arXiv subjects

Detlef Lohse

Publications and source records attributed to Detlef Lohse.

At least 451 records · Page 25Linked to original sources

arXiv2001

Hysteretic clustering in granular gas

Granular material is vibro-fluidized in N=2 and N=3 connected compartments, respectively. For sufficiently strong shaking the granular gas is equi-partitioned, but if the shaking intensity is lowered, the gas clusters in one compartment. The phase transition towards the clustered state is of 2nd order for N=2 and of 1st order for N=3. In particular, the latter is hysteretic. The experimental findings are accounted for within a dynamical model that exactly has the above properties.

nlin.CD↗

arXiv2000

Decaying and kicked turbulence in a shell model

Decaying and periodically kicked turbulence are analyzed within the GOY shell model, to allow for sufficiently large scaling regimes. Energy is transfered towards the small scales in intermittent bursts. Nevertheless, mean field arguments are sufficient to account for the ensemble averaged energy decay E(t) t^{-2} or the parameter dependences for the ensemble averaged total energy in the kicked case. Within numerical precision, the inertial subrange intermittency remains the same, whether the system is forced or decaying.

nlin.CD↗

arXiv2000

Thermal convection for large Prandtl numbers

The Rayleigh-Benard theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)] is extended towards very large Prandtl numbers Pr. The Nusselt number Nu is found here to be independent of Pr. However, for fixed Rayleigh numbers Ra> 10^{10} a maximum around Pr= 2 in the Nu(Pr)-dependence is predicted which is absent for lower Ra. We moreover offer the full functional dependences of Nu(Ra,Pr) and Re(Ra,Pr) within this extended theory, rather than only giving the limiting power laws as done previously. This enables us to more realistically describe the transitions between the various scaling regimes, including their widths.

nlin.CD↗

arXiv2000

Scaling of global momentum transport in Taylor-Couette and pipe flow

We interpret measurements of the Reynolds number dependence of the torque in Taylor-Couette flow by Lewis and Swinney [Phys. Rev. E 59, 5457 (1999)] and of the pressure drop in pipe flow by Smits and Zagarola, [Phys. Fluids 10, 1045 (1998)] within the scaling theory of Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)], developed in the context of thermal convection. The main idea is to split the energy dissipation into contributions from a boundary layer and the turbulent bulk. This ansatz can account for the observed scaling in both cases if it is assumed that the internal wind velocity $U_w$ introduced through the rotational or pressure forcing is related to the the external (imposed) velocity U, by $U_w/U \propto Re^ξ$ with xi = -0.051 and xi = -0.041 for the Taylor-Couette (U inner cylinder velocity) and pipe flow (U mean flow velocity) case, respectively. In contrast to the Rayleigh-Benard case the scaling exponents cannot (yet) be derived from the dynamical equations.

nlin.CD↗

arXiv2000

Periodically kicked turbulence

Periodically kicked turbulence is theoretically analyzed within a mean field theory. For large enough kicking strength A and kicking frequency f the Reynolds number grows exponentially and then runs into some saturation. The saturation level can be calculated analytically; different regimes can be observed. For large enough Re we find the saturation level to be proportional to A*f, but intermittency can modify this scaling law. We suggest an experimental realization of periodically kicked turbulence to study the different regimes we theoretically predict and thus to better understand the effect of forcing on fully developed turbulence.

nlin.CD↗

arXiv2000

Probing structures in channel flow through SO(3) and SO(2) decomposition

SO(3) and SO(2) decompositions of numerical channel flow turbulence are performed. The decompositions are used to probe, characterize, and quantify anisotropic structures in the flow. Close to the wall the anisotropic modes are dominant and reveal the flow structures. The SO(3) decomposition does not converge for large scales as expected. However, in the shear buffer layer it also does not converge for small scales, reflecting the lack of small scales isotropization in that part of the channel flow.

nlin.CD↗

arXiv1999

Scaling in thermal convection: A unifying theory

A systematic theory for the scaling of the Nusselt number $Nu$ and of the Reynolds number $Re$ in strong Rayleigh-Benard convection is suggested and shown to be compatible with recent experiments. It assumes a coherent large scale convection roll (``wind of turbulence'') and is based on the dynamical equations both in the bulk and in the boundary layers. Several regimes are identified in the Rayleigh number versus Prandtl number phase space, defined by whether the boundary layer or the bulk dominates the global kinetic and thermal dissipation, respectively. The crossover between the regimes is calculated. In the regime which has most frequently been studied in experiment (Ra smaller than 10^{11}) the leading terms are $Nu\sim Ra^{1/4}Pr^{1/8}$, $Re \sim Ra^{1/2} Pr^{-3/4}$ for $Pr < 1$ and $Nu\sim Ra^{1/4}Pr^{-1/12}$, $Re \sim Ra^{1/2} Pr^{-5/6}$ for $Pr > 1$. In most measurements these laws are modified by additive corrections from the neighboring regimes so that the impression of a slightly larger (effective) Nu vs Ra scaling exponent can arise. -- The presented theory is best summarized in the phase diagram figure 1.

