Coupling of Internal Waves and Turbulent Stratified Shear Flow

Previously performed laboratory experiments showed turbulence in stratified fluid excites internal waves in a narrow frequency band despite the turbulence having a relatively broad frequency spectrum (e.g. Dohan & Sutherland (2003), Aguilar & Sutherland (2006), Clark & Sutherland (2010)). Here we perform direct numerical simulations of turbulent shear flow with applied uniform stratification to examine the generation of internal waves. For wide-ranging applied buoyancy frequency, the waves are shown to be radiated with phase lines at an angle of approximately 45◦, which is consistent with laboratory experiments. The amplitude of the waves increase if the buoyancy frequency is larger. Using Dynamic Mode Decomposition, we extract the structures of turbulence and overlying stratification which correspond to the observed frequency of the internal waves. This shows that the waves originate from within the turbulence, rather than at the turbulent - non-turbulent interface.