scholarly journals On the frequency-dependent effective viscosity of laminar and turbulent flows

2019 ◽  
Vol 82 ◽  
pp. 35-42
Author(s):  
G.I. Ogilvie
Keyword(s):  
Fluid Flow ◽  
Turbulent Flows ◽  
Effective Viscosity ◽  
Three Dimensional ◽  
Giant Planets ◽  
Frequency Dependent ◽  
Tidal Dissipation ◽  
Jean Paul ◽  
Phd Thesis ◽  
Laminar And Turbulent Flows

The efficiency of tidal dissipation in convective zones of stars and giant planets depends, in part, on the response of a three-dimensional fluid flow to the periodic deformation due to the equilibrium tide — a problem considered by Jean-Paul Zahn in his PhD thesis. We review recent results on this problem and present novel calculations based on some idealized models.

Numerical Simulation Study on the Asymmetric Structures of Oscillatory Flow Field in a Baffled Tube Reactor

2004 ◽  
Author(s):  
Yong-Wen Wu ◽  
Jia Wu
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flows ◽  
Oscillatory Flow ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Structured Grid ◽  
Tube Reactor ◽  
Oscillating Boundary ◽  
The Asymmetry ◽  
Laminar And Turbulent Flows

The oscillatory flow in a baffled tube reactor provides a significant enhancement of radial transfer of momentum, heat and mass and a good control of axial back mixing at a wide range of net flow rate. But little has been known about reliable details of the three-dimensional structure of flow field in this kind of flow because most published studies in the area were based on the two-dimensional simulation techniques. This paper implemented a three-dimensional numerical simulation study on the asymmetry of flow pattern in the baffled tube reactor which was observed experimentally. A systematic study by numerical simulation was carried out which covered a range of oscillatory Reynolds number (Reo) from 100 to 5,000 and employed models respectively for laminar and turbulent flows. It was found in the simulation that under symmetric boundary conditions the transition from axially symmetric flow to asymmetric one depended on the numerical technique employed in simulation. With a structured grid frame the transition occurred at Reo much greater than that with an unstructured grid frame, for both laminar and turbulent flows. It is not rational that the onset of the transition changes with the accuracy of numerical technique. Based on the simulation results, it was postulated that the asymmetry appeared in simulations with symmetric boundary conditions might result from the accumulation of calculation errors but the asymmetry observed in experiments might result from the slight asymmetry of geometry which exists inevitably in any experiment apparatus. To explore the influence of the slight asymmetry of geometry, the effect of the eccentricity of baffles and the declination of oscillating boundary were studied by use of the finite volume method with a structured grid and adaptive time steps. The simulation result showed that both the eccentricity of baffles and the declination of oscillating boundary have obvious influence on the asymmetry of flow patterns for laminar and turbulent flow. More details were discussed in the paper.

Three-dimensional viscous wakes

1962 ◽  
Vol 14 (2) ◽  
pp. 233-240 ◽  
Author(s):  
Martin H. Steiger ◽  
Martin H. Bloom
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Axial Symmetry ◽  
Constant Velocity ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Axial Velocity Distribution ◽  
Fluid Properties ◽  
Laminar And Turbulent Flows

The velocity fields of three-dimensional viscous wakes are examined with the use of the boundary-layer approximations, Oseen's linearization of the convective terms, and the assumption of constant fluid properties. Transform methods yield solutions for general types of initial conditions. As an illustration, the axial velocity distribution of a wake whose initial isovels (lines of constant velocity) are of elliptic shape and their decay to axial symmetry are demonstrated. Both laminar and turbulent flows are considered.

scholarly journals On the miscible Rayleigh–Taylor instability: two and three dimensions

2001 ◽  
Vol 447 ◽  
pp. 377-408 ◽  
Author(s):  
Y.-N. YOUNG ◽  
H. TUFO ◽  
A. DUBEY ◽  
R. ROSNER
Keyword(s):  
Turbulent Flows ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Point Sources ◽  
Three Dimensions ◽  
Working Fluid ◽  
Rayleigh Taylor Instability ◽  
Rt Instability ◽  
Laminar And Turbulent Flows

We investigate the miscible Rayleigh–Taylor (RT) instability in both two and three dimensions using direct numerical simulations, where the working fluid is assumed incompressible under the Boussinesq approximation. We first consider the case of randomly perturbed interfaces. With a variety of diagnostics, we develop a physical picture for the detailed temporal development of the mixed layer: we identify three distinct evolutionary phases in this development, which can be related to detailed variations in the growth of the mixing zone. Our analysis provides an explanation for the observed differences between two- and three-dimensional RT instability; the analysis also leads us to concentrate on the RT models which (i) work equally well for both laminar and turbulent flows, and (ii) do not depend on turbulent scaling within the mixing layer between fluids. These candidate RT models are based on point sources within bubbles (or plumes) and their interaction with each other (or the background flow). With this motivation, we examine the evolution of single plumes, and relate our numerical results (for single plumes) to a simple analytical model for plume evolution.

scholarly journals Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity

2020 ◽  
Vol 497 (3) ◽  
pp. 3400-3417 ◽  
Author(s):  
Craig D Duguid ◽  
Adrian J Barker ◽  
C A Jones
Keyword(s):  
Effective Viscosity ◽  
Turbulent Viscosity ◽  
Low Frequency ◽  
Giant Planets ◽  
Turbulent Convection ◽  
Tidal Dissipation ◽  
Orbital Decay ◽  
Tidal Theory ◽  
Tidal Flows ◽  
Hydrodynamical Simulations

