scholarly journals Disentangling inertial waves from eddy turbulence in a forced rotating-turbulence experiment

2015 ◽  
Vol 91 (4) ◽  
Author(s):  
Antoine Campagne ◽  
Basile Gallet ◽  
Frédéric Moisy ◽  
Pierre-Philippe Cortet
Keyword(s):  
Inertial Waves ◽  
Rotating Turbulence

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 $Ro>Ro^{crit}$.

Evolution of a turbulent cloud under rotation

2014 ◽  
Vol 756 ◽  
pp. 488-509 ◽  
Author(s):  
A. Ranjan ◽  
P. A. Davidson
Keyword(s):  
Rotation Axis ◽  
Spatial Filter ◽  
Dimensionless Time ◽  
Inertial Waves ◽  
Lagrangian Particle ◽  
Rotating Turbulence ◽  
Negative Helicity ◽  
The Waves ◽  
Group Velocities ◽  
Quiescent Fluid

AbstractLocalized patches of turbulence frequently occur in geophysics, such as in the atmosphere and oceans. The effect of rotation, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\boldsymbol{\Omega}$, on such a region (a ‘turbulent cloud’) is governed by inhomogeneous dynamics. In contrast, most investigations of rotating turbulence deal with the homogeneous case, although inhomogeneous turbulence is more common in practice. In this paper, we describe the results of $512^3$ direct numerical simulations (DNS) of a turbulent cloud under rotation at three Rossby numbers ($\mathit{Ro}$), namely 0.1, 0.3 and 0.5. Using a spatial filter, fully developed homogeneous turbulence is vertically confined to the centre of a periodic box before the rotation is turned on. Energy isosurfaces show that columnar structures emerge from the cloud and grow into the adjacent quiescent fluid. Helicity is used as a diagnostic and confirms that these structures are formed by inertial waves. In particular, it is observed that structures growing parallel to the rotation axis (upwards) have negative helicity and those moving antiparallel (downwards) to the axis have positive helicity, a characteristic typical of inertial waves. Two-dimensional energy spectra of horizontal wavenumbers, $k_{\perp }$, versus dimensionless time, $2 \varOmega t$, confirm that these columnar structures are wavepackets which travel at the group velocities of inertial waves. The kinetic energy transferred from the turbulent cloud to the waves is estimated using Lagrangian particle tracking to distinguish between turbulent and ‘wave-only’ regions of space. The amount of energy transferred to waves is 40 % of the initial at $\mathit{Ro}=0.1$, while it is 16 % at $\mathit{Ro}=0.5$. In both cases the bulk of the energy eventually resides in the waves. It is evident from this observation that inertial waves can carry a significant portion of the energy away from a localized turbulent source and are therefore an efficient mechanism of energy dispersion.

Free-surface breakdown in a rapidly rotating liquid

1978 ◽  
Vol 86 (3) ◽  
pp. 457-463 ◽  
Author(s):  
W. E. Scott
Keyword(s):  
Free Surface ◽  
Capillary Waves ◽  
Mode Frequency ◽  
Wave Form ◽  
Inertial Waves ◽  
Rotating Liquid ◽  
Surface Breakdown ◽  
Beat Phenomenon ◽  
Inertial Wave ◽  
Wave Modes

It is shown that the wavelets which appear on the inertial wave form of the inner free surface of a fully spun-up cylindrical mass of liquid contained in a vertical, rapidly rotating and gyrating gyrostat are capillary waves. It is further shown that the interaction between these capillary waves and the excited inertial waves is not the mechanism which effects an observed two-period collapse (‘breakdown’) and reappearance of the free-surface inertial wave form. Rather, the two-period breakdown can be explained by the conjecture that it is a beat phenomenon arising from the interaction of two differently structured inertial wave modes, which have the same frequency at small amplitudes of oscillation of the gyrostat but which, owing to the dependence of the inertial mode frequency on the amplitude of the gyrostatic motion, have slightly different frequencies at larger amplitudes of oscillation of the gyrostat.

