TURBULENT MOTIONS IN THE CONVECTIVE ENVELOPE OF STARS EXCITE A RICH SPECTRUM OF OSCILLATION MODES. THE SUN IS THE BEST-STUDIED EXAMPLE AS SURFACE MOTIONS CAUSED BY ACOUSTIC WAVES CAN BE OBSERVED WITH HIGH SPATIAL RESOLUTION (SEE REVIEW BY CHRISTENSEN-DALSGAARD 2002). GROUND AND SPACE-BASED TELESCOPES PARTICULARLY THE COROT MISSION (BAGLIN ET AL. 2006) NASA'S KEPLER MISSION (BORUCKI ET AL. 2010) AND NASA'S TESS MISSION (RICKER ET AL. 2015) HAVE RECENTLY OBSERVED CONVECTIVELY-EXCITED ACOUSTIC AND /MIXED" MODES IN SUB-GIANT AND REDGIANT- BRANCH (RGB) STARS. MIXED MODES BEHAVE AS ACOUSTIC WAVES IN THE CONVECTIVE ENVELOPE AND AS INTERNAL-GRAVITY WAVES IN THE RADIATIVE CORE OF THE RGB STAR. THESE NEW OBSERVATIONS HAVE YIELDED A WEALTH OF INFORMATION ABOUT THE INTERNAL AND GLOBAL PROPERTIES OF THOUSANDS OF RED GIANTS (SEE REVIEWS BY CHAPLIN AND MIGLIO 2013 HEKKER AND CHRISTENSEN-DALSGAARD 2017). HIGHLIGHTS INCLUDES POWERFUL SCALING RELATIONS THAT CONNECT SEISMIC PARAMETERS TO FUNDAMENTAL STELLAR PARAMETERS (E.G. MASS RADII AND LUMINOSITY) AND MEASUREMENTS OF MIXED-MODE PERIOD SPACINGS WHICH MAKE IT POSSIBLE TO DISTINGUISH AMONG HYDROGEN- AND HELIUM-BURNING RED GIANTS (BEDDING ET AL. 2011 MOSSER ET AL. 2011 STELLO ET AL. 2013 MOSSER ET AL. 2014) AND CONSTRAIN THE CORE ROTATION PRO_LE (BECK ET AL. 2012 MOSSER ET AL. 2012B DEHEUVELS ET AL. 2012 2014). THE PROPOSED WORK AND ITS RELATION TO PREVIOUS ASTEROSEISMIC STUDIES. MOST PREVIOUS STUDIES TREAT THESE OSCILLATION MODES AS SMALL PERTURBATIONS TO THE STAR WITH AMPLITUDES SET BY THE BALANCE OF TURBULENT DRIVING AND DAMPING DUE TO A COMBINATION OF RADIATIVE LOSSES AND TURBULENT VISCOSITY. NONLINEAR E_ECTS HAVE PREVIOUSLY BEEN INVESTIGATED IN THE SOLAR CONTEXT WITH NONLINEAR WAVE INTERACTIONS NEAR THE SURFACE CAUSING REDISTRIBUTION OF ENERGY AMONG MODES AS WELL AS DAMPING BY CONVERSION OF TRAPPED WAVES TO OUT-GOING TRAVELING WAVES (KUMAR AND GOLDREICH 1989B KUMAR ET AL. 1994B). THESE STUDIES FOUND THAT NONLINEAR E_ECTS HAVE ONLY A MODEST IMPACT ON THE OBSERVED AMPLITUDES AND LINEWIDTHS OF MODES IN THE SUN AT BEST COMPARABLE TO THE LINEAR E_ECTS. HOWEVER NONLINEAR E_ECTS MAY BE FAR MORE IMPORTANT IN RGB STARS THAN IN THE SUN AS SHOWN IN RECENT WORK BY THE PI AND CO-I (WEINBERG AND ARRAS 2019). THERE ARE TWO REASONS. FIRST MODE AMPLITUDES ARE OBSERVED TO INCREASE SIGNI_CANTLY AS STARS ASCEND THE RGB (SEE SECTION 1.1). THE LARGER MODE AMPLITUDES IN RGB STARS IMPLY THAT NONLINEAR UID FORCES WILL BE MORE IMPORTANT IN RGB STARS THAN FOR THE SUN. SECOND IN CONTRAST TO PURE ACOUSTIC WAVES MIXED MODES MAY HAVE VASTLY LARGER AMPLITUDES IN THE RADIATIVE CORE OF THE STAR. AS A RESULT NONLINEAR WAVE INTERACTIONS NEAR THE CENTER MAY BE EVEN MORE IMPORTANT THAN THOSE AT THE SURFACE. THIS IMPLIES A QUALITATIVELY NEW TYPE OF INTERACTION UNEXPLORED IN PREVIOUS STUDIES. GOALS AND EXPECTED SIGNI_CANCE. THE GOAL OF THIS PROPOSAL IS TO EXPLORE THE E_ECT OF NONLINEAR WAVE INTERACTIONS ON THE OSCILLATION MODES OBSERVED IN SUB-GIANT AND RED-GIANT-BRANCH STARS AS A FUNCTION OF MASS AND EVOLUTIONARY STAGE. NONLINEAR INTERACTIONS AMONG EXCITED MODES CAN CAUSE THE OBSERVED MODE AMPLITUDES FREQUENCIES AND LINEWIDTHS TO DI_ER FROM PREDICTIONS OF LINEAR THEORY. UNDERSTANDING THE ROLE OF NONLINEAR E_ECTS THEREFORE HAS POTENTIALLY IMPORTANT IMPLICATIONS FOR THE INTERPRETATION AND UNDERSTANDING OF ASTEROSEISMIC OBSERVATIONS.