Continuous dependence and convergence for a Kelvin–Voigt fluid of order one

It is shown that the solution to the boundary - initial value problem for a Kelvin–Voigt fluid of order one depends continuously upon the Kelvin–Voigt parameters, the viscosity, and the viscoelastic coefficients. Convergence of a solution is also shown.

Instability thresholds for thermal convection in a Kelvin–Voigt fluid of variable order

We present numerical techniques for calculating instability thresholds in a model for thermal convection in a complex viscoelastic fluid of Kelvin–Voigt type. The theory presented is valid for various orders of an exponential fading memory term, and the strategy for obtaining the neutral curves and instability thresholds is discussed in the general case. Specific numerical results are presented for a fluid of order zero, also known as a Navier–Stokes–Voigt fluid, and fluids of order 1 and 2. For the latter cases it is shown that oscillatory convection may occur, and the nature of the stationary and oscillatory convection branches is investigated in detail, including where the transition from one to the other takes place.

Thermosolutal Convection with a Navier–Stokes–Voigt Fluid

We present a model for convection in a Navier–Stokes–Voigt fluid when the layer is heated from below and simultaneously salted from below, the thermosolutal convection problem. Instability thresholds are calculated for thermal convection with a dissolved salt field in a complex viscoelastic fluid of Navier–Stokes–Voigt type. The Kelvin–Voigt parameter is seen to play a very important role in acting as a stabilizing agent when the convection is of oscillatory type. The quantitative size of this effect is displayed. Nonlinear stability is also discussed, and it is briefly indicated how the global nonlinear stability limit may be increased, although there still remains a region of potential sub-critical instability, especially when the Kelvin–Voigt parameter increases.