Apart from the solar core, the overshoot layer below the convective zone is the layer where some discrepancies between the standard and seismic solar models continue to exist. Non-local mixing length models are in clear conflict with the seismic evidence. A major difficulty for the development of more sophisticated models is the large degree of arbitrariness in formulating expressions for input parameters like the length scale. We propose that the application of the k-epsilon modelling approach, widely used in physics and engineering, could help in alleviating these difficulties. We present some simple overshoot models calculated with this approach, and we point out that the resulting expression of the length scale naturally reduces to the usual mixing length expression (proportional to the pressure scale height) well inside the convectively unstable region. Implications for the solar Li problem and for dynamo theory will also be discussed.