arXiv subjects

Detlef Lohse

Publications and source records attributed to Detlef Lohse.

465 records · Page 26Linked to original sources

arXiv1996

Why air bubbles in water glow so easily

Sound driven gas bubbles in water can emit light pulses (sonoluminescence). Experiments show a strong dependence on the type of gas dissolved in water. Air is found to be one of the most friendly gases towards this phenomenon. Recently, \cite{loh96} have suggested a chemical mechanism to account for the strong dependence on the gas mixture: the dissociation of nitrogen at high temperatures and its subsequent chemical reactions to highly water soluble gases such as NO, NO$_2$, and/or NH$_3$. Here, we analyze the consequences of the theory and offer detailed comparison with the experimental data of Putterman's UCLA group. We can quantitatively account for heretofore unexplained results. In particular, we understand why the argon percentage in air is so essential for the observation of stable SL.

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arXiv1996

Phase Diagrams for Sonoluminescing Bubbles

Sound driven gas bubbles in water can emit light pulses. This phenomenon is called sonoluminescence (SL). Two different phases of single bubble SL have been proposed: diffusively stable and diffusively unstable SL. We present phase diagrams in the gas concentration vs forcing pressure state space and also in the ambient radius vs gas concentration and vs forcing pressure state spaces. These phase diagrams are based on the thresholds for energy focusing in the bubble and two kinds of instabilities, namely (i) shape instabilities and (ii) diffusive instabilities. Stable SL only occurs in a tiny parameter window of large forcing pressure amplitude $P_a \sim 1.2 - 1.5$atm and low gas concentration of less than $0.4\%$ of the saturation. The upper concentration threshold becomes smaller with increasing forcing. Our results quantitatively agree with experimental results of Putterman's UCLA group on argon, but not on air. However, air bubbles and other gas mixtures can also successfully be treated in this approach if in addition (iii) chemical instabilities are considered. -- All statements are based on the Rayleigh-Plesset ODE approximation of the bubble dynamics, extended in an adiabatic approximation to include mass diffusion effects. This approximation is the only way to explore considerable portions of parameter space, as solving the full PDEs is numerically too expensive. Therefore, we checked the adiabatic approximation by comparison with the full numerical solution of the advection diffusion PDE and find good agreement.

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arXiv1996

Scaling and Linear Response in the GOY Turbulence model

The GOY model is a model for turbulence in which two conserved quantities cascade up and down a linear array of shells. When the viscosity parameter, $ν$, is small the model has a qualitative behavior which is similar to the Kolmogorov theories of turbulence. Here a static solution to the model is examined, and a linear stability analysis is performed to obtain response eigenvalues and eigenfunctions. Both the static behavior and the linear response show an inertial range with a relatively simple scaling structure. Our main results are: (i) The response frequencies cover a wide range of scales, with ratios which can be understood in terms of the frequency scaling properties of the model. (ii) Even small viscosities play a crucial role in determining the model's eigenvalue spectrum. (iii) As a parameter within the model is varied, it shows a ``phase transition'' in which there is an abrupt change in many eigenvalues from stable to unstable values. (iv) The abrupt change is determined by the model's conservation laws and symmetries. This work is thus intended to add to our knowledge of the linear response of a stiff dynamical systems and at the same time to help illuminate scaling within a class of turbulence models.

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arXiv1995

Mechanisms for Stable Sonoluminescence

A gas bubble trapped in water by an oscillating acoustic field is expected to either shrink or grow on a diffusive timescale, depending on the forcing strength and the bubble size. At high ambient gas concentration this has long been observed in experiments. However, recent sonoluminescence experiments show that in certain circumstances when the ambient gas concentration is low the bubble can be stable for days. This paper presents mechanisms leading to stability which predict parameter dependences in agreement with the sonoluminescence experiments.

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arXiv1995

How the viscous subrange determines inertial range properties in turbulence shell models

We calculate static solutions of the 'GOY' shell model of turbulence and do a linear stability analysis. The asymptotic limit of large Reynolds numbers is analyzed. A phase diagram is presented which shows the range of stability of the static solution. We see an unexpected oscillatory dependence of the stability range upon $\lg ν$, where $ν$ is the viscosity. This effect depends upon the discrete structure of the shell model and goes to zero as the separation between the shells is brought to zero. These findings show how viscous effects play a role in determining inertial properties of shell models and give some hints for understanding the effects of viscous dissipation upon real turbulence.

