MAGNETIC AND THERMAL INSTABILITIES IN A PLANE LAYER .1.

A plane layer of electrically conducting Boussinesq fluid between z = +/-d/2 rotating with constant angular velocity Omega = Omega (z) over cap under a vertical gravitational held g = -g (z) over cap is examine d. In order to simulate the Earth's toroidal field, an imposed non-uni form magnetic held of the form B = BB0(z)(y) over cap) is considered w here a is the magnetic held strength and Bolt) is chosen to be antisym metric about z=0. Studying where the most unstable mode of convection neither grows or decays (neutral stability), purely magnetic instabili ties are achieved when the parameter which measures the field strength - the Elsasser number Lambda - exceeds a critical value Lambda(c). Fo r a magnetic held profile B-0(z) = tanh gamma z, an asymptotic analysi s with gamma --> infinity is carried out which yields a value of Lambd a(c) = 2. The magnetic nature of the bounding material is taken to be either perfectly conducting or perfectly insulating. Unstable modes ar e found for all combinations of the magnetic boundary conditions thoug h the symmetry of the flow is broken when the boundaries are different . An adverse temperature gradient T = -beta z is now applied to ensure that the lower boundary is hotter than the upper one. By including th is buoyancy effect, weaker fields are capable of initiating convection when the modified Rayleigh number R - which is a measure of the tempe rature gradient - exceeds some critical Value R-c for a given Lambda. In all cases a stationary pattern of flow is obtained with unique valu es of the horizontal wavenumbers k(c) and I-c associated with the most unstable mode. The flow is therefore in the form of oblique rolls whi ch tend to be aligned more closely with the direction of the imposed m agnetic field for higher values of Lambda.