The Rayleigh–Bénard problem for water with maximum density effects

Linear stability and weakly nonlinear analyses are developed for Rayleigh–Bénard convection in water near 3.98 °C subject to isothermal boundary conditions. The density–temperature relationship (equation of state) is approximated by a cubic polynomial, including linear, quadratic, terms. continuity equation, the Navier–Stokes momentum equation state, energy constitute governing system. analysis used investigate how maximum density property affects onset convective instability choice unstable wave number four different types Then, study done using spectral Fourier method tangential stress-free conditions quantify heat transport system demonstrate transition from regular/periodic chaotic convection. A Stuart-Ginzburg–Landau obtained multiscale expansion method. Streamlines isotherms presented analyzed. influence has been shown delay is, therefore, stabilizing mechanism thermal instability. Due density, also delayed. Among boundaries, impermeable rigid boundaries require highest Rayleigh begin. Increasing temperatures advance improve situation.