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  • Cambridge University Press (CUP)  (8)
  • 1
    Online Resource
    Online Resource
    Inverse cascade suppression and shear-layer formation in magnetohydrodynamic turbulence subject to a guide field and misaligned rotation
    Cambridge University Press (CUP) ; 2022
    In:  Journal of Fluid Mechanics Vol. 935 ( 2022-03-25)
    Details
    In: Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 935 ( 2022-03-25)
    Abstract: Astrophysical flows are often subject to both rotation and large-scale background magnetic fields. Individually, each is known to two-dimensionalize the flow in the perpendicular plane. In realistic settings, both of these effects are simultaneously present and, importantly, need not be aligned. In this work, we numerically investigate three-dimensional forced magnetohydrodynamic turbulence subject to the competing effects of global rotation and a perpendicular background magnetic field. We focus on the case of a strong background field and find that increasing the rotation rate from zero produces significant changes in the structure of the turbulent flow. Starting with a two-dimensional inverse energy cascade at zero rotation, the flow first transitions to a forward cascade of kinetic energy, then to a shear-layer dominated regime and finally to a second shear-layer regime where the kinetic energy flux is strongly suppressed and the energy transfer is mediated by the induced magnetic field. We show that the first two transitions occur at distinct values of the Rossby number, and the third occurs at a distinct value of the Lehnert number. The three-dimensional results are confirmed using an asymptotic two-dimensional, three-component model, which allows us to extend our results to the planetary-relevant case of an arbitrary angle between the rotation vector and guide field. More generally, our results demonstrate that, when considering the simultaneous limits of strong rotation and a strong guide field, the order in which those limits are taken matters in the misaligned case.
    Type of Medium: Online Resource
    ISSN: 0022-1120 , 1469-7645
    URL: Article
    DOI: 10.1017/jfm.2021.968
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 2022
    detail.hit.zdb_id: 1472346-3
    detail.hit.zdb_id: 218334-1
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  • 2
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    Statistical non-locality of dynamically coherent structures
    Cambridge University Press (CUP) ; 2023
    In:  Journal of Fluid Mechanics Vol. 966 ( 2023-07-10)
    Details
    In: Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 966 ( 2023-07-10)
    Abstract: We analyse a class of stochastic advection problems by conditionally averaging the passive tracer equation with respect to a given flow state. In doing so, we obtain expressions for the turbulent diffusivity as a function of the flow statistics spectrum. When flow statistics are given by a continuous-time Markov process with a finite state space, calculations are amenable to analytic treatment. When the flow statistics are more complex, we show how to approximate turbulent fluxes as hierarchies of finite state space continuous-time Markov processes. The ensemble average turbulent flux is expressed as a linear operator that acts on the ensemble average of the tracer. We recover the classical estimate of turbulent flux as a diffusivity tensor, the components of which are the integrated autocorrelation of the velocity field in the limit that the operator becomes local in space and time.
    Type of Medium: Online Resource
    ISSN: 0022-1120 , 1469-7645
    URL: Article
    DOI: 10.1017/jfm.2023.467
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 2023
    detail.hit.zdb_id: 1472346-3
    detail.hit.zdb_id: 218334-1
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  • 3
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    Two-dimensional partially ionized magnetohydrodynamic turbulence
    Cambridge University Press (CUP) ; 2020
    In:  Journal of Fluid Mechanics Vol. 900 ( 2020-10-10)
    Details
    In: Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 900 ( 2020-10-10)
    Abstract: Ionization occurs in the upper atmospheres of hot Jupiters and in the interiors of gas giant planets, leading to magnetohydrodynamic (MHD) effects that couple the momentum and the magnetic field, thereby significantly altering the dynamics. In regions of moderate temperatures, the gas is only partially ionized, which also leads to interactions with neutral molecules. To explore the turbulent dynamics of these regions, we utilize partially ionized magnetohydrodynamics (PIMHD), a two-fluid model – one neutral and one ionized – coupled by a collision term proportional to the difference in velocities. Motivated by planetary settings where rotation constrains the large-scale motions to be mostly two-dimensional, we perform a suite of simulations to examine the parameter space of two-dimensional PIMHD turbulence and pay particular attention to collisions and their role in the dynamics, dissipation and energy exchange between the two species. We arrive at, and numerically confirm, an expression for the energy loss due to collisions in both the weakly and strongly collisional limits, and show that, in the latter limit, the neutral fluid couples to the ions and behaves as an MHD fluid. Finally, we discuss some implications of our findings to current understanding of gas giant planet atmospheres.
