A note on Tennekes hypothesis and its impact on second moment closure models

Tennekes [Lecture Notes on Turbulence, World Scientific (1989) 32] postulated that the shear production term should drop out of the equation for the rate of change of the turbulence macroscale. This hypothesis has been invoked by some second moment closure modelers, to conveniently fix the value for one of the constants in the equation for the turbulence length scale. In this note, we examine Tennekes hypothesis and its impact on second moment turbulence closure models, which are a part of present-day ocean circulation models.