As shown in FIG.  1, many aircraft include a fairing at the upper surface 203 of a junction between the aircraft fuselage 205 and wing 201 (i.e. the upper surface of the wing root).  One function of such fairings is to reduce or eliminate separation of the airflow in the region of the junction and thereby reduce viscous drag on the aircraft. 
A typical prior art wing root fairing 209 is in the form of a concave, wedge-shaped fillet (the upper surface of the which is represented by the mesh in FIG.  1).  The fillet starts at a mid-chord region of the wing root and extends to a maximum cross-sectional area at, or slightly aft of, the trailing edge of the wing root.  These known fairings are referred to herein as a “conventional wing root fairing”. 
When aircraft operate at transonic speeds, at least one shock may develop in the region of the wing root and/or over the upper surface of the inner wing.  The shock may be undesirable for a number of reasons.  For example, the shock can cause considerable wave drag and may also limit the amount of lift that the inner region of the wing generates. 
Embodiments of the present invention seek to provide a fairing for an aircraft, which removes or mitigates at least one of the above-mentioned problems.