Characteristics of the leading Lyapunov vector in a turbulent channel flow

2018 ◽  
Vol 849 ◽  
pp. 942-967 ◽  
Author(s):  
Nikolay Nikitin
Keyword(s):  
Turbulent Flow ◽  
Buffer Layer ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Spatial Scales ◽  
Plane Channel ◽  
Base Flow ◽  
Lyapunov Vector ◽  
Perturbation Growth ◽  
Near Wall

The values of the highest Lyapunov exponent (HLE)$\unicode[STIX]{x1D706}_{1}$for turbulent flow in a plane channel at Reynolds numbers up to$Re_{\unicode[STIX]{x1D70F}}=586$are determined. The instantaneous and statistical properties of the corresponding leading Lyapunov vector (LLV) are investigated. The LLV is calculated by numerical solution of the Navier–Stokes equations linearized about the non-stationary base solution corresponding to the developed turbulent flow. The base turbulent flow is calculated in parallel with the calculation of the evolution of the perturbations. For arbitrary initial conditions, the regime of exponential growth${\sim}\exp (\unicode[STIX]{x1D706}_{1}t)$which corresponds to the approaching of the perturbation to the LLV is achieved already at$t^{+}<50$. It is found that the HLE increases with increasing Reynolds number from$\unicode[STIX]{x1D706}_{1}^{+}\approx 0.021$at$Re_{\unicode[STIX]{x1D70F}}=180$to$\unicode[STIX]{x1D706}_{1}^{+}\approx 0.026$at$Re_{\unicode[STIX]{x1D70F}}=586$. The LLV structures are concentrated mainly in a region of the buffer layer and are manifested in the form of spots of increased fluctuation intensity localized both in time and space. The root-mean-square (r.m.s.) profiles of the velocity and vorticity intensities in the LLV are qualitatively close to the corresponding profiles in the base flow with artificially removed near-wall streaks. The difference is the larger concentration of LLV perturbations in the vicinity of the buffer layer and a relatively larger (by approximately 80 %) amplitude of the vorticity pulsations. Based on the energy spectra of velocity and vorticity pulsations, the integral spatial scales of the LLV structures are determined. It is found that LLV structures are on average twice narrower and twice shorter than the corresponding structures of the base flow. The contribution of each of the terms entering into the expression for the production of the perturbation kinetic energy is determined. It is shown that the process of perturbation development is essentially dictated by the inhomogeneity of the base flow, as well as by the presence of transversal motion in it. Neglecting of these factors leads to a significant underestimation of the perturbation growth rate. The presence of near-wall streaks in the base flow, on the contrary, does not play a significant role in the development of the LLV perturbations. Artificial removal of streaks from the base flow does not change the character of the perturbation growth.

A Functional Scaling Relationship for Laminar to Turbulent Flow Regimes

2011 ◽  
Author(s):  
George Papadopoulos
Keyword(s):  
Turbulent Flow ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Flow Characteristics ◽  
Flow Region ◽  
Flow Regimes ◽  
Transitional Flow ◽  
Turbulent Regime ◽  
Flow Profile ◽  
Scaling Relationship

A dimensional analysis that is based on the scaling of the two-dimensional Navier-Stokes equations is presented for correlating bulk flow characteristics arising from a variety of initial conditions. The analysis yields a functional relationship between the characteristic variable of the flow region and the Reynolds number for each of the two independent flow regimes. A linear relationship is realized for the laminar regime, while a nonlinear relationship is realized for the turbulent regime. Both relationships incorporate mass-flow profile characteristics to fully capture the effects of initial conditions on the variation of the characteristic variables. The union of these two independent relationships is formed utilizing the concept of flow intermittency to further expand into a generic scaling relationship that incorporates transitional flow effects to fully encompass solutions spanning the laminar to turbulent flow regimes. The results of the analysis are discussed within the context of several flow phenomena (e.g. pipe flow, jet flow & separated flow) resulting from various initial and boundary conditions.

