  Linearisation of the Navier-Stokes equations about the mean of a turbulent
flow forms the foundation of popular models for energy amplification and
coherent structures, including resolvent analysis. While the Navier-Stokes
equations can be equivalently written using many different sets of dependent
variables, we show that the properties of the linear operator obtained via
linearisation about the mean depend on the variables in which the equations are
written prior to linearisation. For example, we show that using primitive and
conservative variables leads to differences in the singular values and modes of
the resolvent operator for turbulent jets, and that the differences become more
severe as variable-density effects increase. This lack of uniqueness of
mean-flow-based linear analysis provides new opportunities for optimizing
models by specific choice of variables while also highlighting the importance
of carefully accounting for the nonlinear terms that act as a forcing on the
resolvent operator.
