6,765 research outputs found
Kinetic Theory and Hydrodynamics of Dense, Reacting Fluids far from Equilibrium
The kinetic theory for a fluid of hard spheres which undergo endothermic
and/or exothermic reactions with mass transfer is developed. The exact balance
equations for concentration, density, velocity and temperature are derived. The
Enskog approximation is discussed and used as the basis for the derivation, via
the Chapman-Enskog procedure, of the Navier-Stokes-reaction equations under
various assumptions about the speed of the chemical reactions. It is shown that
the phenomenological description consisting of a reaction-diffusion equation
with a convective coupling to the Navier-Stokes equations is of limited
applicability.Comment: Submitted to Journal of Chemical Physic
Response of bubbles to diagnotic ultrasound:a unifying theoretical approach
The scattering of ultrasound from bubbles of m 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
Logarithmic temperature profiles in the ultimate regime of thermal convection
We report on the theory of logarithmic temperature profiles in very strongly
developed thermal convection in the geometry of a Rayleigh-Benard cell with
aspect ratio one and discuss the degree of agreement with the recently measured
profiles in the ultimate state of very large Rayleigh number flow. The
parameters of the log-profile are calculated and compared with the measure
ones. Their physical interpretation as well as their dependence on the radial
position are discussed.Comment: 14 pages, no figur
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)=>~Re(t)^2$, is calculated for varying
modulation frequencies w 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 1/w. 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.Comment: 11 pages, 6 figure
Velocity profiles in strongly turbulent Taylor-Couette flow
We derive the velocity profiles in strongly turbulent Taylor-Couette flow for
the general case of independently rotating cylinders. The theory is based on
the Navier-Stokes equations in the appropriate (cylinder) geometry. In
particular, we derive the axial and the angular velocity profiles as functions
of distance from the cylinder walls and find that both follow a logarithmic
profile, with downwards-bending curvature corrections, which are more
pronounced for the angular velocity profile as compared to the axial velocity
profile, and which strongly increase with decreasing ratio between inner
and outer cylinder radius. In contrast, the azimuthal velocity does not follow
a log-law. We then compare the angular and azimuthal velocity profiles with the
recently measured profiles in the ultimate state of (very) large Taylor
numbers. Though the {\em qualitative} trends are the same -- down-bending for
large wall distances and (properly shifted and non-dimensionalized) angular
velocity profile being closer to a log-law than (properly shifted
and non-dimensionalized) azimuthal velocity profile -- {\em
quantitative} deviations are found for large wall distances. We attribute these
differences to the Taylor rolls and the height dependence of the profiles,
neither of which are considered in the theoretical approach
Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Benard convection in glycerol
We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in
two-dimensional Rayleigh-Benard flow in glycerol, which shows a dramatic change
in the viscosity with temperature. The results are presented both as functions
of the Rayleigh number (Ra) up to (for fixed temperature difference
between the top and bottom plates) and as functions of
"non-Oberbeck-Boussinesqness'' or "NOBness'' () up to 50 K (for fixed
Ra). For this large NOBness the center temperature is more than 5 K
larger than the arithmetic mean temperature between top and bottom plate
and only weakly depends on Ra. To physically account for the NOB deviations of
the Nusselt numbers from its Oberbeck-Boussinesq values, we apply the
decomposition of into the product of two effects, namely
first the change in the sum of the top and bottom thermal BL thicknesses, and
second the shift of the center temperature as compared to . While
for water the origin of the deviation is totally dominated by the second
effect (cf. Ahlers et al., J. Fluid Mech. 569, pp. 409 (2006)) for glycerol the
first effect is dominating, in spite of the large increase of as compared
to .Comment: 6 pages, 7 figure
On the sound of snapping shrimp
Snapping shrimp produce a snapping sound by an extremely rapid closure of their snapper claw. Source levels reported for Alpheus heterochaelis are as high as 220 dB (peak-to-peak) re. 1 µPa at 1 m distance. The loud snap has been attributed to the mechanical contact made when the snapper claw contracts. The recent ultra-high-speed imaging of the snapper claw closure at 40500 frames per second has revealed that the sound is, in fact, generated by the collapse of a cavitation bubble formed in a fast flowing water jet forced out from between the claws during claw closure. A temporal analysis of the sound recordings and the high-speed images shows that no sound is associated with the claw closure, while a very prominent signal is observed during the collapse of the cavitation bubble. Gallery of Fluid Motion\ud
Award-winning entry 200
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