chao-dyn↗

arXiv1999

Entropy-driven pumping across zeolites and biological channels

When two binary solutions are separated by a permeable barrier, the individual species typically diffuse and mix, dissipating their chemical potential gradients. However, we use model lattice simulations to show that single-file molecular-sized channels (such biomembrane channels and zeolites) can exhibit diffusional pumping, where one type of particle uses its entropy of mixing to drive another up its chemical potential gradient. Quantitative analyses of rates and efficiencies of transport are plotted as functions of transmembrane potential, pore length, and particle-pore interactions. Our results qualitatively explain recent measurements of ``negative'' osmosis and suggest new, more systematic experiments, particularly in zeolite transport systems.

cond-mat.stat-mech↗

arXiv1998

Response of bubbles to diagnostic ultrasound: a unifying theoretical approach

The scattering of ultrasound from bubbles of micrometer-sized radius, such as used in contrast enhancers for ultrasound diagnostics, is studied. We show that sound scattering and ``active'' emission of sound from oscillating bubbles are not contradictory, but are just two different aspects derived from the same physics. Treating the bubble as a nonlinear oscillator, we arrive at general formulas for scattering and absorption cross sections. We show that several well-known formulas are recovered in the linear limit of this ansatz. In the case of strongly nonlinear oscillations, however, the cross sections can be larger than those for linear response by several orders of magnitude. The major part of the incident sound energy is then converted into emitted sound, unlike what happens in the linear case, where the absorption cross sections exceed the scattering cross sections.

cond-mat.soft↗

arXiv1998

Analysis of Rayleigh-Plesset dynamics for sonoluminescing bubbles

Recent work on single bubble sonoluminescence (SBSL) has shown that many features of this phenomenon, especially the dependence of SBSL intensity and stability on experimental parameters, can be explained within a hydrodynamic approach. More specifically, many important properties can already be derived from an analysis of bubble wall dynamics. This dynamics is conveniently described by the Rayleigh-Plesset (RP) equation. In this work we derive analytical approximations for RP dynamics and subsequent analytical laws for parameter dependences. These results include (i) an expression for the onset threshold of SL, (ii) an analytical explanation of the transition from diffusively unstable to stable equilibria for the bubble ambient radius (unstable and stable sonoluminescence), and (iii) a detailed understanding of the resonance structure of the RP equation. It is found that the threshold for SL emission is shifted to larger bubble radii and larger driving pressures if surface tension is enlarged, whereas even a considerable change in liquid viscosity leaves this threshold virtually unaltered. As an enhanced viscosity stabilizes the bubbles against surface oscillations, we conclude that the ideal liquid for violently collapsing, surface stable SL bubbles should have small surface tension and large viscosity, although too large viscosity (>40 times the viscosity of water) will again preclude collapses.

chao-dyn↗

arXiv1998

Water temperature dependence of single bubble sonoluminescence

The strong dependence of the intensity of single bubble sonoluminescence (SBSL) on water temperature observed in experiment can be accounted for by the temperature dependence of the material constants of water, most essentially of the viscosity, of the argon solubility in water, and of the vapor pressure. The strong increase of light emission at low water temperatures is due to the possibility of applying higher driving pressures, caused by increased bubble stability. The presented calculations combine the Rayleigh-Plesset equation based hydrodynamical/chemical approach to SBSL and full gas dynamical calculations of the bubble's interior.

chao-dyn↗

arXiv1997

Sound radiation of 3 MHz driven gas bubbles

The sound radiation of 3 MHz acoustically driven air bubbles in liquid is analysed with respect to possible applications in second harmonic ultrasound diagnostics devices, which have recently come into clinical use. In the forcing pressure amplitude P_a = 1-10 atm and ambient radius R_0 = 0.5-5 μm parameter domain a narrow regime around the resonance radius R_0 \sim 1-1.5 μm and relatively modest P_a \sim 2-2.5 atm is identified in which optimal sound yield in the second harmonic is achieved while maintaining spherical stability of the bubble. For smaller P_a and larger R_0 hardly any sound is radiated; for larger P_a bubbles become unstable towards non-spherical shape oscillations of their surface. The computation of these instabilities is essential for the evaluation of the optimal parameter regime. A region of slightly smaller R_0 and P_a \sim 1-3 atm is best suited to achieve large ratios of the second harmonic to the fundamental intensity. Spherical stability is guaranteed in the suggested regimes for liquids with an enhanced viscosity compared to water, such as blood.

