Second-order velocity structure functions in direct numerical simulations of turbulence with Rλ up to 2250

2020 ◽  
Vol 5 (10) ◽  
Author(s):  
Takashi Ishihara ◽  
Yukio Kaneda ◽  
Koji Morishita ◽  
Mitsuo Yokokawa ◽  
Atsuya Uno
Keyword(s):  
Numerical Simulations ◽  
Velocity Structure ◽  
Structure Functions ◽  
Second Order ◽  
Direct Numerical Simulations

scholarly journals Can We Detect Submesoscale Motions in Drifter Pair Dispersion?

2019 ◽  
Vol 49 (9) ◽  
pp. 2237-2254 ◽  
Author(s):  
Sebastian Essink ◽  
Verena Hormann ◽  
Luca R. Centurioni ◽  
Amala Mahadevan
Keyword(s):  
Bay Of Bengal ◽  
Velocity Structure ◽  
Mesoscale Eddies ◽  
Structure Functions ◽  
Second Order ◽  
Helmholtz Decomposition ◽  
Impact Structure ◽  
Inertial Oscillations ◽  
Geostrophic Velocity ◽  
Local Dispersion

AbstractA cluster of 45 drifters deployed in the Bay of Bengal is tracked for a period of four months. Pair dispersion statistics, from observed drifter trajectories and simulated trajectories based on surface geostrophic velocity, are analyzed as a function of drifter separation and time. Pair dispersion suggests nonlocal dynamics at submesoscales of 1–20 km, likely controlled by the energetic mesoscale eddies present during the observations. Second-order velocity structure functions and their Helmholtz decomposition, however, suggest local dispersion and divergent horizontal flow at scales below 20 km. This inconsistency cannot be explained by inertial oscillations alone, as has been reported in recent studies, and is likely related to other nondispersive processes that impact structure functions but do not enter pair dispersion statistics. At scales comparable to the deformation radius LD, which is approximately 60 km, we find dynamics in agreement with Richardson’s law and observe local dispersion in both pair dispersion statistics and second-order velocity structure functions.

Reynolds number dependence of second-order velocity structure functions

2000 ◽  
Vol 12 (11) ◽  
pp. 3000 ◽  
Author(s):  
R. A. Antonia ◽  
B. R. Pearson ◽  
T. Zhou
Keyword(s):  
Reynolds Number ◽  
Velocity Structure ◽  
Structure Functions ◽  
Second Order ◽  
Reynolds Number Dependence

scholarly journals Exact second-order structure-function relationships

2002 ◽  
Vol 468 ◽  
pp. 317-326 ◽  
Author(s):  
REGINALD J. HILL
Keyword(s):  
Structure Function ◽  
Scaling Laws ◽  
Velocity Structure ◽  
Structure Functions ◽  
Energy Dissipation Rate ◽  
Second Order ◽  
Order Structure ◽  
Third Order ◽  
Navier Stokes Equation ◽  
Local Isotropy

Equations that follow from the Navier–Stokes equation and incompressibility but with no other approximations are ‘exact’. Exact equations relating second- and third- order structure functions are studied, as is an exact incompressibility condition on the second-order velocity structure function. Opportunities for investigations using these equations are discussed. Precisely defined averaging operations are required to obtain exact averaged equations. Ensemble, temporal and spatial averages are all considered because they produce different statistical equations and because they apply to theoretical purposes, experiment and numerical simulation of turbulence. Particularly simple exact equations are obtained for the following cases: (i) the trace of the structure functions, (ii) DNS that has periodic boundary conditions, and (iii) an average over a sphere in r-space. Case (iii) introduces the average over orientations of r into the structure-function equations. The energy dissipation rate ε appears in the exact trace equation without averaging, whereas in previous formulations ε appears after averaging and use of local isotropy. The trace mitigates the effect of anisotropy in the equations, thereby revealing that the trace of the third-order structure function is expected to be superior for quantifying asymptotic scaling laws. The orientation average has the same property.

scholarly journals Gas-Solid Heat Transfer Computation from Particle-Resolved Direct Numerical Simulations

Fluids ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 15
Author(s):  
Mohamed-Amine Chadil ◽  
Stéphane Vincent ◽  
Jean-Luc Estivalèzes
Keyword(s):  
Heat Transfer ◽  
Numerical Simulations ◽  
Penalty Method ◽  
Accurate Estimate ◽  
Second Order ◽  
High Order ◽  
Direct Numerical Simulations ◽  
Transfer Coefficients ◽  
Carrier Fluid ◽  
Heat Transfer Coefficients

Particle-Resolved simulations (PR-DNS) have been conducted using a second order implicit Viscous Penalty Method (VPM) to study the heat transfer between a set of particles and an incompressible carrier fluid. A Lagrange extrapolation coupled to a Taylor interpolation of a high order is utilized to the accurate estimate of heat transfer coefficients on an isolated sphere, a fixed Faced-Centered Cubic array of spheres, and a random pack of spheres. The simulated heat transfer coefficients are compared with success to various existing Nusselt laws of the literature.

Anisotropic statistics of Lagrangian structure functions and Helmholtz decomposition

2021 ◽  
Author(s):  
Han Wang ◽  
Oliver Bühler
Keyword(s):  
Velocity Structure ◽  
Synthetic Data ◽  
Structure Functions ◽  
Second Order ◽  
New Method ◽  
Helmholtz Decomposition ◽  
Data Sets ◽  
Geostrophic Balance ◽  
Surface Drifter ◽  
Rotational Components

<p>Second-order velocity structure functions are commonly estimated from Lagrangian tracer trajectories.  A Helmholtz decomposition of these structure functions, which separates their divergent and rotational components, can indicate the robustness of geostrophic balance at different scales, and serves as a building block for analysis of scale-dependent energy distributions. We present a new method to estimate second-order horizontal velocity structure functions, as well as their Helmholtz decomposition, from sparse data collected by Lagrangian observations.   The novelty compared to existing methods is that we allow for anisotropic statistics in the velocity field as well as in the distribution of the Lagrangian trackers. We conduct the analysis through the lens of azimuthal Fourier expansions, and find Helmholtz decomposition formulae targeted at individual Fourier modes. We also identify an improved statistical angle-weighting technique that generally increases the accuracy of structure function estimations in the presence of anisotropy. The new methods are tested against synthetic data and applied to surface drifter data sets such as LASER and GLAD. Importantly, the new method does not require extra measurements compared to existing methods based on isotropy.</p>

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