Methods to Set Up and Investigate Low Reynolds Number, Fully Developed Turbulent Plane Channel Flows

1998 ◽  
Vol 120 (3) ◽  
pp. 496-503 ◽  
Author(s):  
F. Durst ◽  
M. Fischer ◽  
J. Jovanovic´ ◽  
H. Kikura
Keyword(s):  
Reynolds Number ◽  
Initial Conditions ◽  
Control Volume ◽  
Low Reynolds Number ◽  
Plane Channel ◽  
Finite Size ◽  
Wall Region ◽  
Turbulent Plane ◽  
Low Reynolds ◽  
Near Wall

The tripping of fully developed turbulent plane channel flow was studied at low Reynolds number, yielding unique flow properties independent of the initial conditions. The LDA measuring technique was used to obtain reliable mean velocities, rms values of turbulent velocity fluctuations and skewness and flatness factors over the entire cross-section with emphasis on the near-wall region. The experimental results were compared with the data obtained from direct numerical simulations available in the literature. The analysis of the data indicates the important role of the upstream conditions on the flow development. It is shown that the fully developed turbulent state at low Reynolds number can be reached only by significant tripping of the flow at the inlet of the channel. Effects related to the finite size of the LDA measuring control volume and an inaccuracy in the estimation of the wall shear stress from near-wall velocity measurements are discussed in detail since these can yield systematic discrepancies between the measured and simulated results.

Turbulent flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Turbulent Flow ◽  
Stokes Equations ◽  
Turbulent Shear ◽  
Complex Nature ◽  
Time Averaging ◽  
Surface Shear Stress ◽  
Law Of The Wall ◽  
Wide Range ◽  
Log Law ◽  
Near Wall

In this chapter the principal characteristics of a turbulent flow are outlined and the way that Reynolds’ time-averaging procedure, applied to the Navier-Stokes equations, leads to a set of equations (RANS) similar to those governing laminar flow but including additional terms which arise from correlations between fluctuating velocity components and velocity-pressure correlations. The complex nature of turbulent motion has led to an empirical methodology based upon the RANS and turbulence-transport equations in which the correlations are modelled. An important aspect of turbulent flows is the wide range of scales involved. It is also shown that treating near-wall turbulent shear flow as a Couette flow leads to the Law of the Wall and the log law. The effect of surface roughness on both the velocity distribution and surface shear stress is discussed. It is shown that the distribution of mean velocity within a turbulent boundary layer can be represented by a linear combination of the near-wall log law and an outer-layer Law of the Wake.

Free-stream coherent structures in growing boundary layers: a link to near-wall streaks

2015 ◽  
Vol 778 ◽  
pp. 451-484 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Base Flow ◽  
Interaction Problem ◽  
Near Wall

In a recent paper, Deguchi & Hall (J. Fluid Mech., vol. 752, 2014a, pp. 602–625) described a new kind of exact coherent structure which sits at the edge of an asymptotic suction boundary layer at high values of the Reynolds number $Re$. At a distance $\ln Re$ from the wall, the structure is driven by the fully nonlinear interaction of tiny rolls, waves and streaks convected downstream at almost the free-stream speed. The interaction problem satisfies the unit-Reynolds-number three-dimensional Navier–Stokes equations and is localized in a layer of the same depth as the unperturbed boundary layer. Here, we show that the interaction problem is generic to any boundary layer that approaches its free-stream form through an exponentially small correction. It is shown that away from the layer where it is generated the induced roll–streak flow is dominated by non-parallel effects which now play a major role in the streamwise evolution of the structure. The similarity with the parallel boundary layer case is restricted only to the layer where it is generated. It is shown that non-parallel effects cause the structure to persist only over intervals of finite length in any growing boundary layer and lead to a flow structure reminiscent of turbulent boundary layer simulations. The results found shed light on a possible mechanism to couple near-wall streaks with coherent structures located towards the edge of a turbulent boundary layer. Some discussion of how the mechanism adapts to a three-dimensional base flow is given.

The structure of turbulent boundary layers in the wall region of plane channel flow

2006 ◽  
Vol 463 (2078) ◽  
pp. 593-612 ◽  
Author(s):  
Giancarlo Alfonsi ◽  
Leonardo Primavera
Keyword(s):  
Velocity Field ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Plane Channel ◽  
Navier Stokes ◽  
Wall Region ◽  
Navier Stokes Equations ◽  
Plane Channel Flow ◽  
Proper Orthogonal

The flow of a viscous incompressible fluid in a plane channel is simulated numerically with the use of a computational code for the numerical integration of the Navier–Stokes equations, based on a mixed spectral-finite difference technique. A turbulent-flow database representing the turbulent statistically steady state of the velocity field through 10 viscous time units is assembled at friction Reynolds number Re τ =180 and the coherent structures of turbulence are extracted from the fluctuating portion of the velocity field using the proper orthogonal decomposition (POD) technique. The temporal evolution of a number of the most energetic POD modes is represented, showing the existence of dominant flow structures elongated in the streamwise direction whose shape is altered owing to the interaction with quasi-streamwise, bean-shaped turbulent-flow modes. This process of interaction is responsible for the gradual disruption of the streamwise modes of the flow.