scholarly journals Anisotropic energy transfers in rotating turbulence

2011 ◽  
Vol 318 (4) ◽  
pp. 042005
Author(s):  
Cyril Lamriben ◽  
Pierre-Philippe Cortet ◽  
Frédéric Moisy
Keyword(s):  
Rotating Turbulence ◽  
Anisotropic Energy ◽  
Energy Transfers

scholarly journals Energy intensity of inertial waves in a sphere

1983 ◽  
Vol 25 (2) ◽  
pp. 145-160
Author(s):  
W. W. Wood
Keyword(s):  
Energy Density ◽  
General Theory ◽  
Energy Intensity ◽  
Initial Disturbance ◽  
Inertial Waves ◽  
Inertial Wave

AbstractThe decay at large wavenumbers of the energy density in an inertial wave generated in a sphere by an arbitrary initial disturbance is determined as a first step to a comparison with the general theory of Phillips [17] for a statistically steady field of random inertial waves in an arbitrary cavity.

The role of slow magnetostrophic waves in dipole formation in rapidly rotating dynamos

2021 ◽  
Author(s):  
Aditya Varma ◽  
Binod Sreenivasan
Keyword(s):  
Magnetic Field ◽  
Threshold Value ◽  
Dipole Field ◽  
Wave Frequency ◽  
Alfven Wave ◽  
Inertial Waves ◽  
Axial Dipole ◽  
Wide Range ◽  
The Magnetic Field

<p>It is known that the columnar structures in rapidly rotating convection are affected by the magnetic field in ways that enhance their helicity. This may explain the dominance of the axial dipole in rotating dynamos. Dynamo simulations starting from a small seed magnetic field have shown that the growth of the field is accompanied by the excitation of convection in the energy-containing length scales. Here, this process is studied by examining axial wave motions in the growth phase of the dynamo for a wide range of thermal forcing. In the early stages of evolution where the field is weak, fast inertial waves weakly modified by the magnetic field are abundantly present. As the field strength(measured by the ratio of the Alfven wave to the inertial wave frequency) exceeds a threshold value, slow magnetostrophic waves are spontaneously generated. The excitation of the slow waves coincides with the generation of helicity through columnar motion, and is followed by the formation of the axial dipole from a chaotic, multipolar state. In strongly driven convection, the slow wave frequency is attenuated, causing weakening of the axial dipole intensity. Kinematic dynamo simulations at the same parameters, where only fast inertial waves are present, fail to produce the axial dipole field. The dipole field in planetary dynamos may thus be supported by the helicity from slow magnetostrophic waves.</p>

Modal Decomposition and Linear Modeling of Swirl Fluctuations in the Mixing Section of a Model Combustor Based on PIV Data

2021 ◽  
Author(s):  
Jens Satria Müller ◽  
Finn Lückoff ◽  
Thomas Ludwig Kaiser ◽  
Christian Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Flow Instability ◽  
Theoretical Work ◽  
Navier Stokes ◽  
Inertial Waves ◽  
Linear Modeling ◽  
Swirl Combustor ◽  
Time Resolved ◽  
Flow Response

Abstract In order to determine the flame transfer function of a combustion system only based on isothermal flow field data, three governing mechanisms have been identified which need to be modeled: swirl fluctuations, equivalence fluctuations and velocity fluctuations excited by planar acoustic waves. This study focuses on the generation and propagation of swirl fluctuations downstream of a radial swirl combustor under isothermal conditions. Swirl fluctuations are generated experimentally by imposing acoustic perturbations. Time-resolved longitudinal and crosswise PIV measurements are conducted inside the mixing tube and combustion chamber to quantify the evolution of the swirl fluctuations. The measured flow response is decomposed using spectral proper orthogonal decomposition to unravel the contributions of different dynamical modes. In addition a resolvent analysis is conducted based on the linearized Navier-Stokes equations to reveal the intrinsically most amplified flow structures. Both, the data-driven and analytic approach, show that inertial waves are indeed present in the flow response and an inherent flow instability downstream of the swirler, which confirms the recent theoretical work of Albayrak et al. (Journal of Fluid Mechanics, 879). However, the contribution of these inertial waves to the total swirl fluctuations turns out to be very small. This is suggested to be due to the very structured forcing at the swirler and the amplification of shear-driven modes which are expected to be much more influential for this type of swirler. Overall, this work confirms the presence of inertial waves in highly turbulent swirl combustors and evaluates its relevance for industry-related configurations. It further outlines a methodology to analyze and predict their characteristics based on mean fields only, which is applicable for complex geometries of industrial relevance.

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