Assuming that the surface roughness is of small amplitude and can be modeled by a homogeneous random function in space, the classical Reynolds equation is averaged using a method due to J. B. Keller. The mean Reynolds equation is accurate up to terms of 0(ε2), where ε is the dimensionless amplitude of the surface roughness and has a nonlocal character. Furthermore, by exploiting the slowly varying property of the mean film thickness, this nonlocal character is eliminated. The resulting mean Reynolds equation depends on the surface roughness via its spectral density and, in the limits of either parallel or transverse surface roughness, it reduces to Christensen’s theory.

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