14,315 research outputs found
Logarithmic variance profiles and the corresponding f-1 spectra of temperature fluctuations in turbulent Rayleigh-Bénard convection
No full textWe report experimental results for the temperature variance 2(z) and the corresponding frequency spectra P(f) in turbulent Rayleigh-Bénard convection (RBC) in a cylindrical sample of aspect ratioT= D/L = 1:00 (D = 1:12 m is the diameter and L = 1:12 m the height). The measurements were conducted in the Rayleigh-number range 1011 < Ra < 1:35 1014 and Pr ' 0:8. For Ra = 1:35x1014, 2(z) could be described well by a logarithmic dependence on the vertical position z in a range of z 1 < z < z 2 with z 1 ' 70 and z 2 = 0:1L. Here L=(2Nu) is the thickness of a thin thermal sublayer adjacent to the horizontal plate where the heat flux (denoted by the Nusselt number Nu) is carried mostly by thermal diffusion. In the log layer, we found that the temperature spectra had a significant frequency range over which P(f) f with close to 1. As Ra decreased, increased so that the log layer became thinner. At Ra = 2:05 1011, z 2 < z 1 and therefore there was no range for a log layer. Correspondingly, the temperature spectrum near the horizontal plate did not have the f1 scaling form either
DSM of Newton type for solving operator equations F(u) = f with minimal smoothness assumptions on F.
No full textThis paper is a review of the authors’ results on the DSM (Dynamical Systems Method) for solving operator equation (*) F(u) = f. It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F. It is assumed that F is continuously
Fr´echet differentiable, but no smoothness assumptions on F0(u) are imposed. The DSM for solving equation (*) is developed. Under weak assumptions global existence of the solution u(t) is proved, the existence
of u(1) is established, and the relation F(u(1)) = f is obtained. The DSM is developed for a stable solution of equation (*) when noisy data
f are given, kf − f k
Linear and non-linear vibrations of fluid-filled hollow microcantilevers interacting with small particles
No full textLinear and non-linear vibrations of a U-shaped hollow microcantilever beam filled with fluid and interacting with a small particle are investigated. The microfluidic device is assumed to be subjected to internal flowing fluid carrying a buoyant mass. The equations of motion are derived via extended Hamilton's principle and by using Euler-Bernoulli beam theory retaining geometric and inertial non-linearities. A reduced-order model is obtained applying Galerkin's method and solved by using a pseudo arc-length continuation and collocation scheme to perform bifurcation analysis and obtain frequency response curves. Direct time integration of the equations of motion has also been performed by using Adams-Moulton method to obtain time histories and analyze transient cantilever-particle interactions in depth. It is shown that exploiting near resonant non-linear behavior of the microcantilever could potentially yield enhanced sensor metrics. This is found to be due to the transitions that occur as a matter of particle movement near the saddle-node bifurcation points of the coupled system that lead to jumps between coexisting stable attractors.Accepted Author ManuscriptMicro and Nano Engineerin
On the periodic orbits of the fourth-order differential equation u' ' ' ' qu' '-u= F (u,u',u' ',u' ' ')
No full textAgraïments: The second author is partially supported by a FAPESP-BRAZIL grant 2007/06896-5. Both authors are supported by the joint project CAPES-MEC grant PHB2009-0025-PC.We provide sufficient conditions for the existence of periodic solutions of the fourth-order differential equation u'''' + qu'' - u = εF(u, u', u'', u'''), where q and ε are real parameters, ε is small and F is a nonlinear function
On the periodic orbits of the fourth-order differential equation u' ' ' ' qu' '−u= F (u,u',u' ',u' ' ')
No full textAgraïments: The second author is partially supported by a FAPESP-BRAZIL grant 2007/06896-5. Both authors are supported by the joint project CAPES-MEC grant PHB2009-0025-PC.We provide sufficient conditions for the existence of periodic solutions of the fourth-order differential equation u'''' + qu'' − u = εF(u, u', u'', u'''), where q and ε are real parameters, ε is small and F is a nonlinear function
Measurements of partial branching fractions of inclusive B → X u ℓ + ν ℓ decays with hadronic tagging
No full textDispersive to nondispersive transition in the plane wake and channel flows
No full textBy varying the wavenumber over a large and finely discretized interval of values, we analyse the phase and group velocity of linear three-dimensional travelling waves both in the plane wake and channel flows to get the transition between dispersive and non-dispersive behaviour. The dispersion relation is computed from the Orr-Sommerfeld and Squire eigenvalue problem by observing the least stable mode, see figure 2, panels (a,b) and the comparison with [1, 2, 4–11, 15, 16]. The group velocity vg is also shown. The Reynolds number varies in the 20-100, 1000-8000 ranges for the wake and the channel flow, respectively, while we consider wavenumbers in the range 0.1-10. The wake basic flow consists of the first two orders of the Navier-Stokes matched asymptotic expansion described in [3, 13, 14]. At low wavenumbers we observe a dispersive behaviour where the phase speed and the group velocity substantially differ. The relevant perturbed solution is amenable to the typical solution belonging to the left branch of the eigenvalue spectrum, see the two examples shown in figure 1 (channel flow: Re = 6000; k = 1; wake Re = 100; k = 0:7). By rising the wave number value, we observe a sharp transition from the dispersive to the nondispersive regime. This transition is located at a critical wave number kd which is a function of the Reynolds number Re, the wave angle _, and the wake downstream observation point x0. Precisely, kd increases with Re and decreases with _ for the wake flow, while these trends are reversed for the channel flow, see tables 1,2. Beyond the wavenumber threshold, the observed least-stable mode belongs to the right branch of the spectrum. The asymptotic solutions in the dispersive region are wall modes for the channel flow , and in-wake modes for the wake flow. This means that, for both the flows, the dispersive behaviour is related to perturbations with high momentum variations (high vorticity) in correspondence to the base flow high-shear region. On the contrary, if k > kd the solutions are central modes for the channel case, and out-of-wake modes for the wake flow. In these cases, the disturbance has high variations outside the base flow high-shear region. To understand the physical mechanism of the dispersive-nondispersive transition we focused on time variation of the wave kinetic energy associated to the convective transport. Figure 2 (c,d) shows the convective term as a function of the wavenumber for the two least stable modes. We observe that the dispersive-nondisperive transition allows waves k > kd to keep the lowest possible temporal variation of kinetic energy, i.e. the lowest decay. This remains true also when all the other more stable modes are considered. In practice nondispersive waves maintain their convective energy with k
Turbulent drag reduction using wall jets at flight scale Reynolds number
No full textNumerical experiments have been performed for modelling turbulent drag reduction due to active-control of wall jets using a linearised Navier-Stokes model in a turbulent boundary layer formed over a flat plate at Re _τ = 905 corresponding to flight scale Re_x = 10^6 . Its effect have been seen on transient growth of near-wall streaks and production of turbulent kinetic energy (TKE). Two sets, one corresponding to span wise slot and other corresponding to wall jets along the whole plate have been performed. Simulations are performed by varying magnitude of wall jets, its angle & locations and based on a measure of TKE, reduction in stream wise turbulent kinetic energy is recorded
- …
