 gener nois isotrop turbul gener nois isotrop turbul finit region fix boundari infinit expans compress fluid turbul motion motion gener nois radiat surround fluid acoust properti system studi special case turbul region consist decai isotrop turbul assum reynold number turbul larg mach number small nois appear gener eddi turbul contribut rate dissip kinet energi viscos neglig intens sound larg distanc turbul volum distribut simpl acoust sourc occupi turbul region analog fluid regard stationari uniform acoust medium local acoust power output mass turbul fluid formula numer constant mean-squar veloc fluctuat time veloc sound fluid constant express term well-known veloc correl function assum joint probabl distribut turbul veloc time-deriv point space gaussian numer substitut form correspond heisenberg's theoret spectrum isotrop turbul effect decai small contribut order magnitud chang differ form function 