The asymmetry appearing in the dynamic structure factor of a medium un
der a non-equilibrium state of temperature gradient was experimentally
verified. Brillouin scattering was carried out in water with the opti
cal beating spectroscopy technique at frequencies lower than 60 MHz wh
ere a large asymmetry was expected. The finite-cell-size effect to whi
ch the disagreement between the theory and experiment had been attribu
ted was excluded by a specially designed tall cell which suffers from
the least effect of the finite size. The observed Stokes line was show
n to have intensity 2% to 8% higher than the anti-Stokes line dependin
g on the phonon frequency for a temperature gradient applied into the
same direction as the scattering vector. Based on a concept of anisotr
opic phonon propagation under a temperature gradient, a simple theory
was proposed which succeeded in estimating the asymmetry for the tempe
rature distribution of actual experimental condition including the eff
ect of cell boundaries. The observed asymmetry was quantitatively in g
ood agreement with tie theoretical prediction.