Planetary flow in a circular basin

Imawaki, Shiro; Takano, Kenzo

doi:10.1016/0011-7471(74)90020-5

Cited by 8 publications

(25 citation statements)

References 12 publications

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“…The topic of geostrophic adjustment in a polar basin has been treated analytically and numerically on the polar plane by Luneva et al (2012). Steady state barotropic circulation in a polar circular basin driven by prescribed inflow and outflow is treated analytically and experimentally by Imawaki and Takano (1974). The authors compare the solutions on a polar-cap with those in a uniformaly rotating basin.…”

Section: Introductionmentioning

confidence: 99%

Steady, barotropic wind and boundary-driven circulation on a polar plane

Willmott

Luneva

2015

Geophysical & Astrophysical Fluid Dynamics

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Steady, linear, barotropic wind and boundary forced circulation solutions in the presence of linear bottom friction are analytically derived in a circular basin of uniform depth on a polar tangent plane in which only first order effects of the Earth's curvature are retained. Approximate solutions are constructed by using the well known method of aggregating the interior inviscid Sverdrup balance solution and the frictional wall boundary layer solution. In contrast to the width of mid-latitude frictional western boundary layers that scale as O(µ/f ), the width of the polar frictional boundary layer adjacent to the basin wall is wider, scaling as O (µ/f ) 1/2 , where µ is the bottom friction coefficient, f is the coriolis parameter. Solutions are presented for a variety of wind stress curl distributions and for a prescribed inflow/outflow representative of the exchange of water masses between the Arctic and Atlantic basins. Boundary forced solutions are also derived in a basin with a uniform width step shelf. For this basin geometry the flow is mainly confined to the shelf, although a parameter regime is identified that supports significant flow in the deep basin.

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Section: Introductionmentioning

confidence: 99%

Steady, barotropic wind and boundary-driven circulation on a polar plane

Willmott

Luneva

2015

Geophysical & Astrophysical Fluid Dynamics

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“…Instead of replacing all the latitudes in the coefficients with some constant, we analytically solve the vorticity equation without the above assumption. Although we obtain an analytic solution similar to the approximate solution obtained by Imawaki and Takano (1974), as you see later in this paper, our formulation is more general than theirs and allows the application to a basin having relatively wide zonal band. We also look into the balance of forces acting on fluid elements and the dependence of flow field upon non-dimensional physical parameter the horizontal Ekman number.…”

Section: Introductionmentioning

confidence: 62%

“…that is, Before going further into our analysis, we briefly review that of Imawaki and Takano (1974), in which Eq. (10) is expanded as…”

Section: Formulationmentioning

confidence: 99%

“…Among those studies, Imawaki and Takano (1974) investigated steady, linear, viscous, incompressible two-dimensional fluid motions, vertically integrated from the bottom to the surface of the ocean, on a rotating circular basin. The bottom is horizontal and the surface is free from stress due to wind or sea-ice drift.…”

Section: Introductionmentioning

confidence: 99%

“…This paper revisits the problem done by Imawaki and Takano (1974). Instead of replacing all the latitudes in the coefficients with some constant, we analytically solve the vorticity equation without the above assumption.…”

Section: Introductionmentioning

confidence: 99%

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An analytic solution of steady Stokes flow on a rotating polar cap

Kitauchi

Ikeda

2009

Fluid Dyn. Res.

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An analytic solution of two-dimensional, steady, linear, viscous flow on a polar cap-polar region of a sphere which lies above (or below) a given plane normal to the rotation axis-rotating about its center is obtained. Inflow and outflow on the boundary of the polar cap drive the fluid motion. The solution of stream function is expressed as the Fourier series in longitudes and the associated Legendre functions of complex degrees in cosines of colatitudes. The fluid particles move almost along lines of constant latitudes, some circulate cyclonically and the others anticyclonically, in the geostrophic balance everywhere except near the north pole where the flow is relatively slow and the viscous force dominates over the Coriolis force. Our results support the approximation analysis and laboratory experiment studied by Imawaki and Takano (Deep-Sea Res. 21, 69-77, 1974).

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Topographical Control of the Source‐Sink and Wind Stress‐Driven Planetary Geostrophic Circulation in a Polar Basin

et al. 2020

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The effects of topography on the barotropic circulation in a polar basin are examined analytically and numerically. New approximate linear analytical solutions are presented for steady‐state wind and boundary forced barotropic planetary geostrophic circulation in a circular polar basin with a step shelf. The solutions are obtained by retaining the full spherical geometry in the derivation of the forced potential vorticity equation; thereafter the colatitude is fixed in the coefficients of this governing equation. The accuracy of the analytical solutions is evaluated by comparing them with the equivalent numerical solutions obtained using the NEMO modeling system. Subsequently, the impact of a nonuniform width shelf on source‐sink‐driven circulation is investigated numerically. The equipartition of fluid entering the source strait into cyclonic and anticyclonic shelf currents, exiting the basin at the sink strait, in a basin with a uniform width shelf is shown to be modified when the shelf width varies. In general, the wider shelf supports a current with larger transport, irrespective of the azimuthal extent of the wider shelf. The study concludes with a numerical investigation of wind‐driven circulation in a basin with a step shelf, three straits, and a transpolar ridge, a prototype Arctic Ocean simulation. Topographic steering by the ridge supports a transpolar drift current, the magnitude of which depends on the ridge height. Without the ridge, the transpolar drift current is absent and the circulation is confined to gyres on the shelf and in the deep basin.

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Planetary flow in a circular basin

Cited by 8 publications

References 12 publications

Steady, barotropic wind and boundary-driven circulation on a polar plane

Steady, barotropic wind and boundary-driven circulation on a polar plane

An analytic solution of steady Stokes flow on a rotating polar cap

Topographical Control of the Source‐Sink and Wind Stress‐Driven Planetary Geostrophic Circulation in a Polar Basin

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