The characteristics of the turbulent boundary and passive layers of an isothermal, rapid-flowing dry granular matter with incompressible solid grains are studied by a zero-order turbulent closure model. To this end, the thermodynamic analysis, based on Mueller-Liu entropy principle, is conducted to derive the equilibrium closure relations satisfying turbulence realizability conditions, with the dynamic responses of postulated by a nonlinear theory with respect to two-fold granular coldnesses. The closure model is applied to analysis of an isothermal, stationary dry granular avalanche down an incline. While the mean velocity and volume fraction increases/decreases from their minimum/maximum values on the plane toward the maximum/minimum values on the free surface exponentially, two-fold turbulent kinetic energies and dissipations evolve in a reverse manner. Most two-fold turbulent kinetic energies and dissipations are confined within the turbulent boundary layer immediately above the plane, with nearly vanishing and finite values on the free surface in the passive layer, respectively. These characteristics demonstrate a similarity to that of conventional Newtonian fluids in turbulent boundary layer flows. The turbulent boundary and passive layers are better verified by the distributions of the turbulent kinetic energy and dissipation.