THE GOAL OF THE PROPOSAL IS TO DERIVE A FOURTH-ORDER STATISTICAL CLOSURE FROM A SET OF THE REYNOLDS-AVERAGED NAVIER-STOKES (RANS) EQUATIONS AND VALIDATE THE MODEL IN UNSTEADY SEPARATED FLOWS. AMONG VARIOUS APPROACHES TO MODELING TURBULENT FLOWS A STATISTICAL APPROACH BASED ON SOLVING RANS EQUATIONS IS THE ONE WITH THE EXPLICIT RELATION EXISTING BETWEEN THE AMOUNT OF FLOW PHYSICSINCORPORATED INTO A MODEL AND THE NUMBER OF TRANSPORT EQUATIONS TO BE SOLVED. INDEED BY SOLVING A FULL SET OF RANS EQUATIONS FOR ALL STATISTICAL MOMENTS (VELOCITY CORRELATIONS) ONE CAN COMPLETELY RESOLVE THE TURBULENT FLOW STRUCTURE AS THE KNOWLEDGE OF ALL STATISTICALMOMENTS IS EQUIVALENT TO THE KNOWLEDGE OF THE PROBABILITY DENSITY FUNCTION OF A FLOW FILED. TYPICAL ENGINEERING MODELS THAT EXPLICITLY SOLVE ONLY TRANSPORT EQUATIONS FOR THE MEAN VELOCITY COMPONENTS ARE ON THE OPPOSITE END. IN SUCH MODELS ESSENTIALLY ALL EFFECTS DUE TO TURBULENCE ARE MODELED. BETWEEN THESE TWO ENDS: IMPOSSIBLE AND IMAGINATIVE THERE ARE STATISTICAL CLOSURES OF SECOND- AND HIGHER ORDERS THAT ALLOW ONE TO BRING INTO A MODEL AS MUCH PHYSICS AS NECESSARY TO REPRODUCE AND PREDICT THE FLOW FEATURES OF INTEREST WITH THE REQUIRED ACCURACY. THE PURPOSE OF THE PROPOSAL IS TO DEMONSTRATE THAT FOURTH-ORDER CLOSURES (FORANS) ARE MOST LIKELY TO BE SUFFICIENT FOR REPRODUCING THE FEATURES OF INTEREST IN UNSTEADY SEPARATED FLOWS. THE FIFTH- AND HIGHER-ORDER STATISTICAL MOMENTS WILL BE MODELED USING THE GRAM-CHARLIER SERIES EXPANSION. THIS APPROACH DOES NOT BRING ANY MODEL COEFFICIENTS AND PREVIOUSLY WAS SUCCESSFULLY VALIDATED IN OTHER FLOWS. AS TURBULENT DIFFUSION IN THE THIRD- AND LOWER-ORDER TRANSPORT EQUATIONS OF FORANS DOES NOT NEED ANY MODELING THERE WILL BE NO MODEL COEFFICIENT ASSOCIATED WITH SUCH TERMS. AS PREVIOUSLY DEMONSTRATED ADEQUATE DESCRIPTION OFTURBULENT DIFFUSION AND PRESSURE-CONTAINING CORRELATIONS ALSO ELIMINATES A NEED IN WALL FUNCTIONS. NO MODELING OF THE THIRD- AND FOURTH-RANK DISSIPATION TENSORS IS INITIALLY PROPOSED DUE TO THEIR NEGLIGIBLE CONTRIBUTION OBSERVED IN OTHER APPLICATIONS. HOWEVER VALIDITY OF THIS ASSUMPTION IN SEPARATED FLOWS WILL BE INVESTIGATED. THUS THE MAIN FOCUS OF THE PROPOSAL IS MODELING THE VELOCITY PRESSURE-GRADIENT CORRELATIONS AND THE SECOND-RANK DISSIPATION TENSOR. THE PROPOSAL WILL UTILIZE MODELS PREVIOUSLY DERIVED BY THE PI FOR THE RAPID PART OF THE VELOCITY PRESSURE-GRADIENT CORRELATIONS. IT WAS FOUND THAT IF THE TENSORS PROPERTIES ARE UTILIZED CORRECTLY THE NUMBER OF MODEL COEFFICIENTS IS NOT INCREASED IN MODELS FOR HIGHER-ORDER CORRELATIONS. OTHER COMPONENTS WILL BE MODELED IN THEPROPOSAL FOLLOWING A SIMILAR APPROACH. BY MODELING THE VELOCITY PRESSURE-GRADIENT CORRELATIONS ORIGINALLY PRESENT IN THE RANS EQUATIONS FORANS ELIMINATES PROBLEMS RELATED TO MODELING THE PRESSURE-STRAIN CORRELATIONS. THE PRESSURE-STRAIN CORRELATION MODELS NEGLECT THE PRESSURE DIFFUSION CONTRIBUTION ASSUMING TURBULENCE HOMOGENEITY. NEITHER THIS ASSUMPTION IS JUSTIFIED IN AERODYNAMICFLOWS NOR CAN SUCH MODELS BE EXTENDED IN A RATIONAL MANNER TO MODELING HIGHER-ORDER VELOCITY PRESSURE-GRADIENT CORRELATIONS. STABILITY OF A NUMERICAL PROCEDURE WILL BE ADDRESSED. AS HIGH-FIDELITY DATA FOR HIGHER-ORDER STATISTICS ARE SCARS OR NOT AVAILABLE DNS ARE PROPOSED WITH THE PURPOSE OF GENERATING HIGH-FIDELITY DATABASE FOR MODEL DEVELOPMENT. THE PROPOSAL WILL CONTRIBUTE IN BETTERUNDERSTANDING THE PHYSICS OF TURBULENT FLOWS AND IN THE DEVELOPMENT OF IMPROVED PREDICTION METHODS SUITABLE FOR ACCURATE AND RELIABLE SIMULATIONS OF UNSTEADY SEPARATED FLOWS ACROSS THE SPEED REGIMES. THUS THE PROPOSAL WILL CONTRIBUTE IN ACHIEVING NASA'S KEY GOALS OF REDUCING FUEL BURN NOISE EMISSION AND FILED LENGTH. IT DIRECTLY SUPPORTS THE OBJECTIVES OF THE NASA SWF PROJECT AND THE OTHER THREE FA PROGRAMS.