    Type of Medium: Online Resource
    ISSN: 0022-1120 , 1469-7645
    URL: Article
    DOI: 10.1017/jfm.2020.500
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 2020
    detail.hit.zdb_id: 1472346-3
    detail.hit.zdb_id: 218334-1
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  • 4
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    Dynamics of ventilated coherent cold eddies on a sloping bottom
    Cambridge University Press (CUP) ; 1991
    In:  Journal of Fluid Mechanics Vol. 223, No. -1 ( 1991-2), p. 565-
    Details
    In: Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 223, No. -1 ( 1991-2), p. 565-
    Type of Medium: Online Resource
    ISSN: 0022-1120 , 1469-7645
    URL: Article
    DOI: 10.1017/S0022112091001556
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 1991
    detail.hit.zdb_id: 1472346-3
    detail.hit.zdb_id: 218334-1
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  • 5
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    Convectively driven shear and decreased heat flux
    Cambridge University Press (CUP) ; 2014
    In:  Journal of Fluid Mechanics Vol. 759 ( 2014-11-25), p. 360-385
    Details
    In: Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 759 ( 2014-11-25), p. 360-385
    Abstract: We report on direct numerical simulations of two-dimensional, horizontally periodic Rayleigh–Bénard convection between free-slip boundaries. We focus on the ability of the convection to drive large-scale horizontal flow that is vertically sheared. For the Prandtl numbers ( $\mathit{Pr}$ ) between 1 and 10 simulated here, this large-scale shear can be induced by raising the Rayleigh number ( $\mathit{Ra}$ ) sufficiently, and we explore the resulting convection for $\mathit{Ra}$ up to $10^{10}$ . When present in our simulations, the sheared mean flow accounts for a large fraction of the total kinetic energy, and this fraction tends towards unity as $\mathit{Ra}\rightarrow \infty$ . The shear helps disperse convective structures, and it reduces vertical heat flux; in parameter regimes where one state with large-scale shear and one without are both stable, the Nusselt number of the state with shear is smaller and grows more slowly with $\mathit{Ra}$ . When the large-scale shear is present with $\mathit{Pr}\lesssim 2$ , the convection undergoes strong global oscillations on long timescales, and heat transport occurs in bursts. Nusselt numbers, time-averaged over these bursts, vary non-monotonically with $\mathit{Ra}$ for $\mathit{Pr}=1$ . When the shear is present with $\mathit{Pr}\gtrsim 3$ , the flow does not burst, and convective heat transport is sustained at all times. Nusselt numbers then grow roughly as powers of $\mathit{Ra}$ , but the growth rates are slower than any previously reported for Rayleigh–Bénard convection without large-scale shear. We find that the Nusselt numbers grow proportionally to $\mathit{Ra}^{0.077}$ when $\mathit{Pr}=3$ and to $\mathit{Ra}^{0.19}$ when $\mathit{Pr}=10$ . Analogies with tokamak plasmas are described.
    Type of Medium: Online Resource
    ISSN: 0022-1120 , 1469-7645
    URL: Article
    DOI: 10.1017/jfm.2014.577
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 2014
    detail.hit.zdb_id: 1472346-3
    detail.hit.zdb_id: 218334-1
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  • 6
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    On the instability of geostrophic vortices
    Cambridge University Press (CUP) ; 1988
    In:  Journal of Fluid Mechanics Vol. 197 ( 1988-12), p. 349-388
    Details
    In: Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 197 ( 1988-12), p. 349-388
    Abstract: The instabilities of barotropic and baroclinic, quasi-geostrophic, f -plane, circular vortices are found using a linearized contour dynamics model. We model the vortex using a circular region of horizontally uniform potential vorticity surrounded by an annulus of uniform, but different, potential vorticity. We concentrate mostly upon isolated vortices with no circulation in the basic state outside the outer radius b . In addition to linear analyses, we also consider weakly nonlinear waves. The amplitude equation has a cubic nonlinearity and, depending upon the sign of the coefficient of the cubic term, may give nonlinear stabilization or nonlinear enhancement of the growth. Barotropic isolated eddies are unstable when the outer annulus is narrow enough; on the other hand, if the scale of the whole vortex is sufficiently small compared to the radius of deformation of a baroclinic mode, the break up may be preferentially to a depth-varying disturbance corresponding to a twisting and tilting of the vortex. As the vortex becomes more baroclinic, we find that large-scale vortices show an elliptical mode baroclinic instability as well which is relatively insensitive to the scale of the outer annulus. When the baroclinic currents in the basic state dominate, the twisting mode disappears, and we see only the instabilities associated with either strong enough shear in the annular region or sufficiently large vortices compared with the deformation radius. The finite amplitude results show that the baroclinic instability mode for large enough vortices is nonlinearly stabilized while in most cases, the other two kinds of instability are nonlinearly destabilized.
