<p>An experimental study of the stability of a centrifuged liquid–liquid interface at the non-uniform rotation is hereby presented. Two immiscible liquids, different in density and having high viscosity contrast, fill a horizontal, circular Hele-Shaw (H-S) cell rotating about the vertical axis. At the continuous rotation, the liquids form an axisymmetric core-annular configuration. Then, the rotation rate is modulated as a sum of constant and periodically varying values, and the oscillatory Kelvin–Helmholtz (K–H) instability is sought for. The interface dynamics is assessed by taking photographs and numerically processing the images recorded. With the increase in the amplitude of rotation rate modulation, the interface loses stability giving rise to an azimuthally periodic, quasi-stationary wavy pattern—the “frozen wave” driven by the oscillatory K–H instability. The evolution of its properties in the supercritical regime of oscillations is studied depending on the values of the rotation rate and the frequency and amplitude of librations. The experimental results are analyzed in comparison to the case of a vertical H-S cell at non-uniform rotation. The role of orientation of the gravity field is discussed, and its impact on the threshold of instability onset is found. A conclusion is made that the gravity-induced asymmetry in combination with the choice of the dimensionless frequency may reduce the interface stability by engaging an additional vibrational mechanism.</p>