Rayleigh-Benard convection: experimental study of time-dependent instabilities

The transition from steady thermal convection to turbulent thermal convection in a horizontal layer of water (Prandtl number=5.8) contained by a square cavity of large aspect ratio (48.5) has been studied using laser Doppler velocimetry. Power spectra of the horizontal velocity fluctuations were measured in the Rayleigh number range from 30,000 and 99,000, wherein periodic, quasi-periodic, and broad-band time-dependent instabilities coexist. At Rayleigh numbers greater than 32,000 a narrow-band spectrum emerges. The frequency of this motion scales with x/d² modified by a Prandtl number factor for intermediate values of the Prandtl number. Between 10 Ra_cand 30 Ra_ithe frequency undergoes three abrupt jumps while increasing along an Ra^2/3 power law. A different frequency mode that occurs above 30 Ra_cappears to be associated with fully turbulent convection.