Turbulent convection in an anelastic rotating sphere : a model for the circulation on the giant planets

Kaspi, Yohai

doi:10.1575/1912/2492

Cited by 13 publications

(18 citation statements)

References 122 publications

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“…This note expands the results from slow threedimensional flows (Pedlosky, 1987;Tassoul 2000) and anelastic baroclinic flows (Hide, 1969;Kaspi, 2008) to identify TP-like constraints in baroclinic and highly turbulent flows, where eddy viscosity effects are relevant. The approach in this note suggests that the baroclinic terms are moderated by the Rossby number.…”

Section: Introductionsupporting

confidence: 53%

Taylor–Proudman columns in non‐hydrostatic divergent baroclinic and barotropic flows

Juárez

2009

Quart J Royal Meteoro Soc

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ABSTRACT:The Taylor-Proudman theorem states that the velocity of slow, steady flow in a rotating incompressible fluid does not change along the direction of the rotation axis. This fundamental result has been invoked to explain blocking phenomena observed over topographic features in oceanic and atmospheric flows on Earth and atmospheric patterns observed in giant gas planets even in cases where the assumption of incompressibility fails. The possible existence of Taylor-Proudman columns is analyzed here for a less restrictive family of non-hydrostatic divergent density-stratified flows, including situations where the stratification gradient and rotation axis are not parallel. The results show that Taylor-Proudman-like constraints are possible in baroclinic inviscid and viscous nonlinear flows of constant vorticity, Beltrami flows and low-Rossby-number flows. It is found that (1) the baroclinic term is moderated by a factor of the order of the Rossby number, (2) a conservation law can be found for baroclinic flows and (3) Taylor-Proudman columns will be eroded in viscous flows. One particular result stressed in this note is its interpretation in equatorial regions, where the rotation axis is perpendicular to the main stratification gradient, and it is argued that Taylor-Proudman columns could be difficult to discern with observational parameters from convective cells with only zonal and vertical transport. Copyright

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Section: Introductionsupporting

confidence: 53%

Taylor–Proudman columns in non‐hydrostatic divergent baroclinic and barotropic flows

Juárez

2009

Quart J Royal Meteoro Soc

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“…This implies that to leading order surfaces of constant angular momentum per unit mass are aligned in the direction of the axis of rotation [36,20,21], approximately as cylinders parallel to the rotation axis. Conservation of angular momentum then implies that convective fluid motion in the interior flows along these surfaces [37,36,20], so that u · ∇M Ω = 0 (u is the 3D wind vector) [21], meaning that to leading order there can be no flow through surfaces which are parallel to the axis of rotation [36,20,21]. In the purely barotropic limit this will imply a Taylor-Proudman state, namely that the velocity must be constant along the direction of the axis of rotation [23].…”

Section: S2 Calculating the Dynamical Contribution To Jmentioning

confidence: 99%

“…However meridional entropy gradients due to internal or solar heating (on Neptune internal hating is stronger than the incoming solar heating, while on Uranus the internal heating is very small) can drive these systems away from the barotropic state, resulting in zonal wind shear along the direction of the axis of rotation [20]. The magnitude of this shear will then depend on the details of the interior thermodynamics [36,20]. In addition, the magnetic field can cause a weaker interior flow due to ohmic dissipation [22].…”

Section: S2 Calculating the Dynamical Contribution To Jmentioning

confidence: 99%

“…When H is small the winds are confined to a shallow layer, and when H is large the winds approach the barotropic state where the winds penetrate through the planet along the direction of the spin axis (this state where H is large is similar to what is often referred to as differential rotation). Thus, the choice of the exponential decay along angular momentum surfaces, which is based on the vertical profile of the entropy expansion coefficient that controls the baroclinic shear in 3D anelastic general circulation models [36,20], and the decay of interior flow due to MHD Ohmic dissipation effects [22], allows exploring the full range of wind profiles from deeply rooted winds extending throughout the planet to shallow surface winds. The wind profile is then used to calculate the density anomaly gradients balancing this circulation.…”

Section: S2 Calculating the Dynamical Contribution To Jmentioning

confidence: 99%

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Atmospheric confinement of jet streams on Uranus and Neptune

