arXiv subjects

Helmut Z. Baumert

Publications and source records attributed to Helmut Z. Baumert.

5 recordsLinked to original sources

arXiv2015

Turbulent mixing and a generalized phase transition in shear-thickening fluids

This paper presents a new theory of turbulent mixing in stirred reactors. The degree of homogeneity of a mixed fluid may be characterized by the Kolmogorov micro-scale. The smaller its value, the better homogeneity. The micro-scale scales inversely with the fourth root of the energy dissipation rate in the stirring process. The higher this rate, the smaller lambda, and the better the homogeneity in the reactor. This is true for Newtonian fluids. In non-Newtonian fluids the situation is different. For instance, in shear-thickening fluids it is plausible that high shear rates thicken the fluid and might strangle the mixing. The internal interactions between different fluid-mechanical and colloidal variables are subtle, namely due to the (until recently) very limited understanding of turbulence. Starting from a qualitatively new turbulence theory for inviscid fluids [Baumert, 2013], giving e.g. the Karman constant as $(2π)^{-1/2} = 0.40$ [the super-pipe in Princeton gave 0.40 p/m 0.02, Bailey et al., 2014], we generalize this approach to the case of viscous fluids and derive equations which in the steady state exhibit two solutions. One solution branch describes a state of good mixing, the other a state of strangled turbulence. The physical system cannot be in two different steady states at the same time. But it is physically admissible to switch between the two steady states by non-stationary transitions, maybe in a chaotic fashion.

physics.flu-dyn↗

arXiv2012

Turbulent mixing driven by mean-flow shear and internal gravity waves in oceans and atmospheres

This study starts with balances deduced by Baumert and Peters (2004, 2005) from results of stratified-shear experiments made in channels and wind tunnels by Itsweire (1984) and Rohr and Van Atta (1987), and of free-decay experiments in a resting stratified tank by Dickey and Mellor (1980). Using a modification of Canuto's (2002) ideas on turbulence and waves, these balances are merged with an (internal) gravity-wave energy balance presented for the open ocean by Gregg (1989), without mean-flow shear. The latter was augmented by a linear (viscous) friction term. Gregg's wave-energy source is interpreted on its long-wave spectral end as internal tides, topography, large-scale wind, and atmospheric low-pressure actions. In addition, internal eigen waves, generated by mean-flow shear, and the aging of the wave field from a virginal (linear) into a saturated state are taken into account. Wave packets and turbulence are treated as particles (vortices, packets) by ensemble kinetics so that the loss terms in all three balances have quadratic form. Following a proposal by Peters (2008), the mixing efficiency of purely wave-generated turbulence is treated as a universal constant, as well as the turbulent Prandtl number under neutral conditions. It is shown that: (i) in the wind tunnel, eigen waves are switched off, (ii) due to remotely generated long waves or other non-local energy sources, coexistence equilibria of turbulence and waves are stable even at Richardson numbers as high as $10^3$; (iii) the three-equation system is compatible with geophysically shielded settings like certain stratified laboratory flows. The agreement with a huge body of observations surprises. Gregg's (1989) wave-model component and the a.m. universal constants taken apart, the equations contain only one additional dimensionless parameter for the eigen-wave closure, estimated as $Y\approx 1.35.$

physics.flu-dyn↗

arXiv2012

Universal equations and constants of turbulent motion

This paper presents a parameter-free theory of shear-generated turbulence at asymptotically high Reynolds numbers in incompressible fluids. It is based on a two-fluids concept. Both components are materially identical and inviscid. The first component is an ensemble of quasi-rigid dipole-vortex tubes as quasi-particles in chaotic motion. The second is a superfluid performing evasive motions between the tubes. The local dipole motions follow Helmholtz' law. The vortex radii scale with the energy-containing length scale. Collisions between quasi-particles lead either to annihilation (likewise rotation, turbulent dissipation) or to scattering (counterrotation, turbulent diffusion). There are analogies with birth and death processes of population dynamics and their master equations. For free homogeneous decay the theory predicts the TKE to follow 1/t. With an adiabatic condition at the wall it predicts the logarithmic law with von Karman's constant as 1/\sqrt{2 pi} = 0.399. Likewise rotating couples form dissipative patches almost at rest ($\rightarrow$ intermittency) wherein the spectrum evolves like an "Apollonian gear" as discussed first by Herrmann, 1990. On this basis the prefactor of the 3D-wavenumber spectrum is predicted as (1/3)(4 pi)^{2/3}=1.8; in the Lagrangian frequency spectrum it is simply 2. The results are situated well within the scatter range of observational, experimental and DNS results.

physics.flu-dyn↗

arXiv2011

Universal constants and equations of turbulent motion

In the spirit of Prandtl's conjecture of 1926, for turbulence at high Reynolds number we present an analogy with the kinetic theory of gases, with dipoles made of quasi-rigid and 'dressed' vortex tubes as frictionless, incompressible but deformable quasi-particles. Their movements are governed by Helmholtz' elementary vortex rules applied locally. A contact interaction or 'collision' leads either to random scatter of a trajectory or to the formation of two likewise rotating, fundamentally unstable whirls forming a dissipative patch slowly rotating around its center of mass which is almost at rest. This approach predicts von Karman's constant as 1/sqrt(2 pi) = 0.399 and the spatio-temporal dynamics of energy-containing time and length scales controlling turbulent mixing [Baumert 2009]. A link to turbulence spectra was missing so far. In the present paper it is shown that the above image of random vortex-dipole movements is compatible with Kolmogorov's turbulence spectra if dissipative patches, beginning as two likewise rotating eddies, evolve locally into a space-filling bearing in the sense of Herrmann [1990], i.e. into an "Apollonian gear". Its parts and pieces are incompressible and flexibly deformable vortex tubes which are frictionless, excepting the dissipative scale of size zero. For steady and locally homogeneous conditions our approach predicts the dimensionless pre-factor in the 3D Eulerian wavenumber spectrum as [(4 pi)^2/3]/3 = 1.8, and in the Lagrangian frequency spectrum as 2. Our derivations rest on geometry, methods from many-particle physics, and on elementary conservation laws.

physics.flu-dyn↗

arXiv2009

Primitive turbulence: kinetics, Prandtl's mixing length, and von Karman's constant

The paper presents a theory of shear-generated turbulence at asymptotically high Reynolds numbers. It is based on an ensemble of dipole vortex tubes taken as quasi-particles and realized in form of rings, hairpins or filament couples of potentially finite length. In a not necesserily planar cross sectional area through a vortex tangle, taken locally orthogonal through each individual tube, the dipoles are moving with the classical dipole velocity. The vortex radius is directly related with Prandtl's classical mixing length. The quasi-particles perform dipol chaos which reminds of molecular chaos in real gases. Collisions between quasi-particles lead either to particle annihilation (turbulent dissipation) or to particle scattering (turbulent diffusion). These ideas suffice to develop a closed theory of shear-generated turbulence without empirical parameters, with analogies to birth and death processes of macromolecules. It coincides almost perfectly with the well-known K-Omega turbulence closure applied in many branches of science and technology. In the case of free homogeneous decay the TKE is shown to follow 1/t. For an adiabatic condition at a solid wall the theory predicts a logarithmic mean-flow boundary layer with von Karman's constant as 1/SQRT(2 pi)=0.399.

physics.flu-dyn↗