The test-field model for isotropic turbulence is used to examine the effective eddy viscosity acting on wavenumbers km. In both two and three dimensions, the effective eddy viscosity for k≪km. is independent of k and of local spectrum shape. In two dimensions, this asymptotic eddy viscosity is negative. The physical mechanism responsible for the negative eddy viscosity is the interaction of large-spatial-scale straining fields with the secondary flow associated with small-spatial-scale vorticity fluctuations. This process is examined without appeal to turbulence approximations. For km−k≪km, the effective eddy viscosity rises sharply to a cusp at k=km if km lies in a long energy-transferring inertial range in either two or three dimensions or in a long enstrophy-transferring inertial range in two dimensions. The cusp behavior is associated with a diffusion in wavenumber due to random straining, by large spatial scales,... Abstract The test-field model for isotropic turbulence is used to examine the effective eddy viscosity acting on wavenumbers km. In both two and three dimensions, the effective eddy viscosity for k≪km. is independent of k and of local spectrum shape. In two dimensions, this asymptotic eddy viscosity is negative. The physical mechanism responsible for the negative eddy viscosity is the interaction of large-spatial-scale straining fields with the secondary flow associated with small-spatial-scale vorticity fluctuations. This process is examined without appeal to turbulence approximations. For km−k≪km, the effective eddy viscosity rises sharply to a cusp at k=km if km lies in a long energy-transferring inertial range in either two or three dimensions or in a long enstrophy-transferring inertial range in two dimensions. The cusp behavior is associated with a diffusion in wavenumber due to random straining, by large spatial scales,...