Generic instabilities in a fluid membrane coupled to a thin layer of ordered active polar fluid

We develop an effective two-dimensional coarse-grained description for the coupled system of a planar fluid membrane anchored to a thin layer of polar ordered active fluid below. The macroscopic orientation of the active fluid layer is assumed to be perpendicular to the attached membrane. We demonstrate that {\em activity} or nonequilibrium drive of the active fluid makes such a system generically linearly unstable for either signature of a model parameter $\Delta\mu$ that characterises the strength of activity. Depending upon boundary conditions and within a range of the model parameters, underdamped propagating waves may be present in our model. We discuss the phenomenological significance of our results.