scholarly journals Stochastic modelling and diffusion modes for proper orthogonal decomposition models and small-scale flow analysis

2017 ◽  
Vol 826 ◽  
pp. 888-917 ◽  
Author(s):  
Valentin Resseguier ◽  
Etienne Mémin ◽  
Dominique Heitz ◽  
Bertrand Chapron
Keyword(s):  
Fluid Flow ◽  
Velocity Component ◽  
Large Scale ◽  
Stochastic Modelling ◽  
Wake Flow ◽  
Small Scale ◽  
Cylinder Wake ◽  
Diffusion Term ◽  
Advection Term ◽  
Dimensional Models

We present here a new stochastic modelling approach in the constitution of fluid flow reduced-order models. This framework introduces a spatially inhomogeneous random field to represent the unresolved small-scale velocity component. Such a decomposition of the velocity in terms of a smooth large-scale velocity component and a rough, highly oscillating component gives rise, without any supplementary assumption, to a large-scale flow dynamics that includes a modified advection term together with an inhomogeneous diffusion term. Both of those terms, related respectively to turbophoresis and mixing effects, depend on the variance of the unresolved small-scale velocity component. They bring an explicit subgrid term to the reduced system which enables us to take into account the action of the truncated modes. Besides, a decomposition of the variance tensor in terms of diffusion modes provides a meaningful statistical representation of the stationary or non-stationary structuration of the small-scale velocity and of its action on the resolved modes. This supplies a useful tool for turbulent fluid flow data analysis. We apply this methodology to circular cylinder wake flow at Reynolds numbers $Re=100$ and $Re=3900$. The finite-dimensional models of the wake flows reveal the energy and the anisotropy distributions of the small-scale diffusion modes. These distributions identify critical regions where corrective advection effects, as well as structured energy dissipation effects, take place. In providing rigorously derived subgrid terms, the proposed approach yields accurate and robust temporal reconstruction of the low-dimensional models.

scholarly journals Reply to “Comments on ‘Incorporating the Effects of Moisture into a Dynamical Parameter: Moist Vorticity and Moist Divergence’”

2016 ◽  
Vol 31 (4) ◽  
pp. 1397-1405
Author(s):  
Weihong Qian ◽  
Ning Jiang ◽  
Jun Du
Keyword(s):  
Large Scale ◽  
Value Added ◽  
Heavy Rain ◽  
Heavy Precipitation ◽  
Small Scale ◽  
Precipitation Efficiency ◽  
Long Duration ◽  
Advection Term ◽  
Rain Events ◽  
Mathematical Derivation

Abstract Mathematical derivation, meteorological justification, and comparison to model direct precipitation forecasts are the three main concerns recently raised by Schultz and Spengler about moist divergence (MD) and moist vorticity (MV), which were introduced in earlier work by Qian et al. That previous work demonstrated that MD (MV) can in principle be derived mathematically with a value-added empirical modification. MD (MV) has a solid meteorological basis. It combines ascent motion and high moisture: the two elements necessary for rainfall. However, precipitation efficiency is not considered in MD (MV). Given the omission of an advection term in the mathematical derivation and the lack of precipitation efficiency, MD (MV) might be suitable mainly for heavy rain events with large areal coverage and long duration caused by large-scale quasi-stationary weather systems, but not for local intense heavy rain events caused by small-scale convection. In addition, MD (MV) is not capable of describing precipitation intensity. MD (MV) worked reasonably well in predicting heavy rain locations from short to medium ranges as compared with the ECMWF model precipitation forecasts. MD (MV) was generally worse than (though sometimes similar to) the model heavy rain forecast at shorter ranges (about a week) but became comparable or even better at longer ranges (around 10 days). It should be reiterated that MD (MV) is not intended to be a primary tool for predicting heavy rain areas, especially in the short range, but is a useful parameter for calibrating model heavy precipitation forecasts, as stated in the original paper.

scholarly journals Interaction between Crustal-Scale Darcy and Hydrofracture Fluid Transport: A Numerical Study

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Tamara de Riese ◽  
Paul D. Bons ◽  
Enrique Gomez-Rivas ◽  
Till Sachau
Keyword(s):  
Fluid Flow ◽  
Numerical Model ◽  
Transport Mechanism ◽  
Large Scale ◽  
Fluid Transport ◽  
Numerical Study ◽  
Ballistic Transport ◽  
Accretionary Prism ◽  
Small Scale ◽  
Porous Flow

