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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Print: 2152-5102
ISSN Online: 2152-5110

International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v29.i5.70
16 pages

Three-Dimensional Stability of the Flow near Moving Curved Surface

O. D. Nikishova
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine

ABSTRACT

The paper is concerned with stability of the flow in a boundary layer with respect to three-dimensional longitudinal vortices (Goertler vortices) formed under the action of the centrifugal force. The vortices are shown to be generated on a convex surface that moves along a curved trajectory in contrast to the case when a fixed, curved surface is flowed around and the vortices are formed on the 'concave side. The linear stability of the flow is studied and the stability diagram is constructed. The critical Goertler number is found to far exceed the critical number of the flow over a fixed concave surface. The range of the wave numbers which characterize instability of the flow is narrower in comparison to the case of the flow over a surface. This suggests that the flow near a curved surface moving along a curved trajectory is more stable than the flow near a fixed curved surface. The systematic evaluation of the eigenfunctions is performed for Various values of both the Goertler number Gr and the dimensionless wave number aq, where q is a momentum thickness. These functions are plotted, the positions and the values of the functions' characteristic points (the maximum and minimum values, the points of intersection with the vertical axes) are found. The data presented in the paper allow all the components of both the disturbed velocity and the pressure to be determined approximately provided the information on only one component, e. g., the maximum value of the longitudinal component of the disturbed velocity, that can be measured experimentally, is known. The position of the regions of instability to three-dimensional longitudinal vortices over the body of a dolphin moving rectilinearly, whose stern moves up and down, is discussed.


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