Transformations for variable-property turbulent boundary layers
The Trettel-Larsson (TL) transformation is extended to two dimensions using mass conservation and an interpretation of Morkovin's hypothesis. This extension reveals the previously unknown limitations of the TL transformation. The TL transformation only works in channel flows, in the inner layer of high Reynolds number boundary layers, and in boundary layers where the viscosity varies with the square root of the density. The error in the TL velocity transformation correlates with the second derivative of the transformed coordinate (the semi-local scaling). The second derivative of the transformed coordinate measures the amount that the transformed outer layer coordinate does not equal the untransformed outer layer coordinate. The extended TL theory now includes a streamwise coordinate transformation and production rate scalings. The limitations of the TL theory state that the analogy between compressible turbulent boundary layers and incompressible turbulent boundary layers is limited in theory but nonetheless useful in practice when possible.