Crustal-scale fluid flow can be regarded as a bimodal transport mechanism. At low hydraulic head gradients, fluid flow through rock porosity is slow and can be described as diffusional. Structures such as hydraulic breccias and hydrothermal veins both form when fluid velocities and pressures are high, which can be achieved by localized fluid transport in space and time, via hydrofractures. Hydrofracture propagation and simultaneous fluid flow can be regarded as a “ballistic” transport mechanism, which is activated when transport by diffusion alone is insufficient to release the local fluid overpressure. The activation of a ballistic system locally reduces the driving force, through allowing the escape of fluid. We use a numerical model to investigate the properties of the two transport modes in general and the transition between them in particular. We developed a numerical model in order to study patterns that result from bimodal transport. When hydrofractures are activated due to low permeability relative to fluid flux, many hydrofractures form that do not extend through the whole system. These abundant hydrofractures follow a power-law size distribution. A Hurst factor of ~0.9 indicates that the system self-organizes. The abundant small-scale hydrofractures organize the formation of large-scale hydrofractures that ascend through the whole system and drain fluids in large bursts. As the relative contribution of porous flow increases, escaping fluid bursts become less frequent, but more regular in time and larger in volume. We propose that metamorphic rocks with abundant veins, such as in the Kodiak accretionary prism (Alaska) and Otago schists (New Zealand), represent regions with abundant hydrofractures near the fluid source, while hydrothermal breccias are formed by the large fluid bursts that can ascend the crust to shallower levels.

WAVELET MULTI-RESOLUTION ANALYSIS ON LARGE-EDDY SIMULATION OF TURBURLENT FLOW BEHIND A VEHICLE EXERNAL MIRROR

2013 ◽  
Vol 11 (04) ◽  
pp. 1360007 ◽  
Author(s):  
A. RINOSHIKA ◽  
Y. ZHENG ◽  
E. SHISHIDO
Keyword(s):  
Large Eddy Simulation ◽  
Large Scale ◽  
Three Dimensional ◽  
Wake Flow ◽  
Small Scale ◽  
Three Dimensional Flow ◽  
Eddy Simulation ◽  
Multi Resolution Analysis ◽  
Large Eddy ◽  
Resolution Analysis

The three-dimensional orthogonal wavelet multi-resolution technique was applied to analyze flow structures of various scales around an externally mounted vehicle mirror. Firstly, the three-dimensional flow of mirror wake was numerically analyzed at a Reynolds number of 105 by using the large-eddy simulation (LES). Then the instantaneous velocity and vorticity were decomposed into the large-, intermediate- and relatively small-scale components by the wavelet multi-resolution technique. It was found that a three-dimensional large-scale vertical vortex dominates the mirror wake flow and makes a main contribution to vorticity concentration. Some intermediate- and relatively small-scale vortices were extracted from the LES and were clearly identifiable.

Three-dimensional wavelet analysis on turbulent structure of dune wake flow

2015 ◽  
Vol 13 (06) ◽  
pp. 1550045 ◽  
Author(s):  
Yan Zheng ◽  
Akira Rinoshika ◽  
Shun Fujimoto
Keyword(s):  
Coherent Structure ◽  
Large Scale ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Turbulent Structure ◽  
Wake Flow ◽  
Small Scale ◽  
Intermediate Scale ◽  
Numerical Result ◽  
Scale Structures

The three-dimensional (3D) turbulent structure was simulated by large eddy simulation (LES), and then the numerical result was validated by PIV experiment. In order to give a detailed description of dune wake flow, the instantaneous velocity, vorticity, and pressure were decomposed into the large-, intermediate- and relatively small-scale components by 3D wavelet multi-resolution technique. To get a further understanding of coherent structure, the decomposed wavelet components were employed to calculate Q-criterion. It was found that the rollers and horse-shoe structures in the separation bubble were mainly contributed from large-scale structures and it made the most significance to the vorticity concentration. The observations of intermediate-scale horse-shoe structures indicated that the coherent structure was the combined effect of large- and intermediate-scale structures. Besides, from the visualization of 3D streamlines and pressure iso-surfaces, the separation bubble and pressure distribution are found to be dominated by large-scale structure.

