Empirical turbulent Prandtl number parameterisation as a function of Richardson number

Atmospheric boundary layer profile and flux measurements from an Antarctic ice shelf are presented, showing the behaviour of turbulent Prandtl number (Pr) as a function of gradient Richardson number (Ri). Pr, the ratio of the diffusivities for momentum and heat, is assumed to be near unity for pure turbulent flow, but conceptually, could tend to infinity under stable stratification where turbulence is suppressed but internal waves within the flow remain. Whether such conditions occur naturally, and to what extent, is still uncertain, due to a number of difficulties in measuring Pr as a function of Ri:

· Pr and Ri suffer from self correlation, and some means to avoid such false correlation is required.

· At low stability, both Pr and Ri are sensitive to errors in measured air temperature gradient.

· At moderate stability, waves and sporadic turbulence lead to uncertainty in flux estimates.

· At high stability, data are sparse, and suitable averaging requires large data sets, of the order of months

Three months of data from the austral winter at Halley Station (76oS, 26oW) are presented. The large volume of data allows harsh quality control whilst retaining sufficient records for subsequent analysis of the Pr(Ri) relationship. An empirical Butterworth function is fitted to Pr-1(Ri), using a component variable technique which avoids self-correlation issues.