We present experimental and computational studies of the propagation of internal

waves in a stratified fluid with an exponential density profile that models the deep

ocean. The buoyancy frequency profile N.z/ (proportional to the square root of

the density gradient) varies smoothly by more than an order of magnitude over

the fluid depth, as is common in the deep ocean. The non-uniform stratification is

characterized by a turning depth zc, where N.zc/ is equal to the wave frequency ! and

N.z < zc/ < !. Internal waves reflect from the turning depth and become evanescent

below the turning depth. The energy flux below the turning depth is shown to decay

exponentially with a decay constant given by kc, which is the horizontal wavenumber

at the turning depth. The viscous decay of the vertical velocity amplitude of the

incoming and reflected waves above the turning depth agree within a few per cent

with a previously untested theory for a fluid of arbitrary stratification (Kistovich and

Chashechkin, J. Appl. Mech. Tech. Phys., vol. 39, 1998, pp. 729’737).