Nearly-Lagrangian observations from two EM-APEX velocity and density profiling floats on concentric trajectories determine profiles of ocean eddy vorticity and velocity, and the intrinsic frequency, energy, vertical wavenumber, vertical phase velocity, and vertical group velocity of a near-inertial-wave (NIW). For the first time, NIW 𝐶 and 𝐶 are computed from firs principles (by direct computation of 𝜔⁄𝑚 and 𝜕𝜔⁄𝜕𝑚 vs. depth without a dispersion relation). This novel experiment, moving with turbulent zone produced by a downgoing NIW packet observed stalling at 135-m depth. KE flux convergence initiates KE dissipation at 115 m. Below 135 m, shear production is hypothesized to support dissipation. These observations compare well with a theory of NIW interaction with the eddy, not in solid-body rotation. Theory and observations show that the observed turbulent zone arises from wave stalling and instability in a critical or caustic layer as the vertical group velocity of the wave goes toward zero.