Velocity gradient

About: Velocity gradient is a research topic. Over the lifetime, 3013 publications have been published within this topic receiving 77120 citations.

Combustion-induced local shear layers within premixed flamelets in weakly turbulent flows

Abstract: 3D direct numerical simulation data obtained from statistically stationary, planar, weakly turbulent, premixed flames, which are characterized by two different density ratios (7.53 and 2.50) and are associated with the flamelet combustion regime, are analyzed to investigate differences between velocity and pressure variations (i) in flamelets in a weakly turbulent flow and (ii) in the counterpart laminar flame. Results show that while the thermo-chemical structure of the flamelets is weakly affected by turbulence under the studied conditions, the local velocity, vorticity, and pressure fields within the flamelets differ significantly from the velocity, vorticity, and pressure fields, respectively, within the laminar flame. In particular, local shear layers appear within flamelets in the turbulent flow because acceleration of a reacting mixture by the local pressure gradient is inversely proportional to the mixture density and, hence, depends on the mixture state. The shear layers are characterized by large velocity gradients (both the tangential gradient of the normal velocity with respect to the flamelet surface and the normal gradient of the tangential velocity), whose magnitudes may be comparable with the magnitude of the velocity gradient across the laminar flame. In flamelet zones characterized by a relatively large magnitude of the locally normal gradient of the tangential velocity, the local vorticity magnitude is also large and such zones contribute substantially to the overall generation of vorticity due to baroclinic torque. These results cast doubts on the validity of a simple common modeling approach that consists in directly invoking expressions derived for the laminar flames in order to describe the influence of combustion-induced thermal expansion on weakly turbulent velocity and pressure fields.

Quad-plane stereoscopic PIV for fine-scale structure measurements in turbulence

Abstract: The fine-scale structure in turbulence is investigated by quad-plane stereoscopic particle image velocimetry (QPSPIV). The quad-plane consists of two each of different polarizations and wavelengths, and it provides three velocity components at four independent parallel planes. Measurements have been undertaken in the developed region of a turbulent round jet with a spatial resolution sufficient to capture the small-scale structures. The advantage of the QPSPIV is presented in terms of the spectral response in the evaluation of the out-of-plane velocity gradient. The full velocity gradient tensor is computed with a fourth-order finite difference scheme in the out-of-plane direction as well as the in-plane directions. The turbulence quantities, such as the vorticity components, the energy dissipation rate and the second and third invariants of the velocity gradient tensor, are computed according to their faithful definitions. The coherent fine-scale eddies are extracted from the present QPSPIV data. The probability density functions of the diameter and the maximum azimuthal velocity of the extracted eddies exhibit their peak at approximately $$8\eta $$ and $$1.5u_k$$ , respectively, where $$\eta $$ and $$u_k$$ are the Kolmogorov length and velocity. These values agree well with the data in the literature. The phase-averaged distributions of turbulence quantities around the coherent fine-scale eddy indicate an apparent elliptic feature around the axis. Furthermore, the state of the strain rate exerting the eddy is quantified from the phase-averaged distributions of eigenvalues of the strain rate tensor and the alignment of the corresponding eigenvectors against the axis. The present study gives a solid experimental support of the coherent fine-scale structures in turbulence, and the technique can be applied to various flow fields and to the higher Reynolds number condition.

Probability Density Functions of Large-Scale Turbulence in the Ocean

Abstract: Probability density functions (pdfs) of surface velocity and surface velocity gradients in the ocean are calculated using altimetric data from the Topex / Poseidon satellite. These provide information about turbulence in a high-Reynolds-number geophysical flow. Both velocity pdfs and velocity gradient pdfs calculated over small regions are Gaussian but have more exponential shapes as the size of the region increases. We develop a simple explanation for the non-Gaussianity of velocity pdfs based on the inhomogeneity of eddy kinetic energy in the ocean. (S0031-9007(98)07902-2) Two-dimensional turbulence is a natural paradigm for the high-Reynolds-number fluid flows that dominate ocean variability on scales of 50- 80 km, the "mesoscale." Satel- lite altimeters offer a new means to study two-dimensional turbulent motions of the ocean. In this paper, we use altimeter data to calculate probability density functions (pdfs) for the ocean: pdfs are Gaussian locally but expo- nential over the global ocean. Numerical and theoretical studies have shown that two-dimensional turbulence is characterized by coherent vortices separated by irrotational regions of straining motion (1). This phenomenology provides a good con- ceptual model of the mesoscale and larger-scale oceanic circulation, which is dominated by two-dimensional motions associated with the constraints of strong stratifi- cation and the earth's rotation (2). We therefore expect two-dimensional turbulence theory to illuminate processes such as eddy-induced transports of heat, chemical tracers, and biota, which are important to the earth's climate system (3). In addition, observations can show us how notions of two-dimensional turbulence fail to describe the oceans and atmospheres. We therefore consider pdfs as measurable quantities that can be used to compare real-world turbulence with better understood physical analogs.

Dynamics of an alfvén surface in core collapse supernovae

Abstract: We investigate the dynamics of an Alfven surface (where the Alfven speed equals the advection velocity) in the context of core collapse supernovae during the phase of accretion on the proto-neutron star. Such a surface should exist even for weak magnetic fields because the advection velocity decreases to zero at the center of the collapsing core. In this decelerated flow, Alfven waves created by the standing accretion shock instability or convection accumulate and amplify while approaching the Alfven surface. We study this amplification using one-dimensional MHD simulations with explicit physical dissipation (resistivity and viscosity). In the linear regime, the amplification continues until the Alfven wavelength becomes as small as the dissipative scale. A pressure feedback that increases the pressure in the upstream flow is created via a nonlinear coupling. We derive analytic formulae for the maximum amplification and the nonlinear coupling and check them with numerical simulations to very good accuracy. Interestingly, these quantities diverge if the dissipation is decreased to zero, scaling as the square root of the Reynolds number, suggesting large effects in weakly dissipative flows. We also characterize the nonlinear saturation of this amplification when compression effects become important, leading to either a change of the velocity gradient, or a steepening of the Alfven wave. Applying these results to core collapse supernovae shows that the amplification can be fast enough to affect the dynamics if the magnetic field is strong enough for the Alfven surface to lie in the region of strong velocity gradient just above the neutrinosphere. This requires the presence of a strong magnetic field in the progenitor star, which would correspond to the formation of a magnetar under the assumption of magnetic flux conservation. An extrapolation of our analytic formula (taking into account the nonlinear saturation) suggests that the Alfven wave could reach an amplitude of B ~ 1015 G, and that the pressure feedback could significantly contribute to the pressure below the shock.