

The breakdown of jet flows in a low-Rossby-number rotating fluid

Page

Eabry

1990

J Eng Math

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The behaviour of steady jet-like flows is examined in a low-Rossby-number rotating fluid. Unlike the corresponding non-rotating flow, the momentum flux of a jet in a rotating fluid is not conserved with distance downstream and, as a consequence, the jet loses all of its momentum at a finite distance from the source, apparently developing a singularity as this occurs. The asymptotic properties of the flow leading up to this singular point are calculated for jets of various inflow widths and a structure which resolves the singularity that occurs in each of these cases is described. The properties on the approach to the singularity are shown to be similar to those of the exact solution described by Gadgil [12]. Both the asymptotic structure and the resolution of the singularity are, however, applicable to the expected breakdown of any form of jet in rotating fluid under similar conditions. The consequences of this are discussed, particularly in relation to the separated-flow structure proposed for motion past a cylindrical obstacle in Page [3].

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Low-Rossby-number Flow Past a Circular Cylinder in a Rotating Frame

Page

1987

Boundary-Layer Separation

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On the low-Rossby-number flow of a rotating fluid past a circular cylinder

Cited by 18 publications

References 24 publications

On the unsteady low-Rossby number flow of a rotating fluid past a circular cylinder

On the unsteady low-Rossby number flow of a rotating fluid past a circular cylinder

The breakdown of jet flows in a low-Rossby-number rotating fluid

Low-Rossby-number Flow Past a Circular Cylinder in a Rotating Frame

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