The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Yong Zhou - One of the best experts on this subject based on the ideXlab platform.
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on regularity criteria for the 3d incompressible mhd equations involving one Velocity Component
Journal of Mathematical Fluid Mechanics, 2016Co-Authors: Xuanji Jia, Yong ZhouAbstract:By introducing a new a priori estimate for the \({b_{3}}\)-equation, we establish some regularity criteria for the weak solutions of the 3D incompressible MHD equations in terms of one Velocity Component and two magnetic field Components. Our results improve some recent works.
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remarks on regularity criteria for the navier stokes equations via one Velocity Component
Nonlinear Analysis-real World Applications, 2014Co-Authors: Xuanji Jia, Yong ZhouAbstract:Abstract Recently, Pokorný and Zhou proved that if ‖ u 3 ‖ L ∞ ( 0 , T ; L 10 3 ( R 3 ) ) ≪ 1 or ‖ ∇ u 3 ‖ L ∞ ( 0 , T ; L 30 19 ( R 3 ) ) ≪ 1 , then the weak solution u of the 3D Navier–Stokes equations is regular on R 3 × ( 0 , T ] . In this paper we remove the smallness assumptions by using a new approach which may be of independent interest and further application.
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on the regularity of the solutions of the navier stokes equations via one Velocity Component
Nonlinearity, 2010Co-Authors: Yong Zhou, Milan PokornýAbstract:We consider the regularity criteria for the incompressible Navier?Stokes equations connected with one Velocity Component. Based on the method from Cao and Titi (2008 Indiana Univ. Math. J. 57 2643?61) we prove that the weak solution is regular, provided , , \frac {10}{3} SRC=http://ej.iop.org/images/0951-7715/23/5/004/non327722in003.gif/> or provided , if or if s (3, ?]. As a corollary, we also improve the regularity criteria expressed by the regularity of or .
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on a regularity criterion for the navier stokes equations involving gradient of one Velocity Component
Journal of Mathematical Physics, 2009Co-Authors: Yong Zhou, Milan PokornýAbstract:We improve the regularity criterion for the incompressible Navier–Stokes equations in the full three-dimensional space involving the gradient of one Velocity Component. The method is based on recent results of Cao and Titi [see “Regularity criteria for the three dimensional Navier–Stokes equations,” Indiana Univ. Math. J. 57, 2643 (2008)] and Kukavica and Ziane [see “Navier-Stokes equations with regularity in one direction,” J. Math. Phys. 48, 065203 (2007)]. In particular, for s∊[2,3], we get that the solution is regular if ∇u3∊Lt(0,T;Ls(R3)), 2/t+3/s≤2312.
Jonathan Morrison - One of the best experts on this subject based on the ideXlab platform.
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similarity of the streamwise Velocity Component in very rough wall channel flow
Journal of Fluid Mechanics, 2011Co-Authors: David Birch, Jonathan MorrisonAbstract:The streamwise Velocity Component is studied in fully-developed turbulent channel flow for two very rough surfaces and a smooth surface at comparable Reynolds numbers. One rough surface comprises sparse and isotropic grit with a highly non-Gaussian distribution. The other is a uniform mesh consisting of twisted rectangular elements which form a diamond pattern. The mean roughness heights (+/- the standard deviation) are, respectively, about 76 (+/- 42) and 145 (+/- 150) wall units. The flow is shown to be two-dimensional and fully developed up to the fourth-order moment of Velocity. The mean Velocity profile over the grit surface exhibits self-similarity (in the form of a logarithmic law) within the limited range of 0.04 < y/h < 0.06, but the profile over the mesh surface does not, even though the mean Velocity deficit and higher moments (up to the fourth order) all exhibit outer scaling over both surfaces. The distinction between self-similarity and outer similarity is clarified and the importance of the former is explained. The wake strength is shown to increase slightly over the grit surface but decrease over the mesh surface. The latter result is contrary to recent measurements in rough-wall boundary layers. Single- and two-point Velocity correlations reveal the presence of large-scale streamwise structure with circulation in the plane orthogonal to the mean Velocity. Spanwise correlation length scales are significantly larger than corresponding ones for both internal and external smooth-wall flows.
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scaling of the streamwise Velocity Component in turbulent pipe flow
Journal of Fluid Mechanics, 2004Co-Authors: Jonathan Morrison, Beverley Mckeon, Weimin Jiang, Alexander SmitsAbstract:Statistics of the streamwise Velocity Component in fully developed pipe flow are examined for Reynolds numbers in the range 5.5 x 10^4 ≤ ReD ≤ 5.7 x 10^6. Probability density functions and their moments (up to sixth order) are presented and their scaling with Reynolds number is assessed. The second moment exhibits two maxima: the one in the viscous sublayer is Reynolds-number dependent while the other, near the lower edge of the log region, follows approximately the peak in Reynolds shear stress. Its locus has an approximate (R^+)^{0.5} dependence. This peak shows no sign of ‘saturation’, increasing indefinitely with Reynolds number. Scalings of the moments with wall friction Velocity and $(U_{cl}-\overline{U})$ are examined and the latter is shown to be a better Velocity scale for the outer region, y/R > 0.35, but in two distinct Reynolds-number ranges, one when ReD 7 x 10^4. Probability density functions do not show any universal behaviour, their higher moments showing small variations with distance from the wall outside the viscous sublayer. They are most nearly Gaussian in the overlap region. Their departures from Gaussian are assessed by examining the behaviour of the higher moments as functions of the lower ones. Spectra and the second moment are compared with empirical and theoretical scaling laws and some anomalies are apparent. In particular, even at the highest Reynolds number, the spectrum does not show a self-similar range of wavenumbers in which the spectral density is proportional to the inverse streamwise wavenumber. Thus such a range does not attract any special significance and does not involve a universal constant.