scholarly journals Energy separation in transient and steady-state flow across the cylinder

2018 ◽  
Vol 45 (1) ◽  
pp. 83-94
Author(s):  
Jela Burazer
Keyword(s):  
Fluid Flow ◽  
Steady State ◽  
Energy Equation ◽  
Wake Flow ◽  
Energy Separation ◽  
Cylinder Wake ◽  
Flow Conditions ◽  
Steady State Flow ◽  
State Flow ◽  
Transient And Steady State

Energy separation is a spontaneous energy redistribution within a fluid flow. As a consequence, there are places with higher and lower values of total temperature in the fluid flow. It is characteristic for many flow geometries. This paper deals with the energy separation in a cylinder wake. Two flow conditions are being considered-transient and steady-state flow in the wake. Two different solvers from the open source package OpenFOAM are used in order to capture the phenomenon of energy separation. One of these solvers is modified for the purpose of calculation in a particular case of the vortex street flow. The energy equation based on the internal energy present in this solver is replaced by the energy equation written in the form of a total enthalpy. The other solver has been previously tested in the vortex tube flow, and can also capture the energy separation in the steady-state wake flow of the cylinder. In both cylinder wake flow conditions, a two-dimensional computational domain is used. Standard ?? ? ?? model is used for computations. It is proved that OpenFOAM is capable of capturing the energy separation phenomenon in a proper way in both of the wake flow cases. Good agreement between the experimental results and the ones from computations is obtained in the case of steady-state flow in the wake. Previous research findings are also confirmed in the case of vortex street flow.

scholarly journals An investigation into the controls on fracture tortuosity in rock sequences and the impact on fluid flow in the upper crust

2020 ◽  
Author(s):  
Nathaniel Forbes Inskip ◽  
Tomos Phillips ◽  
Kevin Bisdom ◽  
Georgy Borisochev ◽  
Andreas Busch ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Large Scale ◽  
Small Scale ◽  
Fine Scale ◽  
Geothermal Systems ◽  
Parallel Plates ◽  
Core Flooding ◽  
Fracture Surfaces ◽  
Fracture Orientation ◽  
The Impact

<p>Fractures are ubiquitous in geological sequences, and play an important role in the movement of fluids in the earth’s crust, particularly in fields such as hydrogeology, petroleum geology and volcanology. When predicting or analysing fluid flow, fractures are often simplified as a set of smooth parallel plates. In reality, they exhibit tortuosity on a number of scales: Fine-scale tortuosity, or roughness, is the product of the small-scale (µm – mm) irregularities in the fracture surface, whereas large-scale (> mm) tortuosity occurs as a result of anisotropy and heterogeneity within the host formation that leads to the formation of irregularities in the fracture surfaces. It is important to consider such tortuosity when analysing processes that rely on the movement (or hindrance) of fluids flowing through fractures in the subsurface. Such processes include fluid injection into granitic plutons for the extraction of heat in Engineered Geothermal Systems, or the injection of CO<sub>2</sub> into reservoirs overlain by fine-grained mudrocks acting as seals in Carbon Capture and Storage projects.</p><p>Although it is generally assumed that tortuosity is controlled by factors such as grain size, mineralogy and fracture mode, a systematic study of how these factors quantitatively affect tortuosity is currently lacking. Furthermore, in anisotropic rocks the fracture orientation with respect to any inherent anisotropy is also likely to affect tortuosity.</p><p>In order to address this gap, we have induced fractures in a selection of different rock types (mudrocks, sandstones and carbonates) using the Brazil disk method, and imaged the fracture surfaces using both a digital optical microscope and X-ray Computed Tomography. Using these methods we are able to characterise both the fine-scale (roughness) and large-scale tortuosity. In order to understand the effect of fracture orientation on tortuosity we have also analysed fractures induced at different angles to bedding in samples of a highly anisotropic mudrock taken from South Wales, UK. Results indicate that fine-scale tortuosity is highly dependent on the fracture orientation with regards to the bedding plane, with fractures normal to bedding being rougher than those induced parallel to bedding. Finally, in order to measure the effect of tortuosity on fluid flow, we have carried out a series of core flooding experiments on a subset of fractured samples showing that fracture transmissivity decreases with increasing tortuosity.</p>

