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We revisit the somewhat classical problem of the linear stability of a rigidly rotating liquid column in this communication. Although literature pertaining to this problem dates back to 1959, the relation between inviscid and viscous stability criteria has not yet been clarified. While the viscous criterion for stability, given by $We = n^2+k^2-1$, is both necessary and sufficient, this relation has only been shown to be sufficient in the inviscid case. Here, $We = rho Omega^2 a^3/gamma$ is the Weber number and measures the relative magnitudes of the centrifugal and surface tension forces, with $Omega$ being the angular velocity of the rigidly rotating column, $a$ the column radius, $rho$ the density of the fluid, and $gamma$ the surface tension coefficient; $k$ and $n$ denote the axial and azimuthal wavenumbers of the imposed perturbation. We show that the subtle difference between the inviscid and viscous criteria arises from the surprisingly complicated picture of inviscid stability in the $We-k$ plane. For all $n >1$, the viscously unstable region, corresponding to $We > n^2+k^2-1$, contains an infinite hierarchy of inviscidly stable islands ending in cusps, with a dominant leading island. Only the dominant island, now infinite in extent along the $We$ axis, persists for $n= 1$. This picture may be understood, based on the underlying eigenspectrum, as arising from the cascade of coalescences between a retrograde mode, that is the continuation of the cograde surface-tension-driven mode across the zero Doppler frequency point, and successive retrograde Coriolis modes constituting an infinite hierarchy.
We explore the effect of forcing on the linear shear flow or plane Couette flow, which is also the background flow in the very small region of the Keplerian accretion disk. We show that depending on the strength of forcing and boundary conditions sui
In this article we consider the linear stability of the two-dimensional flow induced by the linear stretching of a surface in the streamwise direction. The basic flow is a rare example of an exact analytical solution of the Navier-Stokes equations. U
We analyze the instability of a vortex column in a dilute polymer solution at large $textit{Re}$ and $textit{De}$ with $textit{El} = textit{De}/textit{Re}$, the elasticity number, being finite. Here, $textit{Re} = Omega_0 a^2/ u_s$ and $textit{De} =
It is proposed that critical balance - a scale-by-scale balance between the linear propagation and nonlinear interaction time scales - can be used as a universal scaling conjecture for determining the spectra of strong turbulence in anisotropic wave
Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of $N$ fluids with arbitrary viscosities, thicknesses, densities, and surface tension