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Hathaway, DH, Somerville RCJ.  1986.  Nonlinear Interactions between Convection, Rotation and Flows with Vertical Shear. Journal of Fluid Mechanics. 164:91-&.   10.1017/s0022112086002483   AbstractWebsite

A three-dimensional and time-dependent numerical model is used to study the nonlinear interactions between thermal convective motions, rotation, and imposed flows with vertical shear. All cases have Rayleigh numbers of 104 and Prandtl numbers of 1.0. Rotating cases have Taylor numbers of 104.For the non-rotating cases, the effects of the shear on the convection produce longitudinal rolls aligned with the shear flow and a downgradient flux of momentum. The interaction between the convection and the shear flow decreases the shear in the interior of the fluid layer while adding kinetic energy to the convective motions. For unit Prandtl number the dimensionless flux of momentum is equal to the dimensionless flux of heat.For rotating cases with vertical rotation vectors, the shear flow favours rolls aligned with the shear and produces a downgradient flux of momentum. However, the Coriolis force turns the flow induced by the convection to produce a more complicated shear that changes direction with height. As in the non-rotating cases, the convective motions become more energetic by extracting energy from the mean flow. For Richardson numbers larger than about − 1.0, the dominant source of eddy kinetic energy is the shear flow rather than buoyancy.For rotating cases with tilted rotation vectors the results depend upon the direction of the shear. For weak shear, convective rolls aligned with the rotation vector are favoured. When the shear flow is directed to the east along the top, the rolls become broader and the convection weaker. For large shear in this direction, the convective motions are quenched by the competition between the shear flow and the tilted rotation vector. When the shear flow is directed to the west along the top, strong shear produces rolls aligned with the shear. The heat and momentum fluxes become large and can exceed those found in the absence of a tilted rotation vector. Countergradient fluxes of momentum can also be produced.

Hathaway, DH, Somerville RCJ.  1987.  Thermal Convection in a Rotating Shear Flow. Geophysical and Astrophysical Fluid Dynamics. 38:43-&.   10.1080/03091928708210105   AbstractWebsite

A three-dimensional and time-dependent numerical model is used to simulate thermal convection imbedded in a shear flow in a rotating atmosphere. The fluid is confined to a plane parallel layer with periodic side boundaries, and the rotation vector is tilted from the vertical to represent a low-latitude region. An eastward mean flow is imposed which is constant with depth but has a jet-like profile in latitude. The convection is driven by a prescribed vertical temperature difference. Interactions between the shear flow and the convection extract energy from the mean flow and decrease the mean shear in the nonrotating case. In the presence of rotation, however, the convection can feed energy into the jet and enhance the mean shear. Mean meridional circulations are also produced by the effects of rotation. The Coriolis force on the vertical flows in these circulations contributes to the changes in the mean zonal wind. Three rotating cases are examined which show this behavior in varying degrees. A simple mechanism is described which explains how the convection can produce this countergradient flux of momentum in a rotating layer. Although the system studied is highly idealized, it exhibits momentum fluxes and wave-like patterns which, for certain parameter values, are similar to those observed on Jupiter.

Hathaway, DH, Somerville RCJ.  1983.  Three-Dimensional Simulations of Convection in Layers with Tilted Rotation Vectors. Journal of Fluid Mechanics. 126:75-&.   10.1017/s0022112083000051   AbstractWebsite

Three-dimensional and time-dependent numerical simulations of thermal convection are carried out for rotating layers in which the rotation vector is tilted from the vertical to represent various latitudes. The vertical component of the rotation vector produces narrow convection cells and a reduced heat flux. As this vertical component of the rotation vector diminishes in the lower latitudes, the vertical heat flux increases. The horizontal component of the rotation vector produces striking changes in the convective motions. It elongates the convection cells in a north–south direction. It also tends to turn upward motions to the west and downward motions to the east in a manner that produces a large-scale circulation. This circulation is directed to the west and towards the poles in the upper half of the layer and to the east and towards the equator in the bottom half. Since the layer is warmer on the bottom this circulation also carries an equatorward flux of heat. When the rotation vector is tilted from the vertical, angular momentum is always transported downwards and toward the equator. For rapidly rotating layers, the pressure field changes in a manner that tends to balance the Coriolis force on vertical motions. This results in an increase in the vertical heat flux as the rotation rate increases through a limited range of rotation rates.

Hathaway, DH, Somerville RCJ.  1985.  Numerical simulation in three space dimensions of time-dependent thermal convection in a rotating fluid. Lectures in Applied Mathematics. 22:309-319. Abstract

Three-dimensional time-dependent convection in a plane layer of fluid, uniformly heated from below and subject to vertical shear and to rotation about an axis tilted from the vertical, was simulated by the numerical solution of the Boussinesq equations, including all Coriolis terms. Rotation about a vertical axis produces smaller convection cells with diminished heat fluxes and considerable vorticity. When the rotation axis is tilted from the vertical to represent tropical latitudes, the convection cells become elongated in a N-S direction. Imposed flows with constant vertical shear produce convective rolls aligned with the mean flow. When the rotation vector is tilted from the vertical, the competing effects due to rotation and shear can stabilize the convective motions.