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arXiv1995

Scaling and Dissipation in the GOY Shell Model

This is a paper about multi-fractal scaling and dissipation in a shell model of turbulence, called the GOY model. This set of equations describes a one dimensional cascade of energy towards higher wave vectors. When the model is chaotic, the high-wave-vector velocity is a product of roughly independent multipliers, one for each logarithmic momentum shell. The appropriate tool for studying the multifractal properties of this model is shown to be the energy current on each shell rather than the velocity on each shell. Using this quantity, one can obtain better measurements of the deviations from Kolmogorov scaling (in the GOY dynamics) than were available up to now. These deviations are seen to depend upon the details of inertial-range structure of the model and hence are {\em not} universal. However, once the conserved quantities of the model are fixed to have the same scaling structure as energy and helicity, these deviations seem to depend only weakly upon the scale parameter of the model. We analyze the connection between multifractality in the velocity distribution and multifractality in the dissipation. Our arguments suggest that the connection is universal for models of this character, but the model has a different behavior from that of real turbulence. We also predict the scaling behavior of time correlations of shell-velocities, of the dissipation,

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arXiv1995

Bubble Shape Oscillations and the Onset of Sonoluminescence

An air bubble trapped in water by an oscillating acoustic field undergoes either radial or nonspherical pulsations depending on the strength of the forcing pressure. Two different instability mechanisms (the Rayleigh--Taylor instability and parametric instability) cause deviations from sphericity. Distinguishing these mechanisms allows explanation of many features of recent experiments on sonoluminescence, and suggests methods for finding sonoluminescence in different parameter regimes.

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arXiv1994

Temperature spectra in shear flow and thermal convection

We show that the $P_u(\om) \propto \om^{-7/3}$ shear velocity power spectrum gives rise to a $P_Θ(\om ) \propto \om^{-4/3}$ power spectrum for a passively advected scalar, as measured in experiment [K. Sreenivasan, Proc. R. Soc. London A {\bf 434}, 165 (1991)]. Applying our argument to high Rayleigh number Rayleigh Benard flow, we can account for the measured scaling exponents equally well as the Bolgiano Obukhov theory (BO59). Yet, of the two explanations, only the shear approach might be able to explain why no classical scaling range is seen in between the shear (or BO59) range and the viscous subrange of the experimental temperature spectrum [I. Procaccia {\it et al.}, Phys. Rev. A {\bf 44}, 8091 (1991)].

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arXiv1994

Bottleneck effects in turbulence: Scaling phenomena in r- versus p-space

We (analytically) calculate the energy spectrum corresponding to various experimental and numerical turbulence data analyzed by Benzi et al.. We find two bottleneck phenomena: While the local scaling exponent $ζ_r(r)$ of the structure function decreases monotonically, the local scaling exponent $ζ_p(p)$ of the corresponding spectrum has a minimum of $ζ_p(p_{min})\approx 0.45$ at $p_{min}\approx (10 η)^{-1}$ and a maximum of $ζ_p(p_{max})\approx 0.77$ at $p_{max}\approx 8 L^{-1}$. A physical argument starting from the constant energy flux in p--space reveals the general mechanism underlying the energy pileups at both ends of the p--space scaling range. In the case studied here, they are induced by viscous dissipation and the reduced spectral strength on the scale of the system size, respectively.

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arXiv1994

Anisotropy and scaling corrections in turbulence

Two parametrizations for second order velocity moments, the Batchelor parametrization for the r-space structure function and a common parametrization for the energy spectrum, $E(p)\propto p^{-5/3}\exp(-p/p_d)$, are examined and compared. In particular, we investigate corrections to the local scaling exponents induced by finite size effects. The behavior of local r-- and p--space exponents differs dramatically. The Batchelor type parametrization leads to energy pileups in p-space at the ends of the ISR. These bottleneck effects result in an extended r-space scaling range, comparable to experimental ones for the same Taylor-Reynolds number $\rel$. Shear effects are discussed in terms of (global) apparent scaling correction $δζ^{app}$ to classical scaling. The scaling properties of $δζ^{app}(\rel )$ differ not only among the parametrizations considered, but also among r-- and p--space for a {\it given} parametrization. The difference can be traced back to the subtleties of the crossovers in the velocity moments. Our observations emphasize the need for more experimental information on crossovers between different subranges.

