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

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

doi:10.1007/s10955-012-0495-9

Cited by 9 publications

(11 citation statements)

References 34 publications

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“…Thus, in the Fourier-space representation, the correlations are independent of the wave vector k. However, as is evident from Eqs. (17) and (18), the nonequilibrium contribution ij to the correlations in shear flow depends on the magnitude as well as the direction of the wave vector, thereby rendering the fluctuations spatially correlated and anisotropic. Figure 1 displays the nonequilibrium contributions of the longitudinal (e (1) direction) and transverse (e (2) direction) velocity correlations for a wave vector in the flow-gradient plane pointing at an angle 45…”

Section: Velocity Fluctuationsmentioning

confidence: 99%

“…(17). Figure 4 shows a comparison of the MPC simulation results for the density correlations and the numerically evaluated theoretical expression (29).…”

Section: Density Correlationsmentioning

confidence: 99%

“…The long-range nature of the correlations may also manifest as nonintensivity of the nonequilibrium contribution to pressure [9]. Moreover, the spatial correlations imply that the long-wavelength components of the fluctuations are strongly affected by the presence of confining walls [10,11,16,17].…”

Section: Introductionmentioning

confidence: 99%

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Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study

2017

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Hydrodynamic fluctuations in simple fluids under shear flow are demonstrated to be spatially correlated, in contrast to the fluctuations at equilibrium, using mesoscopic hydrodynamic simulations. The simulation results for the equal-time hydrodynamic correlations in a multiparticle collision dynamics (MPC) fluid in shear flow are compared with the explicit expressions obtained from fluctuating hydrodynamics calculations. For large wave vectors k, the nonequilibrium contributions to transverse and longitudinal velocity correlations decay as k −4 for wave vectors along the flow direction and as k −2 for the off-flow directions. For small wave vectors, a crossover to a slower decay occurs, indicating long-range correlations in real space. The coupling between the transverse velocity components, which vanishes at equilibrium, also exhibits a k −2 dependence on the wave vector. In addition, we observe a quadratic dependency on the shear rate of the nonequilibrium contribution to pressure.

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Section: Velocity Fluctuationsmentioning

confidence: 99%

“…(17). Figure 4 shows a comparison of the MPC simulation results for the density correlations and the numerically evaluated theoretical expression (29).…”

Section: Density Correlationsmentioning

confidence: 99%

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Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study

2017

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“…A very interesting problem arises when the flows are studied in the presence of noise, [32][33][34][35][36]. As shown for a simple model in Ref.…”

Section: Linear Approachesmentioning

confidence: 99%

Transition to turbulence in shear flows

Eckhardt

2018

Physica A: Statistical Mechanics and its Applications

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Pipe flow and many other shear flows show a transition to turbulence at flow rates for which the laminar profile is stable against infinitesimal perturbations. In this brief review the recent progress in the understanding of this transition will be summarized, with a focus on the linear and nonlinear states that drive the transitions, the extended and localized patterns that appear, and on the spatio-temporal dynamics and their relation to directed percolation.

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“…At nonequilibrium, the equal-time correlations of fluctuations are typically long-ranged [27] and we do not wish to introduce any extra complexities due to the boundary effects from the wall [60]. Therefore, we focus on the bulk behavior of the fluid in a periodic system, which also corresponds to the condition of the theory in Section 2.…”

Section: Boundary Conditionsmentioning

confidence: 99%

Analytical and Computational Studies of Correlations of Hydrodynamic Fluctuations in Shear Flow

Bian¹,

Deng²,

Karniadakis³

2018

CICP

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We study correlations of hydrodynamic fluctuations in shear flow analytically and also by dissipative particle dynamics (DPD) simulations. The hydrodynamic equations are linearized around the macroscopic velocity field and then solved by a perturbation method in Fourier-transformed space. The autocorrelation functions (ACFs) from the analytical method are compared with results obtained from DPD simulations under the same shear-flow conditions. Upto a moderate shear rate, various ACFs from the two approaches agree with each other well. At large shear rates, discrepancies between the two methods are observed, hence revealing strong additional coupling between different fluctuating variables, which is not considered in the analytical approach. In addition, the results at low and moderate shear rates can serve as benchmarks for developing multiscale algorithms for coupling of heterogeneous solvers, such as a hybrid simulation of molecular dynamics and fluctuating hydrodynamics solver, where thermal fluctuations are indispensable.

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

Cited by 9 publications

References 34 publications

Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study

Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study

Transition to turbulence in shear flows

Analytical and Computational Studies of Correlations of Hydrodynamic Fluctuations in Shear Flow

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