same form and , then the Germano identity provides an equation from which the Smagorinsky coefficient (which is no longer a 'constant') can potentially be determined. [Inherent in the procedure is the assumption that the coefficient is invariant of scale (see review )]. In order to do this, two additional steps were introduced in the original formulation. First, one assumed that even though was in principle variable, the variation was sufficiently slow that it can be moved out of the filtering operation . Second, since was a scalar, the Germano identity was contracted with a second rank tensor (the rate of strain tensor was chosen) to convert it to a scalar equation from which could be determined. Lilly found a less arbitrary and therefore more satisfactory approach for obtaining C from the tensor identity. He noted that the Germano identity required the satisfaction of nine equations at each point in space (of which only five are independent) for a single quantity . The problem of obtaining was therefore over-determined. He proposed therefore that be determined using a least square fit by minimizing the residuals. This results in Here and for brevity , Initial attempts to implement the model in LES simulations proved unsuccessful. First, the computed coefficient was not at all "slowly varying" as assumed and varied as much as any other turbulent field. Secondly, the computed could be positive as well as negative. The latter fact in itself should not be regarded as a shortcoming as a priori tests using filtered DNS fields have shown that the local subgrid dissipation rate in a turbulent field is almost as likely to be negative as it is positive even though the integral over the fluid domain is always positive representing a net dissipation of energy in the large scales. A slight preponderance of positive values as opposed to strict positivity of the eddy-viscosity results in the observed net dissipation. This so-called "backscatter" of energy from small to large scales indeed corresponds to negative C values in the Smagorinsky model. Nevertheless, the Germano-Lilly formulation was found not to result in stable calculations. An ad hoc measure was adopted by averaging the numerator and denominator over homogeneous directions (where such directions exist in the flow) When the averaging involved a large enough statistical sample that the computed was positive (or at least only rarely negative) stable calculations were possible. Simply setting the negative