  In gyrokinetic theory there are two quadratic measures of fluctuation energy,
left invariant under nonlinear interactions, that constrain the turbulence. The
recent work of Plunk and Tatsuno [Phys. Rev. Lett. 106, 165003 (2011)] reported
on the novel consequences that this constraint has on the direction and
locality of spectral energy transfer. This paper builds on that work. We
provide detailed analysis in support of the results of Plunk and Tatsuno but
also significantly broaden the scope and use additional methods to address the
problem of energy transfer. The perspective taken here is that the fluctuation
energies are not merely formal invariants of an idealized model
(two-dimensional gyrokinetics) but are general measures of gyrokinetic
turbulence, i.e. quantities that can be used to predict the behavior of the
turbulence. Though many open questions remain, this paper collects evidence in
favor of this perspective by demonstrating in several contexts that constrained
spectral energy transfer governs the dynamics.
