Interaction of Convection and Frictional Convergence

In unstratified or weakly stratified rotating fluid the secondary circulation associated with frictionally induced cross-isobaric flow in the boundary layer can extend through the full depth of the fluid. If the fluid depth is much greater then the boundary layer depth the time scale for spindown is much greater then the rotational time scale. In this case, the steady-state approximation due to time independence may be invoked and the primary balance is between the friction and Coriolis terms.

However, if the fluid is stratified, the secondary circulation is confined to a shallower layer, the convergence is weaker and the spin down is more rapid in the limited depth in which it happens. This occurs for typical atmospheric disturbances with radius scales less than several hundred kilometers. In the case of strong stratification it is the time tendency term in the momentum equation that is in balance with friction and not the Coriolis term.

This is all well known, but the consequences might not have been thought through. In particular we address the question of what comes first, convection or convergence. Causality is important in understanding the dynamics of tropical, convectively coupled disturbances such as ITCZs, tropical waves, tropical cyclones and even the Madden-Julian oscillation.

In the stratified atmosphere where spin down is rapid, if we take away the convection, there is little frictional convergence on scales less than a few hundred kilometers. This implies that there has to be convection in order for convergence to occur. But what triggers the convection? We propose that the moisture mode mechanism plays a crucial role for many cases in the tropics. In this mode the convection results from high relative humidity plus random local noise which overcomes convective inhibition. The convection then leads to convergence and not vice-versa, and frictional convergence plays a minimal role in forcing convection.