  Wind and hydrokinetic energy turbines are often constrained to locations
where the available energy is limited by the operation of the turbines
themselves. In two-dimensions, we describe how an array can manipulate the
steady flow, redirecting more fluid kinetic energy to itself. Two computational
examples of turbine arrays present solutions of the Navier-Stokes equations to
illustrate the feasibility of flow manipulation, and motivate an idealized
model. Using inviscid fluid dynamics, we underscore the relation between bound
vorticity and flow deflection, and between free vorticity and energy
extraction. To understand and design flow manipulations that increase the
kinetic energy incident on the turbines, we consider an idealized
deflector-turbine array constrained to a line segment, acting as an internal
flow-boundary. We impose profiles of bound and shed vorticity on this segment
by parameterizing the flow deflection and the wake deficit, respectively, and
analyze the resulting flow using inviscid fluid dynamics. We find that the
power extracted by the array is the product of two components: (i) the
deflected kinetic energy incident on the array, and (ii) the array efficiency,
both of which vary with deflection strength. The array efficiency, or its
ability to extract a fraction of the incident energy, decreases slightly with
increasing deflection from about 57\% at weak deflection to 39\% at high
deflection. This decrease is outweighed by increasing incident kinetic energy
with deflection, resulting in monotonically improved power extraction, thus
highlighting the benefits from flow deflection.
