Turbulence Parameter Space, Scaling Laws, and Structure Parameter Models for Stably Stratified Inhomogeneous Turbulent Shear Flows from Aircraft Measurements

The Reynolds averaged Navier-Stokes equations with Boussinesq approximation form the basis for evaluating the turbulent kinetic energy components budgets, the temperature variance budget, and the velocity-velocity and temperature-velocity covariance budgets. If each component budget is normalized by itself then all terms in that budget have the "dimension" of frequency. If the dominant frequency terms are of opposite sign, i.e. production and dissipation terms and exclude the time-rate-of-change term then that steady-state balance can form a basis for model development of variance structure parameters. These models are comprised of correlation functions, length scales and velocity scales. All of which can be evaluated by either aircraft measurement or direct numerical simulation (DNS) calculations. All turbulence measurements made to date have been with a single instrumented aircraft. Two aircraft measurements are planned over the next several years to more completely evaluate the advection, time-rate-of-change, pressure gradient-velocity correlation, horizontal production, and turbulent transport terms in the second order turbulence budgets. These measurements will characterize turbulence dynamics at turbulence Reynolds numbers in the 1E7 to 1E8 range, illuminate the turbulence prediction problem, and form a basis for a more critical comparison with DNS calculations of stably stratified turbulent shear flows at turbulent Reynolds numbers currently reachable in the 1E4 to 1E5 range.