Effects of non-unity Lewis numbers in diffusion Flames

The purpose of this work is to carry out direct numerícal simulations of diffusion controlled combustión with non-unity Lewis numbers for the reactants and producís, thus accounting for the düferential diífusion effects of the temperature and concentration fields. We use a formulation (Liñán (1991a)) based on combining the conservation equations in a way to elimínate the reaction terms similar to the method used by Burke and Schumann (1928) for unity Lewis numbers. We present calculations for an axisymmetric fuel jet and for a planar, time evolving mixing layer, leaving out the effects of thermal expansión and variations of the transport coefficients due to the heat reisase. Our results show that the front of the fíame sbifts toward the fuel or oxygen sides owing to the effect of the düferential diífusion and that the location of máximum temperature may not coincide with the fíame. The dependence of the distríbution of the reaction products on their Lewis number has been investigated

Walking droplets have been halted

The swinging motion of the eigenmodes of a free inviscid drop has been known for nearly a century. Yet, as the drop sits on a solid substrate, getting flattened by gravity, analytical solutions waver due to the non-spherical base state and the dynamics of the three-phase contact line. The recent paper by Zhang et al. (J. Fluid Mech., vol. 962, 2023, A10) investigated the effect of gravity on the harmonic modes of sessile droplets for free and pinned contact line conditions. An effective boundary element method has been used to solve both axisymmetric and non-axisymmetric modes for a variety of Bond numbers and static contact angles, also revising on the way a debated capillary instability

Vortex ring instability and its sound

This work carries earlier finite-difference calculations of the Widnall instability of vortex rings into the late non-linear stage. Plots of energy in azimuthal Fourier modes indicate that low-order modes dominate at large times; their structure and dynamics remain unexplored, however. An attempt was made to calculate the acoustic signal using the theory of Mohring (1978), valid for unbounded flow. This theory shows that only low-order azimuthal modes contribute to the sound. As a check on the effects of axial periodicity and a slip wall at large radius imposed by the numerical scheme, the acoustic integrals were also computed in a truncated region. Half of the terms contributing to the sound have large differences between the two regions, and the results are therefore unreliable. The error is less severe for a contribution involving only the m = 2 mode, and its low frequency is consistent with a free elliptic bending wave on a thin ring

Fluctuations of temperature gradients in turbulent thermal convection

Broad theoretical arguments are proposed to show, formally, that the magnitude G of the temperature gradients in turbulent thermal convection at high Rayleigh numbers obeys the same advection-diffusion equation that governs the temperature fluctuation T, except that the velocity field in the new equation is substantially smoothed. This smoothed field leads to a -1 scaling of the spectrum of G in the same range of scales for which the spectral exponent of T lies between -7/5 and -5/3. This result is confirmed by measurements in a confined container with cryogenic helium gas as the working fluid for Rayleigh number Ra=1.5x10^{11}. Also confirmed is the logarithmic form of the autocorrelation function of G. The anomalous scaling of dissipation-like quantities of T and G are identical in the inertial range, showing that the analogy between the two fields is quite deep

A finite-difference scheme for three-dimensional incompressible flows in spherical coordinates

In this study we have developed a flexible and efficient numerical scheme for the simulation of three-dimensional incompressible flows in spherical coordinates. The main idea, inspired by a similar strategy as (Verzicco, R., Orlandi, P., 1996, A Finite-Difference Scheme for Three-Dimensional Incompressible Flows in Cylindrical Coordinates) for cylindrical coordinates, consists of a change of variables combined with a discretization on a staggered mesh and the special treatment of few discrete terms that remove the singularities of the Navier-Stokes equations at the sphere centre and along the polar axis. This new method alleviates also the time step restrictions introduced by the discretization around the polar axis while the sphere centre still yields strong limitations, although only in very unfavourable flow configurations. The scheme is second-order accurate in space and is verified and validated by computing numerical examples that are compared with similar results produced by other codes or available from the literature. The method can cope with flows evolving in the whole sphere, in a spherical shell and in a sector without any change and, thanks to the flexibility of finite-differences, it can employ generic mesh stretching (in two of the three directions) and complex boundary conditions

Wind and boundary layers in Rayleigh-Benard convection. I: analysis and modeling

The aim of this paper is to contribute to the understanding and to model the processes controlling the amplitude of the wind of Rayleigh-Benard convection. We analyze results from direct simulation of an L/H = 4 aspect-ratio domain with periodic sidewalls at Ra = 1e5; 1e6; 1e7; 1e8 and at Pr = 1 by decomposing independent realizations into wind and fluctuations. It is shown that deep inside the thermal boundary layer, horizontal heat-fuxes exceed the average vertical heat-fux by a factor 3 due to the interaction between the wind and the mean temperature field. These large horizontal heat-fluxes are responsible for spatial temperature differences that drive the wind by creating pressure gradients. The wall fluxes and turbulent mixing in the bulk provide damping. Using the DNS results to parameterise the unclosed terms, a simple model capturing the essential processes governing the wind structure is derived. The model consists of two coupled differential equations for wind velocity and temperature amplitude. The equations indicate that the formation of a wind structure is inevitable due to the positive feedback resulting from the interaction between the wind and temperature field. Furthermore, the wind velocity is largely determined by the turbulence in the bulk rather than by the wall-shear stress. The model reproduces the Ra dependence of wind Reynolds number and temperature amplitude

Stochastic Resonance in a simple model of magnetic reversals

We discuss the effect of stochastic resonance in a simple model of magnetic reversals. The model exhibits statistically stationary solutions and bimodal distribution of the large scale magnetic field. We observe a non trivial amplification of stochastic resonance induced by turbulent fluctuations, i.e. the amplitude of the external periodic perturbation needed for stochastic resonance to occur is much smaller than the one estimated by the equilibrium probability distribution of the unperturbed system. We argue that similar amplifications can be observed in many physical systems where turbulent fluctuations are needed to maintain large scale equilibria.Comment: 6 page

Comparing and Connecting: Comacchio and the Early Medieval Trading Towns

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Towards DNS of the Ultimate Regime of Rayleigh--B\'enard Convection

In this contribution we have briefly introduced the problem of turbulent thermal convection with a particular look at its transition to the ultimate regime and the resolution requirements needed for the direct numerical simulation of this flow.Comment: 10 pages, 6 figure

Turbulence decay towards the linearly stable regime of Taylor–Couette flow

Taylor–Couette (TC) flow is used to probe the hydrodynamical (HD) stability of astrophysical accretion disks. Experimental data on the subcritical stability of TC flow are in conflict about the existence of turbulence (cf. Ji et al. (Nature, vol. 444, 2006, pp. 343–346) and Paoletti et al. (Astron. Astroph., vol. 547, 2012, A64)), with discrepancies attributed to end-plate effects. In this paper we numerically simulate TC flow with axially periodic boundary conditions to explore the existence of subcritical transitions to turbulence when no end plates are present. We start the simulations with a fully turbulent state in the unstable regime and enter the linearly stable regime by suddenly starting a (stabilizing) outer cylinder rotation. The shear Reynolds number of the turbulent initial state is up to $Re_s \lesssim 10^5$$Re_s \lesssim 10^5$ and the radius ratio is $\eta =0.714$$\eta =0.714$. The stabilization causes the system to behave as a damped oscillator and, correspondingly, the turbulence decays. The evolution of the torque and turbulent kinetic energy is analysed and the periodicity and damping of the oscillations are quantified and explained as a function of shear Reynolds number. Though the initially turbulent flow state decays, surprisingly, the system is found to absorb energy during this decay