A Functional Relationship for Modeling Laminar to Turbulent Flow Transitions

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
George Papadopoulos
Keyword(s):  
Turbulent Flow ◽  
Functional Relationship ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Flow Region ◽  
Flow Regimes ◽  
Transitional Flow ◽  
Turbulent Regime ◽  
Flow Profile ◽  
Mean Flow

A dimensional analysis which is based on the scaling of the two-dimensional Navier–Stokes equations is presented for correlating bulk flow characteristics arising from a variety of initial conditions. The analysis yields a functional relationship between the characteristic variable of the flow region and the Reynolds number for each of the two independent flow regimes, laminar and turbulent. A linear relationship is realized for the laminar regime, while a nonlinear relationship is realized for the turbulent regime. Both relationships incorporate mass-flow profile characteristics to capture the effects of initial conditions (mean flow and turbulence) on the variation of the characteristic variable. The union of these two independent relationships is formed leveraging the concept of flow intermittency to yield a generic functional relationship that incorporates transitional flow effects and fully encompasses solutions spanning the laminar to turbulent flow regimes. Empirical models to several common flows are formed to demonstrate the engineering potential of the proposed functional relationship.

scholarly journals On the generation of internal waves by river plumes in subcritical initial conditions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. Mendes ◽  
J. C. B. da Silva ◽  
J. M. Magalhaes ◽  
B. St-Denis ◽  
D. Bourgault ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Internal Waves ◽  
Coastal Waters ◽  
Initial Conditions ◽  
Spatial Scales ◽  
River Plumes ◽  
Wide Range ◽  
Near Shore ◽  
Generation Mechanisms ◽  
Douro River

AbstractInternal waves (IWs) in the ocean span across a wide range of time and spatial scales and are now acknowledged as important sources of turbulence and mixing, with the largest observations having 200 m in amplitude and vertical velocities close to 0.5 m s−1. Their origin is mostly tidal, but an increasing number of non-tidal generation mechanisms have also been observed. For instance, river plumes provide horizontally propagating density fronts, which were observed to generate IWs when transitioning from supercritical to subcritical flow. In this study, satellite imagery and autonomous underwater measurements are combined with numerical modeling to investigate IW generation from an initial subcritical density front originating at the Douro River plume (western Iberian coast). These unprecedented results may have important implications in near-shore dynamics since that suggest that rivers of moderate flow may play an important role in IW generation between fresh riverine and coastal waters.

scholarly journals Heat Transfer in Highly Turbulent Separated Flows: A Review

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1005
Author(s):  
Viktor I. Terekhov
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Separated Flow ◽  
Separated Flows ◽  
Turbulence Characteristic ◽  
Wall Jets ◽  
Average Heat ◽  
Free Stream Turbulence ◽  
External Turbulence ◽  
Near Wall

The study of flows with a high degree of turbulence in boundary layers, near-wall jets, gas curtains, separated flows behind various obstacles, as well as during combustion is of great importance for increasing energy efficiency of the flow around various elements in the ducts of gas-dynamic installations. This paper gives some general characteristics of experimental work on the study of friction and heat transfer on a smooth surface, in near-wall jets, and gas curtains under conditions of increased free-stream turbulence. Taking into account the significant effect of high external turbulence on dynamics and heat transfer of separated flows, a similar effect on the flow behind various obstacles is analyzed. First of all, the classical cases of flow separation behind a single backward-facing step and a rib are considered. Then, more complex cases of the flow around a rib oriented at different angles to the flow are analyzed, as well as a system of ribs and a transverse trench with straight and inclined walls in a turbulent flow around them. The features of separated flow in a turbulized stream around a cylinder, leading to an increase in the width of the vortex wake, frequency of vortex separation, and increase in the average heat transfer coefficient are analyzed. The experimental results of the author are compared with data of other researchers. The structure of separated flow at high turbulence—characteristic dimensions of the separation region, parameters of the mixing layer, and pressure distribution—are compared with the conditions of low-turbulent flow. Much attention is paid to thermal characteristics: temperature profiles across the shear layer, temperature distributions over the surface, and local and average heat transfer coefficients. It is shown that external turbulence has a much stronger effect on the separated flow than on the boundary layer on a flat surface. For separated flows, its intensifying effect on heat transfer is more pronounced behind a rib than behind a step. The factor of heat transfer intensification by external turbulence is most pronounced in the transverse cavity and in the system of ribs.

Numerical simulation of reciprocating turbulent flow in a plane channel

2009 ◽  
Vol 21 (9) ◽  
pp. 095106 ◽  
Author(s):  
Massimiliano Di Liberto ◽  
Michele Ciofalo
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flow ◽  
Plane Channel
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