Turbulent Compressible Convection with Rotation. I. Flow Structure and Evolution

Abstract

The e†ects of Coriolis forces on compressible convection are studied using three-dimensional numeri- cal simulations carried out within a local modiÐed f-plane model. The physics is simpliÐed by consider- ing a perfect gas occupying a rectilinear domain placed tangentially to a rotating sphere at various latitudes, through which a destabilizing heat Ñux is driven. The resulting convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers, evaluating conditions where the inÑuence of rotation is both weak and strong. Given the computational demands of these high-resolution simulations, the parameter space is explored sparsely to ascertain the di†erences between laminar and turbulent rotating convection. The Ðrst paper in this series examines the e†ects of rotation on the Ñow structure within the convection, its evolution, and some consequences for mixing. Subsequent papers consider the large-scale mean shear Ñows that are generated by the convection, and the e†ects of rota- tion on the convective energetics and transport properties. It is found here that the structure of rotating turbulent convection is similar to earlier nonrotating studies, with a laminar, cellular surface network disguising a fully turbulent interior punctuated by verti- cally coherent structures. However, the temporal signature of the surface Ñows is modiÐed by inertial motions to yield new cellular evolution patterns and an overall increase in the mobility of the network. The turbulent convection contains vortex tubes of many scales, including large-scale coherent structures spanning the full vertical extent of the domain involving multiple density scale heights. Remarkably, such structures align with the rotation vector via the inÑuence of Coriolis forces on turbulent motions, in contrast with the zonal tilting of streamlines found in laminar Ñows. Such novel turbulent mechanisms alter the correlations which drive mean shearing Ñows and a†ect the convective transport properties. In contrast to this large-scale anisotropy, small-scale vortex tubes at greater depths are randomly orientated by the rotational mixing of momentum, leading to an increased degree of isotropy on the medium to small scales of motion there. Rotation also inÑuences the thermodynamic mixing properties of the con- vection. In particular, interaction of the larger coherent vortices causes a loss of correlation between the vertical velocity and the temperature leaving a mean stratiÐcation which is not isentropic.