Laurent White

Tracer conservation for three-dimensional, finite-element, free-surface, ocean Modeling on moving prismatic meshes

Large-scale free-surface ocean models designed to run over climatic time scales are required to globally conserve the volume and any tracer up to machine precision. In addition, local consistency is critical and requires that the discrete tracer equation preserve constants in a closed domain and if there is no tracer source or sink. Local consistency, together with monotonicity, will ensure that no spurious tracer extrema occur. A three-dimensional, finite-element, shallow-water model is presented. The mesh is unstructured in the horizontal, extruded in the third dimension, and made up of multiple layers of prisms. In addition, the mesh is allowed to move in the vertical and adapts itself to the free-surface motions. It is shown that achieving consistency requires a discrete compatibility between the tracer and continuity equations. In addition, to ensure global tracer conservation in a consistent way, a discrete compatibility between the tracer, continuity, and free-surface elevation equations must be fulfilled. It is suggested that this compatibility constraint, together with the use of a numerically stable scheme, severely restricts the choice of usable finite-element spatial discretizations. A consistent and conservative time-stepping algorithm is described for which a unique time step is used. It is suggested that future research is needed in order to design a consistent and conservative split-explicit algorithm. Some illustrative test cases are presented in which the method is shown to satisfy all conservation properties. A few experiments in which consistency breaks down are carried out, and the consequences of this breakdown process are investigated.

Free and forced thermocline oscillations in Lake Tanganyika

All year long, the thermocline of Lake Tanganyika (Central Africa) oscillates about two equilibrium states. The thermocline is tilted downward toward the north during the dry season, due to the wind bringing the warm surface water from south to north. The equilibrium position of the thermocline is horizontal during the wet season. The oscillations about these two equilibrium states may be of two types. The free oscillations are due to the seasonal cycle of the wind stress, while the forced oscillations are a direct response to the intraseasonal variability of the surface forcing. It has already been suggested that both have a three- to four- week oscillation period. The Factor Separation method is here used to show that the forced oscillations of the thermocline are about twice as large as the free ones. Introduction Lake Tanganyika is located to the east of central Africa, and is shared by four developing countries: Democratic Republic of the Congo, Burundi, Tanzania, and Zambia. It lies between 3° 20′ and 8° 45′ S and 29° 05′ to 31° 15′ E. It is about 650 km long and 50 km wide on average. The mean depth of the lake is about 570 m, with a maximum depth of 1470m (Fig. 9.1). That makes it the second deepest lake in the world, the deepest being Lake Baikal in Russia. Thermal stratification is well marked and present all year long, so that one can identify two distinct layers: the surface and the bottom layers.