Correlation Dimensions of Primitive Equation and Balanced Models

Abstract

Low-order primitive equation and balanced models are compared by evaluating the correlation dimension of each over a range of Rossby numbers. The models are the nine-component primitive equation model of Lorenz and the corresponding three-component balance model. Both models display behavior ranging from stable fixed points and limit cycles to chaotic dynamics. At low Rossby number, the correlation dimensions of the models are (to the accuracy of the calculation) very similar, even in the presence of strange attractors. At higher Rossby number, the behavior differs: in some regions where the balance model goes into a limit cycle the primitive equation model displays chaotic behavior, with a correlation dimension greater than three. This appears to be caused by the (somewhat intermittent) appearance of gravity waves. Since here the calculated correlation dimension is higher than the number of slow modes, the gravity waves cannot be slaved to the slower geostrophic activity.