This work concerns the zero Mach number limit of the compressible primitive equations. The primitive equations with the incompressibility condition are identified as the limiting equations. The convergence with well-prepared initial data (i.e., initial data without acoustic oscillations) is rigorously justified, and the convergence rate is shown to be of order O(ε), as ε→0+, where ε represents the Mach number. As a byproduct, we construct a class of global solutions to the compressible primitive equations, which are close to the incompressible flows.
