  Traditional large eddy simulation is based on Kolmogrov's hypothesis, and
done in the inertial range. In inertial range the LES model coefficient is
scale-invariant. In many cases, such as computing in the boundary layer, the
filter scale is not in the inertial range, and the model coefficient changes
drastically with the filter scale, thus the assumption of scale-invariance is
not proper. In this paper, we propose a general principle of constraint, and
then we deduce two concrete constraints based on the existing spectrum theory
and priori data. The constrained dynamic Smogorinsky model can predict energy
spectrum well in different range of forced and decayed turbulence. Dynamic
mixed models with one of the constraints shows more efficient than some
classical models in predicting energy spectrum and SGS dissipation, and also
displays a strong correlation with the real stress in different range of the
turbulent flows.