L E Kristensen - One of the best experts on this subject based on the ideXlab platform.
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steady wind blown cavities within infalling rotating envelopes application to the broad Velocity Component in young protostars
The Astrophysical Journal, 2020Co-Authors: Lichen Liang, Doug Johnstone, S Cabrit, L E KristensenAbstract:Wind-driven outflows are observed around a broad range of accreting objects throughout the universe, ranging from forming low-mass stars to supermassive black holes. We study the interaction between a central isotropic wind and an infalling, rotating envelope, which determines the steady-state cavity shape formed at their interface under the assumption of weak mixing. The shape of the resulting wind-blown cavity is elongated and self-similar, with a physical size determined by the ratio between wind ram pressure and envelope thermal pressure. We compute the growth of a warm turbulent mixing layer between the shocked wind and the deflected envelope, and calculate the resultant broad-line profile, under the assumption of a linear (Couette-type) Velocity profile across the layer. We then test our model against the warm broad Velocity Component observed in CO J = 16–15 by Herschel/HIFI in the protostar Serpens-Main SMM1. Given independent observational constraints on the temperature and density of the dust envelope around SMM1, we find an excellent match to all its observed properties (line profile, momentum, temperature) and to the SMM1 outflow cavity width for a physically reasonable set of parameters: a ratio of wind to infall mass flux of sime4%, a wind speed of v w sime 30 km s−1, an interstellar abundance of CO and H2, and a turbulent entrainment efficiency consistent with laboratory experiments. The inferred ratio of ejection to disk accretion rate, sime6%–20%, is in agreement with current disk wind theories. Thus, the model provides a new framework to reconcile the modest outflow cavity widths in protostars with large observed flow velocities. Being self-similar, it is applicable over a broader range of astrophysical contexts as well.
Detlef Lohse - One of the best experts on this subject based on the ideXlab platform.
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statistics of turbulence in the energy containing range of taylor couette compared to canonical wall bounded flows
Journal of Fluid Mechanics, 2017Co-Authors: Dominik Krug, Xiang Yang, Charitha M De Silva, Rodolfo Ostillamonico, Roberto Verzicco, Ivan Marusic, Detlef LohseAbstract:Considering structure functions of the streamwise Velocity Component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva et al. (J. Fluid Mech., vol. 823, 2017, pp. 498-510) observed that remarkably the large-scale (energy-containing range) statistics in canonical wall-bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor-Couette flow. In doing so, we find that also the transversal structure function of the spanwise Velocity Component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached-eddy contributions. By taking the effect of streamwise alignment into account, the attached-eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS framework - both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high Reynolds number data are currently available.
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statistics of turbulence in the energy containing range of taylor couette compared to canonical wall bounded flows
arXiv: Fluid Dynamics, 2017Co-Authors: Dominik Krug, Xiang Yang, Charitha M De Silva, Rodolfo Ostillamonico, Roberto Verzicco, Ivan Marusic, Detlef LohseAbstract:Considering structure functions of the streamwise Velocity Component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva \textit{et al.} (\textit{J. Fluid Mech.}, vol. 823,2017, pp. 498-510) observed that remarkably the \textit{large-scale} (energy-containing range) statistics in canonical wall bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor-Couette flow. In doing so, we find that also the transversal structure function of the spanwise Velocity Component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached eddy contributions. By taking the effect of streamwise alignment into account, the attached eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS-framework --- both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high-Reynolds number data are currently available.
Rodolfo Ostillamonico - One of the best experts on this subject based on the ideXlab platform.
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statistics of turbulence in the energy containing range of taylor couette compared to canonical wall bounded flows
Journal of Fluid Mechanics, 2017Co-Authors: Dominik Krug, Xiang Yang, Charitha M De Silva, Rodolfo Ostillamonico, Roberto Verzicco, Ivan Marusic, Detlef LohseAbstract:Considering structure functions of the streamwise Velocity Component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva et al. (J. Fluid Mech., vol. 823, 2017, pp. 498-510) observed that remarkably the large-scale (energy-containing range) statistics in canonical wall-bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor-Couette flow. In doing so, we find that also the transversal structure function of the spanwise Velocity Component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached-eddy contributions. By taking the effect of streamwise alignment into account, the attached-eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS framework - both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high Reynolds number data are currently available.
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statistics of turbulence in the energy containing range of taylor couette compared to canonical wall bounded flows
arXiv: Fluid Dynamics, 2017Co-Authors: Dominik Krug, Xiang Yang, Charitha M De Silva, Rodolfo Ostillamonico, Roberto Verzicco, Ivan Marusic, Detlef LohseAbstract:Considering structure functions of the streamwise Velocity Component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva \textit{et al.} (\textit{J. Fluid Mech.}, vol. 823,2017, pp. 498-510) observed that remarkably the \textit{large-scale} (energy-containing range) statistics in canonical wall bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor-Couette flow. In doing so, we find that also the transversal structure function of the spanwise Velocity Component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached eddy contributions. By taking the effect of streamwise alignment into account, the attached eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS-framework --- both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high-Reynolds number data are currently available.
