Numerical visualization of nappe oscillation
Abstract The unsteady global dynamics of a gravitational liquid sheet interacting with a onesided adjacent air enclosure, typically referred to as nappe oscillation, is addressed, under the assumptions of potential flow and presence of surface tension effects. Preliminary physical insights of the sheet centerline sinuous modes show that the nappe dynamics features the propagation of two wave fronts both directed downstream or one downstream and the other one upstream depending on whether the flow Weber number is greater or less than unity, respectively; moreover, the overall system behaves as a driven damped spring-mass oscillator, where the liquid sheet acts as the mass and the air enclosure as the spring. The findings of the eigenvalues spectral analysis closely agree with direct numerical simulations of the partial differential equation governing in the space-time domain the global evolution of the disturbances, starting from an initial gaussian-like shape.
Global eigenmodes of free-interface vertical liquid sheet flows
The global dynamics of unsteady free-interface vertical liquid sheet flows is studied, where the dynamics is termed global because it refers to the whole fluid system. The formal development of a proper mathematical model is presented initially, which accounts for pressure disturbances produced by the compliant interface in an air enclosure adjacent to the sheet. The linear spectral analysis (here restricted to sinuous disturbances only) shows that the surface tension is globally stabilizing, the spectrum exhibiting two typical branches related to the two characteristics curves of the governing equations. This basic finding is confirmed by means of both computations of the optimal amplifications (i.e. the greatest amplifications over all initial perturbations) of the relevant system energy and direct numerical simulations of the spatio-temporal evolution of an initial disturbance having the form of an interface Gaussian perturbation.
Hobbes and the Reception of Leviathan
Although there has been much discussion of the reception of Hobbes’s work, Hobbes’s response to his own reception has rarely received much consideration. This article looks at Hobbes’s engagements with his critics. Far from being rearguard actions by a philosopher under siege, or disingenuous attempts to curry favour with those in power, they can be read as moments when Hobbes in fact sought to convert what he saw as the “truth of speculation into the utility of practice.”