Kaspi

Showman

Hubbard

et al. 2013

Nature

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Supplementary Informationvalues we use a suite of core/envelope internal structure models, with a wide range of core depths, core densities and envelope density profiles.The core is taken to be of constant density with the core density ranging between 0.8 × 10 4 < ρ core < 1.2 × 10 4 kg m −3 , and core radius extending up to 30% of the planetary radius on Neptune (0 < r core < 0.3 R, where R is the mean planetary radius), and 20% on Uranus, following the widest possible range of core densities given by [16, 17, 19]. We systematically explore this parameter space where for each case of ρ core and r core we then match an envelope represented by a 6th order polynomial with a monotonic density distribution so that ρ static = ρ core for 0 < r < r core (S1)where β = r/R is the normalized radius. The coefficients (a n ) are determined by constraints on the static density (ρ static ). The first constraint on the static density is that the density is zero at the surface, satisfied by setting the sum of the six polynomial coefficients to zero at β = 1. The second constraint is that the integrated density over the entire volume must equal to the planetary mass.The third constraint is that the density derivative at β = 1 equals the derivative of the density at the 1 bar pressure level (equal to -0.1492 and -0.2425 kg m −4 for Uranus and Neptune respectively,[31]). The first degree term in Eq. S2 is missing so that the derivative of the density goes to zero at the center for models with no core, and another constraint sets this value to zero at the core-envelope boundary for models with cores. The last constraint limits the value of J 2 to within the error estimates of the observed value of 3341.29 ± 0.72 × 10 −6 and 3408.43 ± 4.50 × 10 −6 for 1 Uranus and Neptune respectively [14, 15]. Since we are interested in determining the resulting J 4 we do not impose any constraints on J 4 , as done in most studies where the J 4 is constrained to within the observed values of J 4 (e.g., [13]). For cases with no core the density at β = 0 is not constrained, and its derivative at β = 0 is set to zero.Uranus Neptune 25

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“…2. Thermal wind balance then constrains the thermal structure of the atmosphere below the layer with substantial eddy angular momentum fluxes [see, e.g., Ingersoll and Pollard (1982) and Kaspi (2008) for thermal wind equations for deep atmospheres]. The mean meridional circulations adjust entropy gradients and the zonal flow in lower layers such that they satisfy, in a statistically steady state, the constraints that (i) angular momentum flux convergence or divergence and the MHD drag on the zonal flow balance upon averaging over cylinders, and (ii) the zonal flow is in thermal wind balance with the entropy gradients (see, e.g., Haynes et al 1991).…”

Section: Drag At Depth and Mean Meridional Circulationsmentioning

confidence: 99%

Formation of Jets and Equatorial Superrotation on Jupiter

Schneider

Liu

2009

Journal of the Atmospheric Sciences

154

167

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The zonal flow in Jupiter's upper troposphere is organized into alternating retrograde and prograde jets, with a prograde (superrotating) jet at the equator. Existing models posit as the driver of the flow either differential radiative heating of the atmosphere or intrinsic heat fluxes emanating from the deep interior; however, they do not reproduce all large-scale features of Jupiter's jets and thermal structure. Here it is shown that the difficulties in accounting for Jupiter's jets and thermal structure resolve if the effects of differential radiative heating and intrinsic heat fluxes are considered together, and if upper-tropospheric dynamics are linked to a magnetohydrodynamic (MHD) drag that acts deep in the atmosphere. Baroclinic eddies generated by differential radiative heating can account for the off-equatorial jets; meridionally propagating equatorial Rossby waves generated by intrinsic convective heat fluxes can account for the equatorial superrotation. The zonal flow extends deeply into the atmosphere, with its speed changing with depth, up to depths at which the MHD drag acts. The theory is supported by simulations with an energetically consistent general circulation model of Jupiter's outer atmosphere. A simulation that incorporates differential radiative heating and intrinsic heat fluxes reproduces Jupiter's observed jets and thermal structure and makes testable predictions about as-yet unobserved aspects thereof. A control simulation that incorporates only differential radiative heating but not intrinsic heat fluxes produces off-equatorial jets but no equatorial superrotation; another control simulation that incorporates only intrinsic heat fluxes but not differential radiative heating produces equatorial superrotation but no off-equatorial jets.Comment: 23 pages, 10 figure

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Turbulent convection in an anelastic rotating sphere : a model for the circulation on the giant planets

Cited by 13 publications

References 122 publications

Taylor–Proudman columns in non‐hydrostatic divergent baroclinic and barotropic flows

Taylor–Proudman columns in non‐hydrostatic divergent baroclinic and barotropic flows

Atmospheric confinement of jet streams on Uranus and Neptune

Formation of Jets and Equatorial Superrotation on Jupiter

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