# Background

Flow Separation: The presence of the fluid viscosity slows down the fluid particles very close to the solid surface and forms a thin slow-moving fluid layer called a boundary layer.  The flow velocity is zero at the surface to satisfy the no-slip boundary condition.  Inside the boundary layer, flow momentum is quite low since it experiences a strong viscous flow resistance.   Therefore, the boundary layer flow is sensitive to the external pressure gradient (as the form of a pressure force acting upon fluid particles).  If the pressure decreases in the direction of the flow, the pressure gradient is said to be favorable.   In this case, the pressure force can assist the fluid movement and there is no flow retardation.  However, if the pressure is increasing in the direction of the flow, an adverse pressure gradient condition as so it is called exist.  In addition to the presence of a strong viscous force, the fluid particles now have to move against the increasing pressure force.  Therefore, the fluid particles could be stopped or reversed, causing the neighboring particles to move away from the surface.  This phenomenon is called the boundary layer separation.

Wake: Consider a fluid particle flows within the boundary layer around the circular cylinder.  From the pressure distribution measured in an earlier experiment, the pressure is a maximum at the stagnation point and gradually decreases along the front half of the cylinder.  The flow stays attached in this favorable pressure region as expected.  However, the pressure starts to increase in the rear half of the cylinder and the particle now experiences an adverse pressure gradient.  Consequently, the flow separates from the surface and creating a highly turbulent region behind the cylinder called the wake.  The pressure inside the wake region remains low as the flow separates and a net pressure force (pressure drag) is produced.

Vortex Shedding: The boundary layer separates from the surface forms a free shear layer and is highly unstable.  This shear layer will eventually roll into a discrete vortex and detach from the surface (a phenomenon called vortex shedding).  Another type of flow instability emerges as the shear layer vortices shed from both the top and bottom surfaces interact with one another.   They shed alternatively from the cylinder and generates a regular vortex pattern (the Karman vortex street), which will be shown later. The vortex shedding occurs at a discrete frequency and is a function of the Reynolds number.  The dimensionless frequency of the vortex shedding, the shedding Strouhal number, St = f D/V, is approximately equal to 0.21 when the Reynolds number is greater than 1,000.