IN A NUTSHELL THE OBJECTIVES OF THIS RESEARCH ARE THREEFOLD: (1) TO ESTABLISH A STOCHASTIC FRAMEWORK FOR DEFINING SENSITIVITIES IN CHAOTIC FLOWS WITH INCORPORATION OF UNCERTAINTY; (2) TO DEVELOP A COMPU- TATIONAL METHODOLOGY AND ITS IMPLEMENTATION FOR DESIGN SENSITIVITIES IN 3D UNSTEADY CHAOTIC FLOWS WITH THE COMPUTATIONAL COST OF A HANDFUL OF FORWARD MODEL EVALUATIONS; AND (3) TO DEVELOP A SUB- MODAL CLOSURE FOR UNRESOLVED DYNAMICS IN HIGH REYNOLDS NUMBERS. THE NOVELTY OF THIS RESEARCH IS PRODUCTION OF A NEW NONLINEAR STOCHASTIC SENSITIVITY EQUATION WHICH INHERITS THE NONLINEAR STABILITY OF THE FORWARD MODEL. AS A RESULT THIS EQUATION MAY RESOLVE SOME OF THE LONGSTANDING SHORTCOMINGS OF COMPUTING SENSITIVITIES IN CHAOTIC SYSTEMS VIA LINEARIZATION. THE STOCHASTIC SUB-MODAL CLOSURE FACILITATES THE IMPLEMENTATION OF THE EQUATION FOR HIGH REYNOLDS NUMBER FLOW SIMULATIONS. THIS WILL BE THE FIRST TIME THAT SOME OF THE MODERN IDEAS IN TURBULENCE MODELING WILL BE ATTEMPTED IN REDUCED ORDER MODELS OF HIGHLY NONLINEAR CHAOTIC SYSTEMS. IT IS TO BE EMPHASIZED THAT THE SENSITIVITY MODELING PROPOSED HERE IS FUNDAMENTALLY DIFFERENT FROM THE FOKKER-PLANCK ADJOINT EQUATION OR THE LEAST SQUARE SHADOW TRAJECTORY MODEL. THE PROPOSED FRAMEWORK IS EXPECTED TO REDUCE THE COST OF COMPUTING SENSITIVITIES TO ONLY A HANDFUL OF FORWARD SIMULATIONS. THIS SIGNIFICANT REDUCTION WILL BE ACCOMPLISHED BY A BUILT-IN PATTERN RECOGNITION CAPA- BILITY THAT EXPLOITS THE CORRELATIONS BETWEEN RANDOM REALIZATIONS. MOREOVER THE PROPOSED STOCHASTIC FRAMEWORK WILL BE LEVERAGED TO TREAT OTHER SOURCES OF UNCERTAINTIES IN A PRINCIPLED MANNER. THIS MAY HAVE POTENTIAL SIGNIFICANCE FOR DESIGN UNDER UNCERTAINTY. THE RESULTS OF THIS WORK WILL BE OF DIRECT INTEREST TO NASA AS TIME-DEPENDENT OPTIMIZATION PROB- LEMS ARISE IN MANY APPLICATIONS RELEVANT TO NASA S RESEARCH FOCUS. AS EXAMPLES: SEPARATED FLOW CONTROL AIRFRAME VIBRATION NOISE MODULATION TRANSITION TO TURBULENCE DESIGN OPTIMIZATION FOR UN- STEADY FLOWS; AND SHAPE OPTIMIZATION OF HELICOPTER ROTORS TURBOMACHINERY BLADES AIRCRAFT WINGS AND OTHERS. IT IS DESIRED TO ESTABLISH A CLOSE COLLABORATION WITH THE NASA LARC RESEARCHERS ON SEVERAL ASPECTS OF THIS WORK. THIS COLLABORATION IS ENVISIONED BY REGULAR VISITS OF THE PIS AND LONGER STAYS OF THE DOCTORAL&POSTDOCTORAL STUDENTS AT THE LANGLEY CENTER. A SYSTEMATIC PLAN IS PROPOSED TO MAKE A DIRECT TRANSFER OF THE NEW METHODOLOGIES INTO NASA KNOWLEDGE-BASE INCLUDING THEIR COMPUTER CODES (E.G. FUN3D CFL3D OR OTHERS).