Abstract
The effect of two fixed vertical boundaries, a finite distance apart, on the dynamics of a column of buoyant fluid rising in a less buoyant fluid is investigated in the presence of vertical rotation. It is shown that the presence of the boundaries introduces two main effects on a rotating plume. They tend to stabilise the plume but succeed only reducing the value of the growth rate and the plume remains unstable for all finite values of the distance between the boundaries and the plume. In the absence of the sidewalls, two modes of the instability were found known as the sinuous mode and the varicose mode. The influence of the boundaries is such that it reduces the growth rate of the varicose mode more than that of the sinuous mode and consequently the modified sinuous mode is always preferred in the presence of the boundaries.
Highlights
The study of the dynamics of compositional plumes is important for many real life applications in industry ([1][6]), geophysics ([7]-[25]) and environment ([26]-[34])
While the presence of the compositional plumes can be harmful, it is useful in geophysics
The dynamics of a fully developed plume of buoyant fluid, in the form of a channel of finite width, 2x0, rising in a less buoyant fluid contained between two parallel vertical walls, a distance d apart, and two fluids rotate uniformly about the vertical have been investigated
Summary
The study of the dynamics of compositional plumes is important for many real life applications in industry ([1][6]), geophysics ([7]-[25]) and environment ([26]-[34]). The theoretical works on the stability of the plumes showed that the Cartesian plume is always unstable in the absence of rotation (Eltayeb and Loper [16]) and in the presence of rotation (Eltayeb and Hamza [18]) These studies assumed that the plume rises vertically in a fluid of unbounded domains. The mathematical model by Al Mashrafi and Eltayeb [6] investigated the influence of the two fixed vertical boundaries on the dynamics of the plumes They tested the stability of non-rotating Cartesian plumes in a bounded domain to find that the presence of two vertical boundaries affects the stability, but the plumes remain unstable.
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