A finite-difference convective model for Jupiter's equatorial jet

AbstractWe present results of a numerical model for studying the dynamics of Jupiter's equatorial jet. The computed domain is a piece of spherical shell around the equator. The bulk of the region is convective, with a thin radiative layer at the top. The shell is spinning fast, with a Coriolis number = ΩL/V on the order of 50. A prominent super-rotating equatorial jet is generated, and secondary alternating jets appear in the higher latitudes. The roles of terms in the zonal momentum equation are analyzed. Since both the Reynolds number and the Taylor number are large, the viscous terms are small. The zonal momentum balance is primarily between the Coriolis and the Reynolds stress terms.

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On the Steadiness of Separating Meandering Currents

Journal of Physical Oceanography ◽

10.1175/2008jpo3869.1 ◽

2009 ◽

Vol 39 (2) ◽

pp. 437-448 ◽

Cited By ~ 8

Author(s):

Peter Jan van Leeuwen ◽

Will P. M. de Ruijter

Keyword(s):

Momentum Equation ◽

Local Analysis ◽

Momentum Balance ◽

Coastal Current ◽

Scaling Analysis ◽

Free Jet ◽

Zonal Momentum Balance ◽

Steady Solutions ◽

Current Systems ◽

Zonal Momentum

Abstract The existence of inertial steady currents that separate from a coast and meander afterward is investigated. By integrating the zonal momentum equation over a suitable area, it is shown that retroflecting currents cannot be steady in a reduced gravity or in a barotropic model of the ocean. Even friction cannot negate this conclusion. Previous literature on this subject, notably the discrepancy between several articles by Nof and Pichevin on the unsteadiness of retroflecting currents and steady solutions presented in other papers, is critically discussed. For more general separating current systems, a local analysis of the zonal momentum balance shows that given a coastal current with a specific zonal momentum structure, an inertial, steady, separating current is unlikely, and the only analytical solution provided in the literature is shown to be inconsistent. In a basin-wide view of these separating current systems, a scaling analysis reveals that steady separation is impossible when the interior flow is nondissipative (e.g., linear Sverdrup-like). These findings point to the possibility that a large part of the variability in the world’s oceans is due to the separation process rather than to instability of a free jet.

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Zonal Momentum Balance at the Equator

Journal of Physical Oceanography ◽

10.1175/1520-0485(1989)019<0561:zmbate>2.0.co;2 ◽

1989 ◽

Vol 19 (5) ◽

pp. 561-570 ◽

Cited By ~ 38

Author(s):

T. M. Dillon ◽

J. N. Moum ◽

T. K. Chereskin ◽

D. R. Caldwell

Keyword(s):

Momentum Balance ◽

Zonal Momentum Balance ◽

Zonal Momentum

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Mean dynamics of transitional boundary-layer flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.253 ◽

2011 ◽

Vol 682 ◽

pp. 617-651 ◽

Cited By ~ 22

Author(s):

J. KLEWICKI ◽

R. EBNER ◽

X. WU

Keyword(s):

