Turbulence parameter space, budgets, scaling laws,and structure parameter models for stably stratified shear flows from aircraft measurements

During the period 1998 to 2002 five turbulent measurement campaigns were made with Airborne Research Australia's GROB 520T EGRETT instrumented aircraft in an attempt to capture the structure of severe turbulence events that could impact the performance of high energy laser systems or could lead to loss or damage to high altitude manned and unmanned surveillance aircraft. Measurements were confined to the winter subtropical jet stream with one campaign in Japan in February 1999 and the rest were in the vicinity of Adelaide, Australia in August/September in 1998, 1999, 2001, and 2002. One goal is to relate severe turbulence events to measured values of turbulent Reynolds number, turbulent Prandtl number, turbulent Froude number, and bulk gradient Richardson number. Budget equations of the three turbulent kinetic energy components, the temperature variance, the three components of Reynolds stress, and the three components of heat flux are derived from the Reynolds averaged Navier-Stokes equations with Boussinesq approximation. If the budget for each component is normalized by itself then all terms in that budget have the "dimension" of frequency. If the dominant frequency terms are of opposite sign, in quasi-balance between production and dissipation terms, and exclude the time-rate-of-change term then an approximate steady-state balance can form a basis for model development of variance and covariance structure parameters. The steady-state model would not be applicable if the dominant balance is between the dissipation and time-rate-of-change and is in the presence of significant but decaying turbulence. The time variation term and advection of turbulence terms were not explored with the single aircraft measurements. In a balanced state, the net production (shear and/or stratification) at integral scales can be used to model the structure parameters which are representative of the turbulent dissipation. These structure function models are comprised of correlation functions, length scales and velocity scales. A long-term goal of these aircraft turbulence is to contribute to the development and validation of structure function parameter models for velocity components and refraction (temperature) for stably stratified free shear flow where turbulence scaling laws need to be established. The length scales that are used to model the structure function parameters follow from scale definitions derived from the budget equations. The magnitude of these length scales and length scale ratios can be evaluated from the aircraft measurements or from direct numerical simulation (DNS) model studies (Joseph et al., 2004) but cannot be predicted with current meso-scale numerical weather prediction models. The DNS model studies are limited to turbulent Reynolds numbers less then 104. Aircraft measurements are in the 107 to 108 range. A further difficulty evident in the aircraft measurements is the anisotropy in the inertial subrange of the vertical velocity spectra even at these high turbulent Reynolds numbers. One form of severe turbulence event of interest to both propagation and flight safety are the cliff and ramp (ramp and cliff) structures found in the shear layer below (above) the peak jet stream winds. Two aircraft measurements are planned to investigate the evolution of cliff and ramp structures and to more completely evaluate turbulence budgets including the advection, time-rate-of-change, pressure gradient-velocity correlation if possible, horizontal production, and turbulent transport terms in the second order turbulence budgets. In addition these measurements, which characterize turbulence structure and dynamics of stably stratified free shear flows at turbulence Reynolds numbers in the 107 to 108 range, will provide a more complete basis for comparison of aircraft measurements with DNS calculations of stably stratified turbulent shear flows in the 104 to 105 range of turbulent Reynolds numbers.