The equations of motion for perturbed uniformly rotating flows with uniform axial‐time periodic strain, are derived from the Navier–Stokes equations in the low Mach number limit. The perturbation equations admit exponentially growing three‐dimensional solutions for which the amplification factors per period are computed for a range of compression and swirl ratios. It is found that for a given compression ratio, the flow is stable for low swirl ratios, but at high swirl ratios the flow is unstable with the amplification factor dependent on wave angle but independent of wavelength. For an unstable swirl ratio, higher compression ratios yield larger amplification factors.