Transport equations for the normalized nth-order moments of velocity derivatives in grid turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
S.L. Tang ◽  
R.A. Antonia ◽  
L. Djenidi
Keyword(s):  
Large Scale ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Transport Equations ◽  
Small Scale ◽  
Grid Turbulence ◽  
Mean Velocity ◽  
Local Isotropy ◽  
Advection Term ◽  
The Mean

Transport equations for the normalized moments of the longitudinal velocity derivative ${F_{n + 1}}$ (here, $n$ is $1, 2, 3\ldots$ ) are derived from the Navier–Stokes (N–S) equations for shearless grid turbulence. The effect of the (large-scale) streamwise advection of ${F_{n + 1}}$ by the mean velocity on the normalized moments of the velocity derivatives can be expressed as $C_1 {F_{n + 1}}/Re_\lambda$ , where $C_1$ is a constant and $Re_\lambda$ is the Taylor microscale Reynolds number. Transport equations for the normalized odd moments of the transverse velocity derivatives ${F_{y,n + 1}}$ (here, $n$ is 2, 4, 6), which should be zero if local isotropy is satisfied, are also derived and discussed in sheared and shearless grid turbulence. The effect of the (large-scale) streamwise advection term on the normalized moments of the velocity derivatives can also be expressed in the form $C_2 {F_{y,n + 1}}/Re_\lambda$ , where $C_2$ is a constant. Finally, the contribution of the mean shear in the transport equation for ${F_{n + 1}}$ can be modelled as $15 B/Re_\lambda$ , where $B$ ( $=S^*{S_{s,n + 1}}$ ) is the product of the non-dimensional shear parameter $S^*$ and the normalized mixed longitudinal-transverse velocity derivatives ${{S_{s,n + 1}}}$ ; if local isotropy is satisfied, $S_{s,n + 1}$ should be zero. These results indicate that if ${F_{n + 1}}$ , ${F_{y,n + 1}}$ and $B$ do not increase as rapidly as $Re_\lambda$ , then the effect of the large-scale structures on small-scale turbulence will disappear when $Re_\lambda$ becomes sufficiently large.

scholarly journals Stochastic Modelling of Small-Scale Perturbation

Water ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2950
Author(s):  
Franco Flandoli ◽  
Umberto Pappalettera
Keyword(s):  
Large Scale ◽  
Stochastic Modelling ◽  
Small Scale ◽  
Reduction Procedure ◽  
Full Generality ◽  
Scale Perturbation ◽  
Stratonovich Noise ◽  
Scale Structures ◽  
Small Scale Structures ◽  
Transport Type

In this paper we propose a stochastic model reduction procedure for deterministic equations from geophysical fluid dynamics. Once large-scale and small-scale components of the dynamics have been identified, our method consists in modelling stochastically the small scales and, as a result, we obtain that a transport-type Stratonovich noise is sufficient to model the influence of the small scale structures on the large scales ones. This work aims to contribute to motivate the use of stochastic models in fluid mechanics and identifies examples of noise of interest for the reduction of complexity of the interaction between scales. The ideas are presented in full generality and applied to specific examples in the last section.

Contribution of Fluctuating Large-Scale Motions in Turbulent Fluid Flow Through a Channel

2019 ◽  
Author(s):  
Yoichi Mito
Keyword(s):  
Fluid Flow ◽  
Large Scale ◽  
Wall Turbulence ◽  
Small Scale ◽  
Large Contribution ◽  
Turbulent Fluid Flow ◽  
Turbulent Fluid ◽  
Fluid Turbulence ◽  
Turbulence Structures ◽  
Flow Through

Abstract The key mechanism that sustains fluid turbulence flowing through a channel is examined using the Lagrangian experiment, done in a direct numerical simulation (DNS) of the turbulent fluid flow and that being damped by addition of a small amount of small particles. The results indicate large contribution of the fluctuations of large-scale fluid motions, which are seen as their multi-directionality and multi-dimensionality, to sustenance of wall turbulence. Small-scale fluid turbulence structures, such as vortices and packets of them, are seen to induce the fluctuations of large-scale fluid motions.

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