Voyager 1 observed Kolmogorov-like (k−5/3) compressible turbulence just upwind of the heliopause. Subsequent measurements by Voyager 1 further from the heliopause revealed that the observed fluctuations were now fully incompressible, with a k−5/3 spectrum that was essentially identical to that of the earlier compressible spectrum. Zank et al. showed that only compressible fast magnetosonic modes could be transmitted from the inner heliosheath into the very local interstellar medium (VLISM), and could exhibit a k−5/3 spectrum. We show here that the small plasma beta VLISM admits three-wave interactions between a fast magnetosonic mode, a zero-frequency mode, and an Alfvén wave. The fast magnetosonic mode is converted to an incompressible Alfvén (or zero-frequency) mode with wavenumber almost identical to that of the initial compressible fast mode. The initial compressible and generated incompressible spectra are essentially identical. For the wavelength range observed by Voyager 1, we estimate that compressible fast modes are fully mode-converted to incompressible fluctuations within ∼10 au of the heliopause. We suggest that the VLISM magnetic field spectrum is a superposition of a higher amplitude ∼k−5/3 spectrum of heliospheric origin with an estimated correlation length ∼30 au, having a minimum wavenumber ∼(100)−1 (au)−1, and a lower amplitude (possibly local) ISM k−5/3 spectrum, the latter possessing an outer scale ≥2 pc. We suggest that the transmission of compressible turbulence from an inner asterosheath into the local circumstellar interstellar medium surrounding a star, and the subsequent mode conversion to incompressible turbulence, may be a general mechanism by which stars drive turbulence in the interstellar medium.