Energy decay laws in strongly anisotropic MHD turbulence

We investigate the influence of a uniform magnetic field ${\mathbf{B}}_{\mathbf{0}}=B_{0}e\mathrm{/}\mathrm{/}$ on energy decay laws in incompressible magnetohydrodynamic (MHD) turbulence. The nonlinear transfer reduction along $B_0$ is included in a model that distinguishes parallel and perpendicular directions, following a phenomenology {\it `a la} Kraichnan. We predict a slowing down of the energy decay due to anisotropy in the limit of strong $B_0$, with distinct power laws for energy decay of shear- and pseudo-Alfv'en waves. Numerical results from the kinetic equations of Alfv'en wave turbulence recover these predictions, and MHD numerical results clearly tend to follow them in the lowest perpendicular planes.