Biomedical subjects

Siegfried Grossmann

Publications and source records attributed to Siegfried Grossmann.

5 recordsLinked to original sources

PubMed2005

Wind reversals in turbulent Rayleigh-Bénard convection.

The phenomenon of irregular cessation and subsequent reversal of the large-scale circulation in turbulent Rayleigh-Bénard convection is theoretically analyzed. The force and thermal balance on a single plume detached from the thermal boundary layer yields a set of coupled nonlinear equations, whose dynamics is related to the Lorenz equations. For Prandtl and Rayleigh numbers in the range 10(-2) < or = Pr < or = 10(3) and 10(7) < or = Ra < or = 10(12), the model has the following features: (i) chaotic reversals may be exhibited at Ra > or = 10(7); (ii) the Reynolds number based on the root mean square velocity scales as Re(rms) approximately Ra([0.41...0.47]) (depending on Pr), and as Re(rms) approximately Pr(-[0.66...0.76]) (depending on Ra); and (iii) the mean reversal frequency follows an effective scaling law omega/(nu L(-2)) approximately Pr(-(0.64 +/- 0.01))Ra(0.44 +/- 0.01). The phase diagram of the model is sketched, and the observed transitions are discussed.

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PubMed2003

Response maxima in modulated turbulence. II. Numerical simulations.

Numerical simulations of fully developed turbulence driven by a modulated energy input rate or driving force are performed within two dynamical cascade models, the Gkedzer-Ohkitani-Yamada shell model and a reduced wave vector set approximation of the Navier-Stokes equation. The frequency behavior of the system response is studied and compared with predictions from a variable range mean-field theory, which excludes turbulent fluctuations. In agreement with the mean-field approach, we find a constant response amplitude for low driving frequencies and a 1/omega decay of the amplitude for high frequencies. In the mean-field theory, the finite cascade time scale had led to an oscillating behavior of the response amplitude as a function of the driving frequency. In the simulations of both models we observe the main maximum. The higher maxima and minima are completely washed out by fluctuations, though the statistical properties of the fluctuations are different in the two models.

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PubMed2003

Response maxima in modulated turbulence.

Isotropic and homogeneous turbulence driven by an energy input modulated in time is studied within a variable range mean-field theory. The response of the system, observed in the second-order moment of the large-scale velocity difference D(L,t)=<<(u(x+L)-u(x))(2)>> proportional, variant Re(2)(t), is calculated for varying modulation frequencies omega and weak modulation amplitudes. For low frequencies the system follows the modulation of the driving with almost constant amplitude, whereas for higher driving frequencies the amplitude of the response decreases on average proportional, variant 1/omega. In addition, at certain frequencies the amplitude of the response either almost vanishes or is strongly enhanced. These frequencies are connected with the frequency scale of the energy cascade and multiples thereof.

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PubMed2002

Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection.

The Prandtl and Rayleigh number dependences of the Reynolds number in turbulent thermal convection following from the unifying theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000); Phys. Rev. Lett. 86, 3316 (2001)] are presented and compared with various recent experimental findings. This dependence Re(Ra,Pr) is more complicated than a simple global power law. For Pr=5.5 and 10(8)<Ra<10(10) the effective or local power law exponent of Re as a function of Ra is definitely less than 0.50, namely, Re approximately Ra(0.45), in agreement with Qiu and Tong's experimental findings [Phys. Rev. E 64, 036304 (2001)]. We also calculated the kinetic boundary layer width. Both in magnitude and in Ra scaling it is consistent with the data.

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PubMed2002

Scaling hypothesis leading to generalized extended self-similarity in turbulence.

A scaling hypothesis leading to generalized extended self-similarity (GESS) for velocity structure functions, valid for intermediate scales in isotropic, homogeneous turbulence, is proposed. By introducing an effective scale ŕ, monotonically depending on the physical scale r, with the use of the large deviation theory, the asymptotic forms of the probability densities for the velocity differences u(r) and for the coarse-grained energy-dissipation rate fluctuations epsilon(r), compatible with this GESS, are proposed. The probability density for epsilon(r) is shown to have the form P(r)(epsilon) approximately equal to epsilon(-1)(ŕ/L)(S(ŕ)[z(ŕ)](epsilon))) with z(ŕ)(epsilon)=ln(epsilon/epsilon(L))/ln(L/ŕ), where L and epsilon(L) are the stirring scale and the coarse-grained energy-dissipation rate over the scale L. The concave function S(ŕ)(z), the spectrum, plays the central role of the present approach. Comparing the results with numerical and experimental data, we explicitly obtain the fluctuation spectra S(ŕ)(z).

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