ABSTRACT Turbulent convection is thought to act as an effective viscosity (νE) in damping tidal flows in stars and giant planets. However, the efficiency of this mechanism has long been debated, particularly in the regime of fast tides, when the tidal frequency (ω) exceeds the turnover frequency of the dominant convective eddies (ωc). We present the results of hydrodynamical simulations to study the interaction between tidal flows and convection in a small patch of a convection zone. These simulations build upon our prior work by simulating more turbulent convection in larger horizontal boxes, and here we explore a wider range of parameters. We obtain several new results: (1) νE is frequency dependent, scaling as ω−0.5 when ω/ωc ≲ 1, and appears to attain its maximum constant value only for very small frequencies (ω/ωc ≲ 10−2). This frequency reduction for low-frequency tidal forcing has never been observed previously. (2) The frequency dependence of νE appears to follow the same scaling as the frequency spectrum of the energy (or Reynolds stress) for low and intermediate frequencies. (3) For high frequencies (ω/ωc ≳ 1 − 5), νE ∝ ω−2. 4) The energetically dominant convective modes always appear to contribute the most to νE, rather than the resonant eddies in a Kolmogorov cascade. These results have important implications for tidal dissipation in convection zones of stars and planets, and indicate that the classical tidal theory of the equilibrium tide in stars and giant planets should be revisited. We briefly touch upon the implications for planetary orbital decay around evolving stars.

Hydrodynamics in Tubes Perturbed by Curvilinear Obstructions

1984 ◽  
Vol 106 (3) ◽  
pp. 262-269 ◽  
Author(s):  
A. K. Rastogi
Keyword(s):  
Fluid Flow ◽  
Turbulent Flows ◽  
Separated Flows ◽  
Curvilinear Coordinates ◽  
Two Dimensional ◽  
Governing Equations ◽  
Curved Boundaries ◽  
Numerical Grid ◽  
Orthogonal Curvilinear Coordinates ◽  
Laminar And Turbulent Flows

A calculation procedure for two-dimensional separated flows over curved boundaries, e.g., flow in constricted tubes, is described. The method is based on the numerical solution with finite differences of the governing equations in orthogonal curvilinear coordinates. A body fitted curvilinear orthogonal numerical grid is generated first which is then employed for the solution of partial differential equations governing fluid flow. Results of calculations are presented for laminar and turbulent flows in constricted tubes. For turbulent flow calculations the k-ε turbulence model has been employed. Comparison between computed and measured values of flow quantities is also presented and is discussed in some detail. Although the present paper deals only with constricted pipes, the method developed is general and can be used without difficulty for two-dimensional flows over other curved boundaries.

The Unsteady Boundary Layer in a Shock Tube

1976 ◽  
Vol 190 (1) ◽  
pp. 287-296 ◽  
Author(s):  
B. E. L. Deckker ◽  
M. E. Weekes
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Rectangular Duct ◽  
Unsteady Boundary Layer ◽  
High Quality ◽  
Schlieren System ◽  
Theoretical Predictions ◽  
Laminar And Turbulent Flows

SYNOPSIS The unsteady boundary layer behind a moving shock wave in a rectangular duct 7.62 cm wide × 5.08 cm high has been studied using a high quality schlieren system. Growth of the boundary layer has been compared with the results of calculations for laminar and turbulent flows. The experimental results indicate that three dimensional effects are present which cause, in some cases, very early transition from laminar to turbulent flow. Agreement with theory is satisfactory only in the case of the weakest shock wave examined although the trends in growth rates generally conform to theoretical predictions.

scholarly journals Tidal dissipation in stars and giant planets: Jean-Paul Zahn's pioneering work and legacy

2019 ◽  
Vol 82 ◽  
pp. 5-33 ◽  
Author(s):  
S. Mathis
Keyword(s):  
Binary Stars ◽  
Planetary Systems ◽  
Giant Planets ◽  
Tidal Dissipation ◽  
Turbulent Friction ◽  
Jean Paul ◽  
Tidal Flows ◽  
Order Of Magnitude ◽  
Celestial Bodies ◽  
Work Done

In this lecture opening the session focused on tides in stellar and planetary systems, I will review the Jean-Paul Zahn's key contributions to the theory of tidal dissipation in stars and fluid planetary layers. I will first recall the general principles of tidal friction in celestial bodies. Then, I will focus on the theories of the stellar equilibrium and dynamical tides founded by Jean-Paul and their predictions for the evolution of binary stars. I will underline their essential legacy for ongoing studies of tidal dissipation in stars hosting planets and in fluid planetary regions. I will also discuss his pioneering work on the turbulent friction applied on tidal flows by stellar convection and the corresponding still unsolved challenging problems. Next, I will present the results we obtained on tidal dissipation in the potential dense rocky/icy core of gaseous giant planets such as Jupiter and Saturn within the Encelade international team. This mechanism provides important keys to interpret the high-precision astrometric measurements of the rates of tidal orbital migration of the moons of these planets, which are found to be larger than expected. This corresponds to a Jovian and Saturnian tidal frictions which are higher by one order of magnitude than the usually used values calibrated on formation scenarios. Finally, I will review the work done by Jean-Paul and Michel Rieutord on potential Ekman boundary layers associated to tidal flows. As a consequence, a coherent physical modeling of tides is now mandatory to understand the properties and the evolution of stellar and planetary systems. To progress on this forefront research subject, we are walking on the path first drawn by Jean-Paul.

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