Segregation of helicity in inertial wave packets

Ranjan, Avishek

doi:10.1103/physrevfluids.2.033801

Cited by 10 publications

(6 citation statements)

References 34 publications

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“…In this regard, the dynamical role of inertial waves in geodynamo simulations is being investigated and will be discussed in a subsequent study (Davidson & Ranjan 2017). Whether there are other vertically-propagating waves, such as the intermediate magnetic-Coriolis (MC) waves (Bardsley & Davidson 2016, 2017, which contribute to the creation of columnar structures in the simulations is still unclear. It is encouraging, however, that the frequency range displayed in Fig. is close to that of inertial waves, and according to Bardsley & Davidson (2017) is transformed in the same way as u r .…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, those waves which travel parallel to the rotation vector have negative helicity, u • (∇ × u) < 0, and those that travel anti-parallel have positive helicity (Moffatt 1970). This property of a monochromatic wave extends to inertial wave packets as well (Ranjan 2017). Although governed by the same set of equations, the formation of a Taylor column is different to the generation of a columnar structure by an eddy or blob (Fig.…”

Section: Introductionmentioning

confidence: 99%

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Internally driven inertial waves in geodynamo simulations

Ranjan

Davidson

Christensen

et al. 2018

Geophysical Journal International

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Inertial waves are oscillations in a rotating fluid, such as the Earth's outer core, which result from the restoring action of the Coriolis force. In an earlier work, it was argued by Davidson that inertial waves launched near the equatorial regions could be important for the α 2 dynamo mechanism, as they can maintain a helicity distribution which is negative (positive) in the north (south). Here we identify such internally-driven inertial waves, triggered by buoyant anomalies in the equatorial regions in a strongly-forced geodynamo simulation. Using the time-derivative of vertical velocity, ∂u z /∂t, as a diagnostic for travelling wave-fronts, we find that the horizontal movement in the buoyancy field near the equator is well-correlated with a corresponding movement of the fluid far from the equator. Moreover, the azimuthally-averaged spectrum of ∂u z /∂t lies in the inertial wave frequency range. We also test the dispersion properties of the waves by computing the spectral energy as a function of frequency, ϖ, and the dispersion angle, θ. Our results suggest that the columnar flow in the rotation-dominated core, which is an important ingredient for the maintenance of a dipolar magnetic field, is maintained despite the chaotic evolution of the buoyancy field on a fast-time scale by internally-driven inertial waves.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Internally driven inertial waves in geodynamo simulations

Ranjan

Davidson

Christensen

et al. 2018

Geophysical Journal International

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“…A third weakness of the inertial-wave model for establishing planetary helicity distributions is that the magnetic field within a planet will modify the inertial waves, forming hybrid magnetic-Coriolis waves. This process is discussed in, for example, Bardsley & Davidson (2016, 2017, where it is noted that the main effect of the magnetic field is to reduce the magnitude of the group velocity. However, such hybrid waves still carry negative helicity northward and positive helicity to the south, just like inertial waves.…”

Section: Discussion: Implications For Numerical Dynamos and Planetarymentioning

confidence: 99%

“…Evidently the vorticity and velocity fields are parallel and in phase, and so monochromatic inertial waves have maximum possible helicity, with the positive sign in (2.9) corresponding to negative helicity, and the negative sign to positive helicity (Moffatt, 1978). Although this argument applies only to a single Fourier mode, wave packets containing a range of wavenumbers also have a high relative helicity, and of the sign expected for a monochromatic wave (Davidson & Ranjan, 2015, Ranjan, 2017. Thus, when wave packets disperse from a localised disturbance, waves with negative helicity propagate…”

Section: Inertial Waves At Low Rossby Numbermentioning

confidence: 99%

On the spatial segregation of helicity by inertial waves in dynamo simulations and planetary cores

