Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe friction factor of two-dimensional rough-boundary turbulent soap film flows
148
0
0.0
(
0
)
Added by
Nicholas Guttenberg
Publication date
2009
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $fproptotextrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $textrm{Re}^{-1/4}$. For large Re, $f sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory, and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the 3D pipe data of Nikuradse.
rate research
Read More
We present experimental evidence of statistical conformal invariance in isocontours of fluid thickness in experiments of two-dimensional turbulence using soap films. A Schlieren technique is used to visualize regions of the flow with constant film thickness, and association of isocontours with Schramm-Lowner evolution (SLE) is used to identify conformal invariance. In experiments where an inverse energy cascade develops, statistical evidence is consistent with such an association. The diffusivity of the associated one-dimensional Brownian process is close to 8/3, a value previously identified in isocontours of vorticity in high-resolution numerical simulations of two-dimensional turbulence (D. Bernard et al., Nature Phys. 2, 124, 2006). In experiments where the inverse energy cascade is not sufficiently developed, no statistical evidence of conformal invariance is found.
Phoresis, the drift of particles induced by scalar gradients in a flow, can result in an effective compressibility, bringing together or repelling particles from each other. Here, we ask whether this effect can affect the transport of particles in a turbulent flow. To this end, we study how the dispersion of a cloud of phoretic particles is modified when injected in the flow, together with a blob of scalar, whose effect is to transiently bring particles together, or push them away from the center of the blob. The resulting phoretic effect can be quantified by a single dimensionless number. Phenomenological considerations lead to simple predictions for the mean separation between particles, which are consistent with results of direct numerical simulations. Using the numerical results presented here, as well as those from previous studies, we discuss quantitatively the experimental consequences of this work and the possible impact of such phoretic mechanisms in natural systems.
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.
We investigate the gravitational settling of a long, model elastic filament in homogeneous isotropic turbulence. We show that the flow produces a strongly fluctuating settling velocity, whose mean is moderately enhanced over the still-fluid terminal velocity, and whose variance has a power-law dependence on the filaments weight but is surprisingly unaffected by its elasticity. In contrast, the tumbling of the filament is shown to be closely coupled to its stretching, and manifests as a Poisson process with a tumbling time that increases with the elastic relaxation time of the filament.
We perform direct numerical simulations (DNS) of passive heavy inertial particles (dust) in homogeneous and isotropic two-dimensional turbulent flows (gas) for a range of Stokes number, ${rm St} < 1$, using both Lagrangian and Eulerian approach (with a shock-capturing scheme). We find that: The dust-density field in our Eulerian simulations have the same correlation dimension $d_2$ as obtained from the clustering of particles in the Lagrangian simulations for ${rm St} < 1$; The cumulative probability distribution function of the dust-density coarse-grained over a scale $r$ in the inertial range has a left-tail with a power-law fall-off indicating presence of voids; The energy spectrum of the dust-velocity has a power-law range with an exponent that is same as the gas-velocity spectrum except at very high Fourier modes; The compressibility of the dust-velocity field is proportional to ${rm St}^2$. We quantify the topological properties of the dust-velocity and the gas-velocity through their gradient matrices, called $mathcal{A}$ and $mathcal{B}$, respectively. The topological properties of $mathcal{B}$ are the same in Eulerian and Lagrangian frames only if the Eulerian data are weighed by the dust-density -- a correspondence that we use to study Lagrangian properties of $mathcal{A}$. In the Lagrangian frame, the mean value of the trace of $mathcal{A} sim - exp(-C/{rm St}$, with a constant $Capprox 0.1$. The topology of the dust-velocity fields shows that as ${rm St} increases the contribution to negative divergence comes mostly from saddles and the contribution to positive divergence comes from both vortices and saddles. Compared to the Eulerian case, the density-weighed Eulerian case has less inward spirals and more converging saddles. Outward spirals are the least probable topological structures in both cases.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
