scholarly journals Rossby-number effects on columnar eddy formation and the energy dissipation law in homogeneous rotating turbulence

2019 ◽  
Vol 885 ◽  
Author(s):  
T. Pestana ◽  
S. Hickel
Keyword(s):  
Energy Dissipation ◽  
Rossby Number ◽  
Rotating Turbulence ◽  
Eddy Formation ◽  
Image Position

scholarly journals Mean flow anisotropy without waves in rotating turbulence

2020 ◽  
Vol 889 ◽  
Author(s):  
Jonathan A. Brons ◽  
Peter J. Thomas ◽  
Alban Pothérat
Keyword(s):  
Mean Flow ◽  
Rotating Turbulence ◽  
Image Position ◽  
Flow Anisotropy

scholarly journals Water wave transmission and energy dissipation by a floating plate in the presence of overwash

2020 ◽  
Vol 889 ◽  
Author(s):  
Filippo Nelli ◽  
Luke G. Bennetts ◽  
David M. Skene ◽  
Alessandro Toffoli
Keyword(s):  
Energy Dissipation ◽  
Water Wave ◽  
Wave Transmission ◽  
Floating Plate ◽  
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scholarly journals A physical conjecture for the dipolar–multipolar dynamo transition

2019 ◽  
Vol 874 ◽  
pp. 995-1020 ◽  
Author(s):  
B. R. McDermott ◽  
P. A. Davidson
Keyword(s):  
Numerical Simulations ◽  
Rotation Axis ◽  
Three Dimensional ◽  
Low Frequency ◽  
Rossby Number ◽  
Length Scale ◽  
Inertial Waves ◽  
Rotation Rates ◽  
Rotating Turbulence ◽  
Planetary Dynamos

In numerical simulations of planetary dynamos there is an abrupt transition in the dynamics of both the velocity and magnetic fields at a ‘local’ Rossby number of 0.1. For smaller Rossby numbers there are helical columnar structures aligned with the rotation axis, which efficiently maintain a dipolar field. However, when the thermal forcing is increased, these columns break down and the field becomes multi-polar. Similarly, in rotating turbulence experiments and simulations there is a sharp transition at a Rossby number of ${\sim}0.4$. Again, helical axial columnar structures are found for lower Rossby numbers, and there is strong evidence that these columns are created by inertial waves, at least on short time scales. We perform direct numerical simulations of the flow induced by a layer of buoyant anomalies subject to strong rotation, inspired by the equatorially biased heat flux in convective planetary dynamos. We assess the role of inertial waves in generating columnar structures. At high rotation rates (or weak forcing) we find columnar flow structures that segregate helicity either side of the buoyant layer, whose axial length scale increases linearly, as predicted by the theory of low-frequency inertial waves. As the rotation rate is weakened and the magnitude of the buoyant perturbations is increased, we identify a portion of the flow which is more strongly three-dimensional. We show that the flow in this region is turbulent, and has a Rossby number above a critical value $Ro^{crit}\sim 0.4$, consistent with previous findings in rotating turbulence. We suggest that the discrepancy between the transition value found here (and in rotating turbulence experiments), and that seen in the numerical dynamos ($Ro^{crit}\sim 0.1$), is a result of a different choice of the length scale used to define the local $Ro$. We show that when a proxy for the flow length scale perpendicular to the rotation axis is used in this definition, the numerical dynamo transition lies at $Ro^{crit}\sim 0.5$. Based on this we hypothesise that inertial waves, continually launched by buoyant anomalies, sustain the columnar structures in dynamo simulations, and that the transition documented in these simulations is due to the inability of inertial waves to propagate for $Ro>Ro^{crit}$.

scholarly journals Exact two-dimensionalization of rapidly rotating large-Reynolds-number flows

