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On arresting the complex growth rates in ferromagnetic convection in a rotating porous medium

Jyoti Prakash and Renu Bala

It is proved analytically that the complex growth rate ( are respectively the real and imaginary parts of ) of an arbitrary oscillatory motion of growing amplitude in ferromagnetic convection in a rotating porous medium for the case of free boundaries, must lie inside a semicircle in the right half of the - plane whose centre is origin and 􁈺 􁈻 = greater of { }, where R is the Rayleigh number, is the magnetic number, is the Prandtl number and is the Taylor number. Further, bounds for the case of rigid boundaries are also derived separately.