Linear and nonlinear thermosolutal instabilities in an inclined porous layer

We investigate the double-diffusive instability in an inclined porous layer with a concentration-based internal heat source by conducting linear instability and nonlinear energy analyses. The effects of different dimensionless parameters, such as the thermal ( Ra T ) and solutal ( Ra S ) Rayleigh numbers, the angle of inclination ( ϕ ), the Lewis number ( Le ) and the concentration-based internal heat source ( Q ) are examined. A comparison between the linear and nonlinear thresholds for the longitudinal and transverse rolls provides the region of subcritical instability. We found that the system becomes more unstable when the thermal diffusivity is greater than the solute and the internal heat source strength increases. It is observed that the system is stabilized by increasing the angle of inclination. While the longitudinal roll remains stationary without the region of subcritical instability, as the angle of inclination increases, the transverse roll switches from stationary-oscillatory-stationary mode. Our numerical results show that for Ra S < 0, for all Q values, the subcritical instability only exists for transverse rolls. For Ra S ≥ 0, however, the subcritical instability appears only for Q = 0 and Q ≥ 0, respectively, for longitudinal and transverse rolls.

Subharmonic resonant excitation of edge waves by breaking surface waves

Parametric excitation of edge waves with a frequency 2 times less than the frequency of surface waves propagating perpendicular to the inclined bottom is investigated in laboratory experiments. The domain of instability on the plane of surface wave parameters (amplitude–frequency) is found. The subcritical instability is observed in the system of parametrically excited edge waves. It is shown that breaking of surface waves initiates turbulent effects and can suppress the parametric generation of edge waves.

Subharmonic resonant excitation of edge waves by breaking surface waves

Parametric excitation of edge waves with a frequency two times less than the frequency of surface waves propagating perpendicular to the inclined bottom is investigated in laboratory experiments. The domain of instability on the plane of surface wave parameters (amplitude–frequency) is found. The subcritical instability is observed in the system of parametrically excited edge waves. It is shown that breaking of surface waves initiates turbulent effects and can suppress the parametric generation of edge waves.

Investigation of Subcritical Instability in Ducted Premixed Flames

An experimental investigation of the bistable region of instability in a thermoacoustic system comprising of ducted, pre-mixed laminar flames has been performed. The stability diagram of the system is obtained and the bistable region for a range of flame locations at different fuel-air mixture equivalence ratios is identified. Subsequently, threshold amplitudes for triggering instability in the system using sinusoidal acoustic forcing, introduced externally, is obtained. It is observed that depending on how close the system is to the Hopf point and the nature of oscillations at the Hopf point, the triggered oscillations can exhibit different dynamical behavior.

Practical Stability Limits in Turning

In this paper we establish a practical formula that could be used to augment existing linear stability charts for turning to include the occurrence of contact loss between tool and workpiece in turning. We show that the contact loss discontinuity in the global model is responsible for the creation of the experimentally observed coexistence of subcritical instability and hysteresis in the cutting process. Comparison of experimental data with extensive numerical simulations nicely support the theoretical findings.

A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid

A nonlinear (energy) stability analysis is performed for a magnetized ferrofluid layer, heated and soluted from below, with stress-free boundaries. A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. For ferrofluids we find that the existence of subcritical instabilities is possible, however, it is noted that, in case of a nonferrofluid, the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of the magnetic parameters, this coincidence is immediately lost. The effects of the magnetic parameter, M3, and the solute gradient, S1, on the subcritical instability region have also been analyzed. It is shown that with the increase of the magnetic parameter the subcritical instability region between the two theories decreases quickly, while with the increase of the solute gradient the subcritical region expands. We also demonstrate the coupling between the buoyancy and magnetic forces in the nonlinear energy stability analysis.