This paper proposes the spherical harmonic and the cylindrical harmonic decompositions of the acoustic velocity vectors of the outgoing sound field. The spherical harmonic coefficients and the cylindrical harmonic coefficients of the pressure of the outgoing sound field can be measured by a spherical microphone array and a cylindrical microphone array surrounding the source, respectively. By using the sound field translation formula, the spherical harmonic coefficients and the cylindrical harmonic coefficients of the acoustic velocity vectors of the outgoing sound field are obtained. Simulations show the proposed spherical harmonic and cylindrical harmonic decompositions of the acoustic velocity vectors can accurately model a monopole, a dipole and a quadrupole. The proposed decompositions can be used in exterior noise control, where an array of loudspeakers controls the acoustic velocity vectors of the outgoing sound field.