No Arabic abstract
Boundary-layer transition triggered by a roughness element generates a turbulent wedge that spreads laterally as the flow proceeds downstream. The spreading half angle is about $6^{circ}$ in zero-pressure-gradient flows regardless of Reynolds number and roughness shape. Recent simulations and experiments have sought to explain the lateral-spreading mechanism and have observed high- and low-speed streaks along the flanks of the wedge that appear central to the spreading process. To better elucidate the role of streaks, a naphthalene flow-visualization survey and hotwire measurements are conducted over a wider range of Reynolds numbers and a longer streamwise domain than previous experiments. The results reconfirm the spreading half angle is insensitive to Reynolds numbers based on roughness location, $Re_{x,k}$, and roughness height, $Re_{kk}$. When made nondimensional by the unit Reynolds number, the distance from the roughness to the effective origin of the turbulent wedge and to the first high-speed flanking streaks depends on $Re_{kk}$ but not $Re_{x,k}$. The distance between the first and second high-speed streaks is also observed to depend on $Re_{kk}$. In spite of a long measurement domain, third streaks are not observed and it remains unknown whether subsequent streak-to-streak distances collapse to a universal value. The reason downstream streaks are not observed may be low-frequency meandering of streak structures. Hotwire measurements confirm breakdown to turbulence first occurs via a shear-layer instability above low-speed streaks. Farther downstream, high-intensity broadband fluctuations are observed in equivalent positions on secondary low-speed streaks.
Axisymmetric fountains in stratified environments rise until reaching a maximum height, where the vertical momentum vanishes, and then falls and spread radially as an annular plume following a well-known top-hat profile. Here, firstly, we generalize the model of Morton et al. (Proc. R. Soc. Lond. A textbf{234}, 1, 1956), in order to correctly determine the dependence of the maximum height and the spreading height with the parameters involved. We obtain the critical conditions for the collapse of the fountain, textit i.e. when the jet falls up to the source level, and show that the spreading height must be expressed as a function of at least two parameters. To improve the quantitative agreement with the experiments we modify the criterion to take the mixing process in the down flow into account. Numerical simulations were implemented to estimate the parameter values that characterizes this merging. We show that our generalized model agrees very well with the experimental measurements.
A series of Direct Numerical Simulations (DNS) of lean methane/air flames was conducted in order to investigate the enhancement of the turbulent flame speed and modifications to the reaction layer structure associated with the systematic increase of the integral scale of turbulence $l$ while the Karlovitz number and the Kolmogorov scale are kept constant. Four turbulent slot jet flames are simulated at increasing Reynolds number and up to $Re approx 22000$, defined based on the bulk velocity, slot width, and the reactants properties. The turbulent flame speed $S_T$ is evaluated locally at select streamwise locations and it is observed to increase both in the streamwise direction for each flame and across flames for increasing Reynolds number, in line with a corresponding increase of the turbulent integral scale. In particular, the turbulent flame speed $S_T$ increases exponentially with the integral scale for $l$ up to about 6 laminar flame thicknesses, while the scaling becomes a power-law for larger values of $l$. These trends cannot be ascribed completely to the increase in the flame surface, since the turbulent flame speed looses its proportionality to the flame area as the integral scale increases; in particular, it is found that the ratio of turbulent flame speed to area attains a power-law scaling $l^{0.2}$. This is caused by an overall broadening of the reaction layer for increasing integral scale, which is not associated with a corresponding decrease of the reaction rate, causing a net enhancement of the overall burning rate. This observation is significant since it suggests that a continuous increase in the size of the largest scales of turbulence might be responsible for progressively stronger modifications of the flames inner layers even if the smallest scales, i.e., the Karlovitz number, are kept constant.
This paper is a detailed report on a programme of simulations used to settle a long-standing issue in the dynamo theory and demonstrate that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>>1 and small magnetic Prandtl number Pm<<1. The dependence of the critical Rm_c vs. the hydrodynamic Reynolds number Re is obtained for 1<Re<6700. In the limit Pm<<1, Rm_c is ~3 times larger than for Pm>1. The stability curve Rm_c(Re) (and, it is argued, the nature of the dynamo) is substantially different from the case of the simulations and liquid-metal experiments with a mean flow. It is not as yet possible to determine numerically whether the growth rate is ~Rm^{1/2} in the limit Re>>Rm>>1, as should be the case if the dynamo is driven by the inertial-range motions. The magnetic-energy spectrum in the low-Pm regime is qualitatively different from the Pm>1 case and appears to develop a negative spectral slope, although current resolutions are insufficient to determine its asymptotic form. At 1<Rm<Rm_c, the magnetic fluctuations induced via the tangling by turbulence of a weak mean field are investigated and the possibility of a k^{-1} spectrum above the resistive scale is examined. At low Rm<1, the induced fluctuations are well described by the quasistatic approximation; the k^{-11/3} spectrum is confirmed for the first time in direct numerical simulations.
We study the spreading of viruses, such as SARS-CoV-2, by airborne aerosols, via a new first-passage-time problem for Lagrangian tracers that are advected by a turbulent flow: By direct numerical simulations of the three-dimensional (3D) incompressible, Navier-Stokes equation, we obtain the time $t_R$ at which a tracer, initially at the origin of a sphere of radius $R$, crosses the surface of the sphere textit{for the first time}. We obtain the probability distribution function $mathcal{P}(R,t_R)$ and show that it displays two qualitatively different behaviors: (a) for $R ll L_{rm I}$, $mathcal{P}(R,t_R)$ has a power-law tail $sim t_R^{-alpha}$, with the exponent $alpha = 4$ and $L_{rm I}$ the integral scale of the turbulent flow; (b) for $l_{rm I} lesssim R $, the tail of $mathcal{P}(R,t_R)$ decays exponentially. We develop models that allow us to obtain these asymptotic behaviors analytically. We show how to use $mathcal{P}(R,t_R)$ to develop social-distancing guidelines for the mitigation of the spreading of airborne aerosols with viruses such as SARS-CoV-2.
The ultimate goal of a sound theory of turbulence in fluids is to close in a rational way the Reynolds equations, namely to express the tensor of turbulent stress as a function of the time average of the velocity field. Based on the idea that dissipation in fully developed turbulence is by singular events resulting from an evolution described by the Euler equations, it has been recently observed that the closure problem is strongly restricted, and that it implies that the turbulent stress is a non local function in space of the average velocity field, a kind of extension of classical Boussinesq theory of turbulent viscosity. This leads to rather complex nonlinear integral equation(s) for the time averaged velocity field. This one satisfies some symmetries of the Euler equations. Such symmetries were used by Prandtl and Landau to make various predictions about the shape of the turbulent domain in simple geometries. We explore specifically the case of mixing layer for which the average velocity field only depends on the angle in the wedge behind the splitter plate. This solution yields a pressure difference between the two sides of the splitter which contributes to the lift felt by the plate. Moreover, because of the structure of the equations for the turbulent stress, one can satisfy the Cauchy-Schwarz inequalities, also called the realizability conditions, for this turbulent stress. Such realizability conditions cannot be satisfied with a simple turbulent viscosity.