  Using an exact law for incompressible Hall magnetohydrodynamics (HMHD)
turbulence, the energy cascade rate is computed from three-dimensional HMHD-CGL
(bi-adiabatic ions and isothermal electrons) and Landau fluid (LF) numerical
simulations that feature different intensities of Landau damping over a broad
range of wavenumbers, typically $0.05\lesssim k_\perp d_i \lesssim100$. Using
three sets of cross-scale simulations where turbulence is initiated at large,
medium and small scales, the ability of the fluid energy cascade to "sense" the
kinetic Landau damping at different scales is tested. The cascade rate
estimated from the exact law and the dissipation calculated directly from the
simulation are shown to reflect the role of Landau damping in dissipating
energy at all scales, with an emphasis on the kinetic ones. This result
provides new prospects on using exact laws for simplified fluid models to
analyze dissipation in kinetic simulations and spacecraft observations, and new
insights into theoretical description of collisionless magnetized plasmas.
