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The present numerical simulation explores a thermal–convective mechanism for oscillatory thermocapillary convection in a shallow rectangular cavity for a Prandtl number 6.78 fluid. The computer program developed for this simulation integrates the two-dimensional, time-dependent Navier–Stokes equations and the energy equation by a time-accurate method on a stretched, staggered mesh. Flat free surfaces are assumed. The instability is shown to depend upon temporal coupling between large-scale thermal structures within the flow field and the temperature sensitive free surface. A primary result of this study is the development of a stability diagram presenting the critical Marangoni number separating the steady from the time-dependent flow states as a function of aspect ratio for the range of values between 2.3 and 3.8. Within this range, a minimum critical aspect ratio near 2.3 and a minimum critical Marangoni number near 20 000 are predicted, below which steady convection is found.

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In this numerical study, randomly and sinusoidally modulated gravitational fields imposed on three-dimensional Rayleigh–Bénard convection are investigated in an effort to understand the effects of vibration (G-Jitter) on fluid systems. The time-dependent, Navier–Stokes equations and the energy equation with Boussinesq approximations are solved by a semi-implicit, pseudospectral procedure. An analysis of energy balances indicates that with increasing modulation amplitude, transition from synchronous to relaxation oscillation goes through the subharmonic response. Random modulations are found to be less stabilizing than sinusoidal and are shown to impose local three-dimensionality on the flow for some parameter ranges both at terrestrial and zero base gravity conditions.

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Separated flow past a hump in a turbulent boundary layer is studied numerically using detached-eddy simulation (DES), zonal detached-eddy simulation (ZDES), delayed detached-eddy simulation (DDES), and Reynolds-averaged Navier–Stokes (RANS) modeling. The geometry is smooth so the separation point is a function of the flow solution. Comparisons to experimental data show that RANS with the Spalart–Allmaras turbulence model predicts the mean-field statistics well. The ZDES and DDES methods perform better than the DES formulation and are comparable to RANS in most statistics. Analyses motivate that modeled-stress depletion near the separation point contributes to differences observed in the DES variants. The order of accuracy of the flow solver ACUSOLVE is also documented.

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