Boundary Layer ◽

Reynolds Number ◽

Reynolds Stress ◽

Boundary Layer Flow ◽

Layer Structure ◽

Momentum Equation ◽

Stress Profile ◽

Transitional Regime ◽

The Mean ◽

Layer Flow

The dynamical mechanisms underlying the redistribution of mean momentum and vorticity are explored for transitional two-dimensional boundary-layer flow at nominally zero pressure gradient. The analyses primarily employ the direct numerical simulation database of Wu & Moin (J. Fluid Mech., vol. 630, 2009, p. 5), but are supplemented with verifications utilizing subsequent similar simulations. The transitional regime is taken to include both an instability stage, which effectively generates a finite Reynolds stress profile, −ρuv(y), and a nonlinear development stage, which progresses until the terms in the mean momentum equation attain the magnitude ordering of the four-layer structure revealed by Wei et al. (J. Fluid Mech., vol. 522, 2005, p. 303). Self-consistently applied criteria reveal that the third layer of this structure forms first, followed by layers IV and then II and I. For the present flows, the four-layer structure is estimated to be first realized at a momentum thickness Reynolds number Rθ = U∞ θ/ν ≃ 780. The first-principles-based theory of Fife et al. (J. Disc. Cont. Dyn. Syst. A, vol. 24, 2009, p. 781) is used to describe the mean dynamics in the laminar, transitional and four-layer regimes. As in channel flow, the transitional regime is marked by a non-negligible influence of all three terms in the mean momentum equation at essentially all positions in the boundary layer. During the transitional regime, the action of the Reynolds stress gradient rearranges the mean viscous force and mean advection profiles. This culminates with the segregation of forces characteristic of the four-layer regime. Empirical and theoretical evidence suggests that the formation of the four-layer structure also underlies the emergence of the mean dynamical properties characteristic of the high-Reynolds-number flow. These pertain to why and where the mean velocity profile increasingly exhibits logarithmic behaviour, and how and why the Reynolds stress distribution develops such that the inner normalized position of its peak value, ym+, exhibits a Reynolds number dependence according to $y_m^+ {\,\simeq\,} 1.9 \sqrt{\delta^+}$.

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Is the Coefficient of Eddy Potential Vorticity Diffusion Positive? Part I: Barotropic Zonal Channel

Journal of Physical Oceanography ◽

10.1175/jpo-d-17-0229.1 ◽

2018 ◽

Vol 48 (7) ◽

pp. 1589-1607 ◽

Cited By ~ 1

Author(s):

V. O. Ivchenko ◽

V. B. Zalesny ◽

B. Sinha

Keyword(s):

Potential Vorticity ◽

Independent Solution ◽

Zonal Flow ◽

Momentum Balance ◽

Eddy Fluxes ◽

The Mean ◽

Zonal Momentum Balance ◽

Circumpolar Current ◽

The Antarctic ◽

Zonal Momentum

AbstractThe question of whether the coefficient of diffusivity of potential vorticity by mesoscale eddies is positive is studied for a zonally reentrant barotropic channel using the quasigeostrophic approach. The topography is limited to the first mode in the meridional direction but is unlimited in the zonal direction. We derive an analytic solution for the stationary (time independent) solution. New terms associated with parameterized eddy fluxes of potential vorticity appear both in the equations for the mean zonal momentum balance and in the kinetic energy balance. These terms are linked with the topographic form stress exerted by parameterized eddies. It is demonstrated that in regimes with zonal flow (analogous to the Antarctic Circumpolar Current), the coefficient of eddy potential vorticity diffusivity must be positive.

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Zonal Momentum Balance, Potential Vorticity Dynamics, and Mass Fluxes on Near-Surface Isentropes

Journal of the Atmospheric Sciences ◽

10.1175/jas3341.1 ◽

2005 ◽

Vol 62 (6) ◽

pp. 1884-1900 ◽

Cited By ~ 33

Author(s):

Tapio Schneider

Keyword(s):

Potential Vorticity ◽

Momentum Balance ◽

Near Surface ◽

Global Circulation ◽

Balance Condition ◽

Mass Fluxes ◽

Vorticity Dynamics ◽

The Mean ◽

Zonal Momentum Balance ◽

Zonal Momentum

Abstract While it has been recognized for some time that isentropic coordinates provide a convenient framework for theories of the global circulation of the atmosphere, the role of boundary effects in the zonal momentum balance and in potential vorticity dynamics on isentropes that intersect the surface has remained unclear. Here, a balance equation is derived that describes the temporal and zonal mean balance of zonal momentum and of potential vorticity on isentropes, including the near-surface isentropes that sometimes intersect the surface. Integrated vertically, the mean zonal momentum or potential vorticity balance leads to a balance condition that relates the mean meridional mass flux along isentropes to eddy fluxes of potential vorticity and surface potential temperature. The isentropic-coordinate balance condition formally resembles balance conditions well known in quasigeostrophic theory, but on near-surface isentropes it generally differs from the quasigeostrophic balance conditions. Not taking the intersection of isentropes with the surface into account, quasigeostrophic theory does not adequately represent the potential vorticity dynamics and mass fluxes on near-surface isentropes—a shortcoming that calls into question the relevance of quasigeostrophic theories for the macroturbulence and global circulation of the atmosphere.

