  This work introduces a formulation of resolvent analysis that uses wavelet
transforms rather than Fourier transforms in time. This allows resolvent
analysis to be extended to turbulent flows with non-stationary means in
addition to statistically-stationary flows. The optimal resolvent modes for
this formulation correspond to the potentially time-transient structures that
are most amplified by the linearized Navier-Stokes operator. We validate this
methodology for turbulent channel flow and show that the wavelet-based and
Fourier-based resolvent analyses are equivalent for statistically-stationary
flows. We then apply the wavelet-based resolvent analysis to study the
transient growth mechanism in the buffer layer of a turbulent channel flow by
windowing the resolvent operator in time and frequency. The method is also
applied to temporally-evolving parallel shear flows such as an oscillating
boundary layer and three-dimensional channel flow, in which a lateral pressure
gradient perturbs a fully-developed turbulent flow in a channel.
