Velocity fluctuations in laminar fluid flow

Sengers, J. V.; Zárate, José M. Ortiz de

doi:10.1016/j.jnnfm.2010.01.020

Cited by 10 publications

(16 citation statements)

References 35 publications

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“…Specifically, for the fluctuations in the spanwise direction the expression in terms of the Galerkin approximation in Refs. [16,17] Equation (42) contains an equilibrium contribution that is about 17% percent lower than the exact result, Eq. (37).…”

Section: Comparison With Galerkin Approximationmentioning

confidence: 88%

“…Specifically, we have shown how the thermally excited wall-normal velocity fluctuations can be described by a stochastic Orr-Sommerfeld equation [15] and the thermally excited vorticity fluctuations by a stochastic Squire equation [16]. Accounting for realistic boundary conditions we obtained solutions of the stochastic Sommerfeld and Squire equations based on semi-quantitative Galerkin approximations [15][16][17]. We now have derived more exact solutions of these stochastic equations in terms of an expansion of the eigenfunctions (hydrodynamic modes) of the hydrodynamic operator.…”

Section: Introductionmentioning

confidence: 99%

“…(1) and (2) using a Galerkin method that allowed for analytical but approximate expressions for the correlation functions of the wall-normal velocity and vorticity fluctuations [15,16]. We have summarized these approximate solutions of the two stochastic equations in a subsequently publication [17]. While the Galerkinapproximation technique enabled us to obtain relatively simple analytical results, the approximation is somewhat uncontrolled.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hydrodynamic Fluctuations in Laminar Fluid Flow. II. Fluctuating Squire Equation

Zárate

Sengers

2012

J Stat Phys

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Section: Comparison With Galerkin Approximationmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hydrodynamic Fluctuations in Laminar Fluid Flow. II. Fluctuating Squire Equation

Zárate

Sengers

2012

J Stat Phys

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“…The UCs would also depend on the particular NESS. For example, correlations are much stronger and longer range in the case of a fluid with a temperature gradient than in a fluid with a velocity gradient or shear [53,54]. In principle the NE work properties might also depend on the particular thermodynamic path.…”

Section: To Obtain Eq(42) We Usedmentioning

confidence: 99%

Work, work fluctuations, and the work distribution in a thermal nonequilibrium steady state

Kirkpatrick¹,

Dorfman²,

Sengers³

2016

Phys. Rev. E

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Long-ranged correlations generically exist in non-equilibrium fluid systems. In the case of a nonequilibrium steady state caused by a temperature gradient the correlations are especially long-ranged and strong. The anomalous light scattering predicted to exist in these systems is well-confirmed by numerous experiments. Recently the Casimir force or pressure due to these fluctuations or correlations have been discussed in great detail. In this paper the notion of a Casimir work is introduced and a novel way to measure the non-equilibrium Casimir force is suggested. In particular, the non-equilibrium Casimir force is related to a non-equilibrium heat and not, as in equilibrium, to a volume derivative of an average energy. The non-equilibrium work fluctuations are determined and shown to be very anomalous compared to equilibrium work fluctuations. The non-equilibrium work distribution is also computed, and contrasted to work distributions in systems with shortrange correlations. Again, there is a striking difference in the two cases. Formal theories of work and work distributions in non-equilibrium steady states are not explicit enough to illustrate any of these interesting features.

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“…(20), the autocorrelation function of velocity fluctuations is related to the kinetic energy of fluctuations [35][36][37]. The auto-correlation of transverse component, namely.…”

mentioning

confidence: 99%

Rheology modulated non-equilibrium fluctuations in time-dependent diffusion processes

Maity¹,

Bandopadhyay²,

Chakraborty³

2016

Physica A: Statistical Mechanics and its Applications

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HIGHLIGHTS· The auto-correlation function (static and dynamic structure factor) of concentration fluctuations is determined for viscoelastic fluids · The transverse component of velocity fluctuations which influences Rayleigh spectrum is obtained for viscoelastic fluids · Criteria for the appearance of peaks at non-zero frequency for the case of dynamic structure factor is obtained for viscoelastic fluids · Contrary to the equilibrium scenario the non-equilibrium Rayleigh line is influenced by viscoelastic effects KEYWORDSFluctuating Hydrodynamics; Rheology; Diffusion; Rayleigh spectrum ABSTRACTThe effect of non-Newtonian rheology, manifested through a viscoelastic linearized Maxwell model, on the time-dependent non-equilibrium concentration fluctuations due to free diffusion as well as thermal diffusion of a species is analyzed theoretically. Contrary to the belief that nonequilibrium Rayleigh line is not influenced by viscoelastic effects, through rigorous calculations, we put forward the fact that viscoelastic effects do influence the non-equilibrium Rayleigh line, while the effects are absent for the equilibrium scenario. The non-equilibrium process is quantified through the concentration fluctuation auto-correlation function, also known as the structure factor. The analysis reveals that the effect of rheology is prominent for both the cases of free diffusion and thermal diffusion at long times, where the influence of rheology dictates not only the location of the peaks in concentration dynamic structure factors, but also the magnitudes; such peaks in dynamic structure factors are absent in the case of Newtonian fluid. At smaller times, for the case of free diffusion, presence of time-dependent peak(s) are observed, which are weakly dependent on the influence of rheology, a phenomenon which is absent in the 2 case of thermal diffusion. Different regimes of the frequency dependent overall dynamic structure factor, depending on the interplay of the fluid relaxation time and momentum diffusivity, are evaluated. The static structure factor is not affected to a great extent for the case of free-diffusion and is unaffected for the case of thermal diffusion.

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Velocity fluctuations in laminar fluid flow

Cited by 10 publications

References 35 publications

Hydrodynamic Fluctuations in Laminar Fluid Flow. II. Fluctuating Squire Equation

Hydrodynamic Fluctuations in Laminar Fluid Flow. II. Fluctuating Squire Equation

Work, work fluctuations, and the work distribution in a thermal nonequilibrium steady state

Rheology modulated non-equilibrium fluctuations in time-dependent diffusion processes

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