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A Zonal Momentum Balance on Density Layers for the Central and Eastern Equatorial Pacific

Journal of Physical Oceanography ◽

10.1175/jpo3090.1 ◽

2007 ◽

Vol 37 (7) ◽

pp. 1939-1955 ◽

Cited By ~ 10

Author(s):

Jaclyn N. Brown ◽

J. Stuart Godfrey ◽

Russell Fiedler

Keyword(s):

Nonlinear Term ◽

Baroclinic Instability ◽

Three Dimensional ◽

Momentum Equation ◽

Surface Flow ◽

Equatorial Pacific ◽

Momentum Balance ◽

Equatorial Pacific Ocean ◽

Geostrophic Flow ◽

Zonal Momentum

Abstract Brown et al. analyzed the kinematics of flow in the equatorial Pacific Ocean, along time-varying isopycnals in a three-dimensional eddy-permitting model. Here the dynamics of these flows is explored in the same model via the zonal momentum equation (ZME). Previous work has shown that the dominant terms of the ZME, on and near the equator, are the pressure gradient, wind stress, and Coriolis term. In one model study, the nonlinear and friction terms were significant but negated each other. In this study, with a higher-resolution model and more realistic friction scheme it is shown that the nonlinear term is important along and north of the equator, while the explicit friction term is negligible. The part of the nonlinear term derived from high-frequency eddy flows acts like a friction on the Equatorial Undercurrent, while the remaining part of the nonlinear term from smooth flows enhances it. In density coordinates, meridional tropical cells lie on either side of the equator in the first half of the year (January–June) as expected. In July–December, a continuous southward surface flow appears from 4°N into the Southern Hemisphere and arises from variations in the geostrophic flow and the nonlinear term. Variations in the geostrophic flow are due to both seasonal variability in the thermocline and a surface bolus effect arising from baroclinic instability. The nonlinear term increases in the surface layers at the same time assisting the southward flow, most likely because of tropical instability waves.

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Tropical Zonal Momentum Balance in the NCEP Reanalyses

Journal of the Atmospheric Sciences ◽

10.1175/jas3486.1 ◽

2005 ◽

Vol 62 (7) ◽

pp. 2499-2513 ◽

Cited By ~ 52

Author(s):

Ioana M. Dima ◽

John M. Wallace ◽

Ian Kraucunas

Keyword(s):

Rossby Wave ◽

Wave Pattern ◽

Reanalysis Data ◽

Momentum Balance ◽

Stationary Waves ◽

Upper Troposphere ◽

The Cross ◽

Zonal Momentum Balance ◽

Zonal Momentum ◽

Tropical Upper Troposphere

Abstract The seasonal cycle of the zonal-mean zonal momentum balance in the Tropics is investigated using NCEP reanalysis data. It is found that the climatological stationary waves in the tropical upper troposphere, which are dominated by the equatorial Rossby wave response to tropical heating, produce an equatorward eddy flux of westerly momentum in the equatorial belt. The resulting westerly acceleration in the tropical upper troposphere is balanced by the advection of easterly momentum associated with the cross-equatorial mean meridional circulation. The eddy momentum fluxes and the cross-equatorial flow both tend to be strongest during the monsoon seasons, when the maximum diabatic heating is off the equator, and weakest during April–May, the season of strongest equatorial symmetry of the heating. The upper-level Rossby wave pattern exhibits a surprising degree of equatorial symmetry and follows a similar seasonal progression. Solutions of the nonlinear shallow water wave equation also show a predominantly equatorially symmetric response to a heat source centered off the equator.

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