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arXiv1994

Finite size corrections to scaling in high Reynolds number turbulence

We study analytically and numerically the corrections to scaling in turbulence which arise due to the finite ratio of the outer scale $L$ of turbulence to the viscous scale $η$, i.e., they are due to finite size effects as anisotropic forcing or boundary conditions at large scales. We find that the deviations $\dzm$ from the classical Kolmogorov scaling $ζ_m = m/3$ of the velocity moments $\langle |\u(\k)|^m\rangle \propto k^{-ζ_m}$ decrease like $δζ_m (Re) =c_m Re^{-3/10}$. Our numerics employ a reduced wave vector set approximation for which the small scale structures are not fully resolved. Within this approximation we do not find $Re$ independent anomalous scaling within the inertial subrange. If anomalous scaling in the inertial subrange can be verified in the large $Re$ limit, this supports the suggestion that small scale structures should be responsible, originating from viscosity either in the bulk (vortex tubes or sheets) or from the boundary layers (plumes or swirls).

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arXiv1994

Crossover from high to low Reynolds number turbulence

The Taylor-Reynolds and Reynolds number ($Re_λ$ and $Re$) dependence of the dimensionless energy dissipation rate $\ceps =\eps L / \u1rms^3$ is derived for statistically stationary isotropic turbulence, employing the results of a variable range mean field theory. Here, $\eps$ is the energy dissipation rate, $L$ is the (fixed) outer length scale, and $\u1rms$ a rms velocity component. Our fit-parameter free results for $\ceps (Re_λ)$ and also for $Re_λ(Re)$ are in good agreement with experimental data. Using the $Re$-dependence of $\ceps$ we account for the time dependence of the mean vorticity $ω(t)$ for decaying isotropic turbulence, which was recently experimentally examined [M.\ Smith, R.\ J.\ Donelly, N.\ Goldenfeld, and W.\ F.\ Vinen, Phys.\ Rev.\ Lett.\ 71, 2583 (1993)]. The lifetime of decaying turbulence, depending on the initial $Re_{λ,0}$, is predicted and found to saturate at $0.18 L^2/ν\propto Re_{λ,0}^2$ ($ν$ is the viscosity) for large $Re_{λ,0}$.

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arXiv1993

Universality in fully developed turbulence

We extend the numerical simulations of She et al. [Phys.\ Rev.\ Lett.\ 70, 3251 (1993)] of highly turbulent flow with $15 \le$ Taylor-Reynolds number $Re_λ\le 200$ up to $Re_λ\approx 45000$, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equation. First, also for these extremely high Reynolds numbers $Re_λ$, the energy spectra as well as the higher moments -- when scaled by the spectral intensity at the wave number $k_p$ of peak dissipation -- can be described by {\it one universal} function of $k/k_p$ for all $Re_λ$. Second, the ISR scaling exponents $ζ_m$ of this universal function are in agreement with the 1941 Kolmogorov theory (the better, the large $Re_λ$ is), as is the $Re_λ$ dependence of $k_p$. Only around $k_p$ viscous damping leads to slight energy pileup in the spectra, as in the experimental data (bottleneck phenomenon).

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arXiv1993

Scale resolved intermittency in turbulence

The deviations $δζ_m$ ("intermittency corrections") from classical ("K41") scaling $ζ_m=m/3$ of the $m^{th}$ moments of the velocity differences in high Reynolds number turbulence are calculated, extending a method to approximately solve the Navier-Stokes equation described earlier. We suggest to introduce the notion of scale resolved intermittency corrections $δζ_m(p)$, because we find that these $δζ_m(p)$ are large in the viscous subrange, moderate in the nonuniversal stirring subrange but, surprisingly, extremely small if not zero in the inertial subrange. If ISR intermittency corrections persisted in experiment up to the large Reynolds number limit, our calculation would show, that this could be due to the opening of phase space for larger wave vectors. In the higher order velocity moment $\langle|u(p)|^m\rangle$ the crossover between inertial and viscous subrange is $(10ηm/2)^{-1}$, thus the inertial subrange is {\it smaller} for higher moments.

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arXiv1993

Fractal dimension crossovers in turbulent passive scalar signals

The fractal dimension $δ_g^{(1)}$ of turbulent passive scalar signals is calculated from the fluid dynamical equation. $δ_g^{(1)}$ depends on the scale. For small Prandtl (or Schmidt) number $Pr<10^{-2}$ one gets two ranges, $δ_g^{(1)}=1$ for small scale r and $δ_g^{(1)}$=5/3 for large r, both as expected. But for large $Pr> 1$ one gets a third, intermediate range in which the signal is extremely wrinkled and has $δ_g^{(1)}=2$. In that range the passive scalar structure function $D_θ(r)$ has a plateau. We calculate the $Pr$-dependence of the crossovers. Comparison with a numerical reduced wave vector set calculation gives good agreement with our predictions.

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