Instability behaviors of a cylinder array under both increasing and decreasing flow velocities

An instability criterion for viscoelastic flow past a confined cylinder

It has been known that there is a viscoelastic instability in the channel flow past a cylinder at high Deborah (De) number. Some of our numerical simulations and a boundary layer analysis indicated that this instability is related to the shear flow in the gap between the cylinder and the channel walls in our previous work. The critical condition for instability initiation may be related to an i...

slow and periodic flow past a cylinder

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Flow and instability of thin films on a cylinder and sphere

We investigate the dynamics of thin films driven by gravity on the outer surface of a cylinder and sphere. The surface is rigid, stationary and the axis of the cylinder is horizontal. An instantaneous release of a constant volume of fluid at the top of the cylinder or sphere results initially in a two-dimensional or axisymmetric current respectively. The resultant flow of a thin film of fluid i...

Dynamic Instability of Cp under Ricci Flow

The intent of this short note is to provide an independent proof of the unpublished discovery of Klaus Kröncke [Kro13] that complex projective space with its canonical Fubini–Study metric is dynamically unstable under Ricci flow in all complex dimensions N ≥ 2. The unstable perturbation is not Kähler. This provides a counterexample to a well known conjecture widely attributed to Hamilton. Moreo...

Instability of the vertical annular flow with a radial heating and rotating inner cylinder