Overfire

In the interest of smoke abatement, overfire jets are now installed on thousands of commercial and industrial coal-fired furnaces. [...] The overfire jet is a device for providing turbulence and/or overfire air above the fuel bed of hand-fired and stoker-fired furnaces.

Source: wiktionary

Volatile matter in the vapor form and carbon monoxide just above the bed must be fully mixed with overfire air to complete the combustion process. At low firing rates it is important to minimize the amount of overfire air to prevent cooling of the volatile matter resulting in incomplete combustion and soot formation.

Source: wiktionary

The primary flame zone can be operated fuel rich to reduce oxygen concentration, then additional air can be added downstream. This overfire air provides oxygen to complete combustion of unburned fuel and oxidizes carbon monoxide to carbon dioxide, creating a second combustion zone. Because there is so little fuel in this overfire zone, the peak flame temperature is low.

Source: wiktionary

Over-fire boilers are the simplest and cheapest domestic boilers for burning wood logs. [...] In over-fire boilers, combustion takes place in the whole fuel batch more or less at the same time, as in wood-stoves. The boiler is normally equipped with a primary air inlet under the grate and a secondary air inlet over the fuel batch, into the gas combustion zone.

Source: wiktionary