chao-dyn↗

arXiv1997

Different intermittency for longitudinal and transversal turbulent fluctuations

Scaling exponents of the longitudinal and transversal velocity structure functions in numerical Navier-Stokes turbulence simulations with Taylor-Reynolds numbers up to $\rel = 110$ are determined by the extended self similarity method. We find significant differences in the degree of intermittency: For the sixth moments the scaling corrections to the classical Kolmogorov expectations are $δξ_6^L= -0.21 \pm 0.01$ and $\dx_6^T= -0.43 \pm 0.01$, respectively, independent of $\rel$. Also the generalized extended self similarity exponents $ρ_{p,q} = \dx_p/\dx_q$ differ significantly for the longitudinal and transversal structure functions. Within the She-Leveque model this means that longitudinal and transversal fluctuations obey different types of hierarchies of the moments. Moreover, the She-Leveque model hierarchy parameters $β^L $ and $β^T$ show small but significant dependences on the order of the moment.

chao-dyn↗

arXiv1997

Inert gas accumulation in sonoluminescing bubbles

In this paper we elaborate on the idea [Lohse et al., Phys. Rev. Lett. 78, 1359-1362 (1997)] that (single) sonoluminescing air bubbles rectify argon. The reason for the rectification is that nitrogen and oxygen dissociate and their reaction products dissolve in water. We give further experimental and theoretical evidence and extend the theory to other gas mixtures. We show that in the absence of chemical reactions (e.g., for inert gas mixtures) gas accumulation in strongly acoustically driven bubbles can also occur.

chao-dyn↗

arXiv1997

Sonoluminescing air bubbles rectify argon

The dynamics of single bubble sonoluminescence (SBSL) strongly depends on the percentage of inert gas within the bubble. We propose a theory for this dependence, based on a combination of principles from sonochemistry and hydrodynamic stability. The nitrogen and oxygen dissociation and subsequent reaction to water soluble gases implies that strongly forced air bubbles eventually consist of pure argon. Thus it is the partial argon (or any other inert gas) pressure which is relevant for stability. The theory provides quantitative explanations for many aspects of SBSL.

chao-dyn↗

arXiv1997

Scaling of the irreducible SO(3)-invariants of velocity correlations in turbulence

The scaling behavior of the SO(3) irreducible amplitudes $d_n^l(r)$ of velocity structure tensors (see L'vov, Podivilov, and Procaccia, Phys. Rev. Lett. (1997)) is numerically examined for Navier-Stokes turbulence. Here, l characterizes the irreducible representation by the index of the corresponding Legendre polynomial, and n denotes the tensorial rank, i.e., the order of the moment. For moments of different order n but with the same representation index l extended self similarity (ESS) towards large scales is found. Intermittency seems to increase with l. We estimate that a crossover behavior between different inertial subrange scaling regimes in the longitudinal and transversal structure functions will hardly be detectable for achievable Reynolds numbers.

chao-dyn↗

arXiv1997

Application of extended self similarity in turbulence

From Navier-Stokes turbulence numerical simulations we show that for the extended self similarity (ESS) method it is essential to take the third order structure function taken with the modulus and called $D_3^*(r)$, rather than the standard third order structure function $D_3(r)$ itself. If done so, we find ESS towards scales larger than roughly 10 eta, where eta is the Kolmogorov scale. If $D_3(r)$ is used, there is no ESS. We also analyze ESS within the Batchelor parametrization of the second and third order longitudinal structure function and focus on the scaling of the transversal structure function. The Re-asymptotic inertial range scaling develops only beyond a Taylor-Reynolds number of about 500.

chao-dyn↗

arXiv1996

Developed turbulence: From full simulations to full mode reductions

Developed Navier-Stokes turbulence is simulated with varying wavevector mode reductions. The flatness and the skewness of the velocity derivative depend on the degree of mode reduction. They show a crossover towards the value of the full numerical simulation when the viscous subrange starts to be resolved. The intermittency corrections of the scaling exponents of the pth order velocity structure functions seem to depend mainly on the proper resolution of the inertial subrange. Universal scaling properties (i.e., independent of the degree of mode reduction) are found for the relative scaling exponents rho which were recently defined by Benzi et al.

chao-dyn↗