    Type of Medium: Online Resource
    ISSN: 0022-1120 , 1469-7645
    URL: Article
    DOI: 10.1017/S0022112088003283
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 1988
    detail.hit.zdb_id: 1472346-3
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  • 7
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    Transport and emergent stratification in the equilibrated Eady model: the vortex-gas scaling regime
    Cambridge University Press (CUP) ; 2022
    In:  Journal of Fluid Mechanics Vol. 948 ( 2022-10-10)
    Details
    In: Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 948 ( 2022-10-10)
    Abstract: We numerically and theoretically investigate the Boussinesq Eady model, where a rapidly rotating density-stratified layer of fluid is subject to a meridional temperature gradient in thermal wind balance with a uniform vertically sheared zonal flow. Through a suite of numerical simulations, we show that the transport properties of the resulting turbulent flow are governed by quasigeostrophic (QG) dynamics in the rapidly rotating strongly stratified regime. The ‘vortex gas’ scaling predictions put forward in the context of the two-layer QG model carry over to this fully three-dimensional system: the functional dependence of the meridional flux on the control parameters is the same, the two adjustable parameters entering the theory taking slightly different values. In line with the QG prediction, the meridional heat flux is depth-independent. The vertical heat flux is such that turbulence transports buoyancy along isopycnals, except in narrow layers near the top and bottom boundaries, the thickness of which decreases as the diffusivities go to zero. The emergent (re)stratification is set by a simple balance between the vertical heat flux and diffusion along the vertical direction. Overall, this study demonstrates how the vortex-gas scaling theory can be adapted to quantitatively predict the magnitude and vertical structure of the meridional and vertical heat fluxes, and of the emergent stratification, without additional fitting parameters.
    Type of Medium: Online Resource
    ISSN: 0022-1120 , 1469-7645
    URL: Article
    DOI: 10.1017/jfm.2022.501
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 2022
    detail.hit.zdb_id: 1472346-3
    detail.hit.zdb_id: 218334-1
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  • 8
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    Barotropic flow over finite isolated topography: steady solutions on the beta-plane and the initial value problem
    Cambridge University Press (CUP) ; 1993
    In:  Journal of Fluid Mechanics Vol. 250 ( 1993-05), p. 553-586
    Details
    In: Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 250 ( 1993-05), p. 553-586
    Abstract: Solutions for inviscid rotating flow over a right circular cylinder of finite height are studied, and comparisons are made to quasi-geostrophic solutions. To study the combined effects of finite topography and the variation of the Coriolis parameter with latitude a steady inviscid model is used. The analytical solution consists of one part which is similar to the quasi-geostrophic solution that is driven by the potential vorticity anomaly over the topography, and another, similar to the solution of potential flow around a cylinder, that is driven by the matching conditions on the edge of the topography. When the characteristic Rossby wave speed is much larger than the background flow velocity, the transport over the topography is enhanced as the streamlines follow lines of constant background potential vorticity. For eastward flow, the Rossby wave drag can be very much larger than that predicted by quasi-geostrophic theory. The combined effects of finite height topography and time-dependence are studied in the inviscid initial value problem on the f -plane using the method of contour dynamics. The method is modified to handle finite topography. When the topography takes up most of the layer depth, a stable oscillation exists with all of the fluid which originates over the topography rotating around the topography. When the Rossby number is order one, a steady trapped vortex solution similar to the one described by Johnson (1978) may be reached.
    Type of Medium: Online Resource
    ISSN: 0022-1120 , 1469-7645
    URL: Article
    DOI: 10.1017/S0022112093001569
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 1993
    detail.hit.zdb_id: 1472346-3
    detail.hit.zdb_id: 218334-1
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