Davidson

Ranjan

2018

J. Fluid Mech.

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The distribution of kinetic helicity in a dipolar planetary dynamo is central to the success of that dynamo. Motivated by the helicity distributions observed in numerical simulations of the Earth’s dynamo, we consider the relationship between the kinetic helicity, $h=\boldsymbol{u}\boldsymbol{\cdot }\unicode[STIX]{x1D735}\times \boldsymbol{u}$, and the buoyancy field that acts as a source of helicity, where $\boldsymbol{u}$ is velocity. We show that, in the absence of a magnetic field, helicity evolves in accordance with the equation $\unicode[STIX]{x2202}h/\unicode[STIX]{x2202}t=-\unicode[STIX]{x1D735}\boldsymbol{\cdot }\boldsymbol{F}+S_{h}$, where the flux, $\boldsymbol{F}$, represents the transport of helicity by inertial waves, and the helicity source, $S_{h}$, involves the product of the buoyancy and the velocity fields. In the numerical simulations it is observed that the helicity outside the tangent cylinder is predominantly negative in the north and positive in the south, a feature which the authors had previously attributed to the transport of helicity by waves (Davidson & Ranjan, Geophys. J. Intl, vol. 202, 2015, pp. 1646–1662). It is also observed that there is a strong spatial correlation between the distribution of $h$ and of $S_{h}$, with $S_{h}$ also predominantly negative in the north and positive in the south. This correlation tentatively suggests that it is the in situ generation of helicity by buoyancy that establishes the distribution of $h$ outside the tangent cylinder, rather than the dispersal of helicity by waves, as had been previously argued by the authors. However, although $h$ and $S_{h}$ are strongly correlated, there is no such correlation between $\unicode[STIX]{x2202}h/\unicode[STIX]{x2202}t$ and $S_{h}$, as might be expected if the distribution of $h$ were established by an in situ generation mechanism. We explain these various observations by showing that inertial waves interact with the buoyancy field in such a way as to induce a source $S_{h}$ which has the same sign as the helicity in the local wave flux, and that the sign of $h$ is simply determined by the direction of that flux. We conclude that the observed distributions of $h$ and $S_{h}$ outside the tangent cylinder are consistent with the transport of helicity by waves.

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“…In all the runs, the external force is applied in the wavenumber band 10 ≤ k ≤ 14. With respect to the helical cases, α = 0.5 for Runs 2 and 4 and α = 0.2 for Run 5, which are not fully helical ones, are adopted since the relative helicity [u i ω i /(|u i ||ω i |)] in realistic turbulence is modulated from the maximally helical case of the inertial wave, α = ±1, due to buoyancy and nonlinear interaction of turbulence [33]. L GS 0 denotes the characteristic length scale of the turbulence and Ro GS 0 denotes the Rossby number respectively defined by…”

Section: A Governing Equations and Numerical Setupmentioning

confidence: 99%

Mechanism of mean flow generation in rotating turbulence through inhomogeneous helicity

2017

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Recent numerical simulations showed that mean flow is generated in the inhomogeneous turbulence of an incompressible fluid that is accompanied by helicity and system rotation. In order to investigate the mechanism of the phenomenon, we perform a numerical simulation of inhomogeneous turbulence in a rotating system. In the simulation, an external force is applied to inject inhomogeneous turbulent helicity, and the rotation axis is perpendicular to the inhomogeneous direction. Mean velocity is set to zero in the initial condition of the simulation. The simulation results show that the mean flow directed to the rotation axis is generated and sustained only in the case with both the helical forcing and the system rotation. We investigate the physical origin of this flow-generation phenomenon by considering the budget of the Reynolds-stress transport equation. The results indicate that the pressure diffusion term significantly contributes to the Reynolds-stress equation and supports the generated mean flow. The results also reveal that a model expression for the pressure diffusion is expressed by the turbulent helicity gradient coupled with the angular velocity of the system rotation. This implies that inhomogeneous helicity plays a significant role in the generation of the large-scale velocity distribution in incompressible turbulent flows.

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Segregation of helicity in inertial wave packets

Cited by 10 publications

References 34 publications

Internally driven inertial waves in geodynamo simulations

Internally driven inertial waves in geodynamo simulations

On the spatial segregation of helicity by inertial waves in dynamo simulations and planetary cores

Mechanism of mean flow generation in rotating turbulence through inhomogeneous helicity

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