Linear global and asymptotic stability analysis of the flow past rectangular cylinders moving along a wall

The primary instability of the steady two-dimensional flow past rectangular cylinders moving parallel to a solid wall is studied, as a function of the cylinder length-to-thickness aspect ratio AR = L/D and the dimensionless distance from the wall g = G/D. For all A, two kinds of primary instability are found: a Hopf bifurcation leading to an unsteady two-dimensional flow for g >= 0.5, and a regular bifurcation leading to a steady three-dimensional flow for g < 0.5. The critical Reynolds number Re-c,Re- (2-D) of the Hopf bifurcation (Re = U infinity D/nu, where U-infinity is the free stream velocity, D the cylinder thickness and. the kinematic viscosity) changes with the gap height and the aspect ratio. For AR <= 1, Re-c, (2-D) increases monotonically when the gap height is reduced. For AR > 1, Re-c, (2-D) decreases when the gap is reduced until g approximate to 1.5, and then it increases. The critical Reynolds number Re-c, (3-D) of the three-dimensional regular bifurcation decreases monotonically for all AR, when the gap height is reduced below g < 0.5. For small gaps, g < 0.5, the hyperbolic/elliptic/centrifugal character of the regular instability is investigated by means of a short-wavelength approximation considering pressureless inviscid modes. For elongated cylinders, AR > 3, the closed streamline related to the maximum growth rate is located within the top recirculating region of the wake, and includes the flow region with maximum structural sensitivity; the asymptotic analysis is in very good agreement with the global stability analysis, assessing the inviscid character of the instability. For cylinders with AR <= 3, however, the local analysis fails to predict the three-dimensional regular bifurcation.