Showing papers by "Manhar R. Dhanak published in 1993"

Motion of an elliptical vortex under applied periodic strain

Abstract: The effect of subjecting a uniform elliptical vortex to a periodically varying plane straining field is considered. For plane steady straining fields, it is known that a Rankine‐type vortex core of uniform vorticity and elliptical shape can exist in a state in which it (a) is steady and stationary, (b) rotates about its axis or nutates about a fixed axis, or (c) elongates indefinitely, smearing the core into a thin layer. In state (a), for sufficiently weak straining fields, a vortex of small enough aspect ratio of the ellipse persists under such a plane strain, being robust to small two‐dimensional disturbances present in the flow field. It is shown that if, however, a small periodically varying component is added to the basic straining field, then at frequencies corresponding to the natural frequency of vibration of the vortex and their harmonics, a resonance phenomenon takes place which destabilizes the apparently stable stationary vortex in finite time, causing it to flip from state (a) into states (b) or (c), in which action of instabilities associated with a higher, nonelliptical, mode of deformation of the vortex boundary by disturbances in the flow field would lead to disintegration of the vortex structure. In fact it is found that the vortex also flips to states (b) and (c) for a range of non‐natural frequencies of oscillation of the straining field. The effect of the periodic plane straining on the three‐dimensional Crow instability is also discussed.

On the instability of flow in a streamwise corner

Abstract: The linear stability of an incompressible laminar flow in the blending boundary layer between the boundary layer in a 90 deg streamwise corner and a Blasius boundary layer well away from the corner is examined using a locally parallel flow approximation. It is shown that the influence of the outer boundary conditions associated with oblique modes of disturbances which are anti-symmetric about the bisector plane have a profound effect on the stability of the flow. As a result, in good agreement with observation, the critical streamwise Reynolds number, associated with a spanwise location is significantly reduced as the corner is approached, being R(sub Cr) = 60 approximately for spanwise distance of z* = 6x*R(sup -1) from the corner compared with R(sub Cr) = 322 approximately for z* = 20x*R(sup -1), where x* measures downstream distance from the leading edges. At R = 600, the growth rate of the most amplified mode of disturbance at the former location is over six times greater than that at the latter; the corresponding wave angle at the two locations is respectively 44 deg and 5 deg, approximately.

The motion and stability of a vortex array above a pulsed surface

Abstract: A model inviscid and incompressible flow problem is studied in which an infinite array of equi-spaced identical rectilinear line vortices moves in a uniform stream over a wall in which is embedded an equi-spaced array of discrete line sources of variable strength. It is shown that for a suitable choice of source spacing and strength, a flow that is periodic both in time and in the streamwise direction is possible. The flow is shown to be stable to small two-dimensional disturbances for a range of values of vortex height above the wall and source strength. The implications for the corresponding viscous problem and active flow control are discussed.