  The current paper presents an experimental study of the energy budget of a
two-dimensional internal wave attractor in a trapezoidal domain filled with
uniformly stratified fluid. The injected energy flux and the dissipation rate
are simultaneously measured from a \ch{two-dimensional, two components,}
experimental velocity field. The pressure perturbation field needed to quantify
the injected energy is determined from the linear inviscid theory. The
dissipation rate in the bulk of the domain is directly computed from the
measurements, while the energy sink occurring in the boundary layers are
estimated using the theoretical expression of the velocity field in the
boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech. 841, 614
(2018)). In the linear regime, we show that the energy budget is closed, in the
steady-state and also in the transient regime, by taking into account the bulk
dissipation and, more important, the dissipation in the boundary layers without
any adjustable parameters. The dependence of the different sources on the
thickness of the experimental set-up is also discussed. In the nonlinear
regime, the analysis is extended by estimating the dissipation due to the
secondary waves generated by triadic resonant instabilities showing the
importance of the energy transfer from large scales to small scales. The method
tested here on internal wave attractors can be generalized straightforwardly to
any quasi two-dimensional stratified flow.
