Dynamics and scaling in quasi-two-dimensional turbulent convection

High Rayleigh number (4 × 104−3 × 107) quasi-two-dimensional convection is studied experimentally, numerically, and theoretically. The fluid is contained in an isothermal Hele-Shaw cell, which enforces the two dimensionality, and the convection is driven by an externally imposed vertical concentration gradient. The full two dimensional concentration field is imaged experimentally and is sampled at regular intervals spanning between five and fifty convective times (the time it takes a plume to cross the cell). The most prominent and dynamically significant features of the flow are solutal plumes which form within the concentration boundary layer. Tip splitting of plumes leading to smaller length scales and merging of plumes leading to larger length scales are observed. A model of Hele-Shaw convection, which includes a friction term due to the boundaries parallel to the velocity field, is simulated. The evolution of the pattern and dynamics of the concentration field, as well as time averaged spatial spectra, are obtained from the experiment and simulation. Results for exponents which describe how the Nusselt number and Reynolds number scale with Rayleigh number are obtained theoretically and compared with the values from simulation.