Which type of turbulence is characterized by showery precipitation and gusty winds?

The type of turbulence characterized by showery precipitation and gusty winds is unstable turbulence. This form of turbulence occurs in conjunction with areas of rising air, often associated with convective processes like thunderstorms. In unstable atmospheric conditions, warm air rises and cools, leading to the formation of clouds and, consequently, precipitation. The accompanying gusty winds are often an indication of the turbulent air movement as the rising air interacts with colder air aloft, creating instability in the atmosphere.

In contrast, stable turbulence generally occurs in a more stratified atmosphere where air layers resist vertical movement, typically leading to smoother conditions. Shear turbulence results from varying wind speeds and directions at different altitudes but does not inherently involve precipitation. Thermal turbulence is specifically linked to convective currents caused by surface heating, but it is not solely characterized by the presence of precipitation, making unstable turbulence the most fitting description for the conditions outlined in the question.