2015 ◽  
Vol 783 ◽  
pp. 412-447 ◽  
Author(s):  
Basile Gallet
Keyword(s):  
Reynolds Number ◽  
Stokes Equation ◽  
Three Dimensional ◽  
Threshold Value ◽  
Navier Stokes ◽  
Rossby Number ◽  
Navier Stokes Equation ◽  
Rotating Turbulence ◽  
2D Flow ◽  
Long Time

We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body force. This system admits vertically invariant solutions that satisfy the 2D Navier–Stokes equation. At high Reynolds number and without global rotation, such solutions are usually unstable to three-dimensional perturbations. By contrast, for strong enough global rotation, we prove rigorously that the 2D (and possibly turbulent) solutions are stable to vertically dependent perturbations. We first consider the 3D rotating Navier–Stokes equation linearized around a statistically steady 2D flow solution. We show that this base flow is linearly stable to vertically dependent perturbations when the global rotation is fast enough: under a Reynolds-number-dependent threshold value$Ro_{c}(Re)$of the Rossby number, the flow becomes exactly 2D in the long-time limit, provided that the initial 3D perturbations are small. We call this property linear two-dimensionalization. We compute explicit lower bounds on$Ro_{c}(Re)$and therefore determine regions of the parameter space$(Re,Ro)$where such exact two-dimensionalization takes place. We present similar results in terms of the forcing strength instead of the root-mean-square velocity: the global attractor of the 2D Navier–Stokes equation is linearly stable to vertically dependent perturbations when the forcing-based Rossby number$Ro^{(f)}$is lower than a Grashof-number-dependent threshold value$Ro_{c}^{(f)}(Gr)$. We then consider the fully nonlinear 3D rotating Navier–Stokes equation and prove absolute two-dimensionalization: we show that, below some threshold value$Ro_{\mathit{abs}}^{(f)}(Gr)$of the forcing-based Rossby number, the flow becomes two-dimensional in the long-time limit, regardless of the initial condition (including initial 3D perturbations of arbitrarily large amplitude). These results shed some light on several fundamental questions of rotating turbulence: for arbitrary Reynolds number$Re$and small enough Rossby number, the system is attracted towards purely 2D flow solutions, which display no energy dissipation anomaly and no cyclone–anticyclone asymmetry. Finally, these results challenge the applicability of wave turbulence theory to describe stationary rotating turbulence in bounded domains.

Scaling of the turbulent energy dissipation correlation function

2020 ◽  
Vol 891 ◽  
Author(s):  
S. L. Tang ◽  
R. A. Antonia ◽  
L. Djenidi ◽  
Y. Zhou
Keyword(s):  
Correlation Function ◽  
Energy Dissipation ◽  
Turbulent Energy ◽  
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On the measurement of energy dissipation using nanoindentation and the continuous stiffness measurement technique

2013 ◽  
Vol 28 (21) ◽  
pp. 3029-3042 ◽  
Author(s):  
Erik G. Herbert ◽  
Kurt E. Johanns ◽  
Robert S. Singleton ◽  
George M. Pharr
Keyword(s):  
Energy Dissipation ◽  
Measurement Technique ◽  
Stiffness Measurement ◽  
Continuous Stiffness Measurement ◽  
Image Position

Abstract

Energy dissipation mechanisms in hollow metallic microlattices

2014 ◽  
Vol 29 (16) ◽  
pp. 1755-1770 ◽  
Author(s):  
Ladan Salari-Sharif ◽  
Tobias A. Schaedler ◽  
Lorenzo Valdevit
Keyword(s):  
Energy Dissipation ◽  
Image Position

Abstract

scholarly journals Influence of chemical disorder on energy dissipation and defect evolution in advanced alloys

2016 ◽  
Vol 31 (16) ◽  
pp. 2363-2375 ◽  
Author(s):  
Yanwen Zhang ◽  
Ke Jin ◽  
Haizhou Xue ◽  
Chenyang Lu ◽  
Raina J. Olsen ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Chemical Disorder ◽  
Defect Evolution ◽  
Image Position

Abstract

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