A numerical study is made of the basic-state ¯ow ®eld of a ¯uid with a density maximum in a dierentially rotating cylinder. The ¯uid density reaches a maximum q m at temperature T m , and a quadratic q±T relationship is used to model the ¯uid behavior near T m . The temperature at the bottom (top) endwall disk is T B T T , with DT T T À T B > 0, and T m lies between T B and T T . The rotation rate of the bottom (top) endwall disk is X B X T , with e X T À X B =X B ( 1. Numerical solutions were obtained of the Navier± Stokes equations for large rotational Reynolds number and large Rayleigh number. Detailed ¯ow and density ®elds are portrayed to be strongly dependent on the density inversion factor c T m À T B =T T À T B . When c 0, the results are qualitatively similar to those of a usual Boussinesq ¯uid with a linear q±T relationship. It is shown that a modi®ed thermal wind relation prevails in the interior, in which the vertical shear of azimuthal velocity is balanced by the radial gradient of density. As c increases, the overall strength of meridional circulation grows. The vertical pro®les of azimuthal velocity are plotted as c varies. The Ekman layer suction is intensi®ed as c increases. The behavior of average Nusselt number Nu at the bottom disk with varying c is discussed and physical rationalizations are given.