Nonlinear western boundary current flow near a corner

Page, Michael A.; Johnson, E. R.

doi:10.1016/0377-0265(91)90001-v

Cited by 6 publications

(3 citation statements)

References 23 publications

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“…For both models, it is found that a solution of this form exists only for A ~ Ac' for some critical value of A. For the Stommel problem [8], [10],…”

Section: Introductionmentioning

confidence: 93%

On The Parametric Model of Western Boundary Outflow

Mallier

1994

Stud Appl Math

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A simple model equation for western boundary outflow in the Stommel model of the large scale ocean circulation is obtained by evaluating the potential vorticity equation at the western boundary. A series solution to this model equation demonstrates similar behavior to the boundary layer solution of the potential vorticity equation, in particular that “resonances” are present at a discrete series of parameter values which necessitate the addition of logarithms to the series; these resonances occur because the model equation has a logarithmic branch point at these values.

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“…For both models, it is found that a solution of this form exists only for A ~ Ac' for some critical value of A. For the Stommel problem [8], [10],…”

Section: Introductionmentioning

confidence: 93%

On The Parametric Model of Western Boundary Outflow

Mallier

1994

Stud Appl Math

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“…For example, for both equations, solutions of the form sought could only exist if the parameter λ was less than a critical value λ c . The critical value λ c was reported in [5,6,8] for the Stommel model and in [3,4] for the Munk model. The failure of these equations to have a solution is coincident with the separation of the boundary layer [16], and in [17], it was shown that as λ is increased beyond λ c , the separation point moved further south.…”

Section: Introductionmentioning

confidence: 99%

On the Abel Equation of the Second Kind with Sinusoidal Forcing

Alobaidi

Mallier

2007

NAMC

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We consider the Abel equation of the second kind with sinusoidal forcing, which is a model equation for western boundary outflow in the Stommel model of the large scale ocean circulation. Series solutions of this equation indicate the presence of resonances at certain discrete values of a parameter which measures the nonlinearity of the flow, but numerical solutions using a standard scheme show no evidence of these resonances. We discuss and resolve this apparent contradiction.

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“…A novel technique for the numerical solution of the boundary-layer equation, based on a downstream-upstream iteration procedure, is described. Some modifications of the asymptotic layer structure described in Page & Johnson (1991) and Johnson & Page (1993) for the weakly nonlinear low-friction regime are outlined for the case of a lenticular obstacle.…”

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confidence: 99%

Wavefields forced by long obstacles on a beta-plane

Page

Johnson

2000

J. Fluid Mech.

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This paper presents analytical and numerical solutions for steady flow past long obstacles on a β-plane. In the oceanographically-relevant limit of small Rossby and Ekman numbers nonlinear advection remains important but viscosity appears only through the influence of Ekman pumping. A reduced boundary-layer-type equation is derived giving the long-obstacle limit of an equation described in Page & Johnson (1990). Analytical solutions are presented or described in various asymptotic limits of this equation and compared with previous results for this or related flows. A novel technique for the numerical solution of the boundary-layer equation, based on a downstream–upstream iteration procedure, is described. Some modifications of the asymptotic layer structure described in Page & Johnson (1991) and Johnson & Page (1993) for the weakly nonlinear low-friction regime are outlined for the case of a lenticular obstacle.

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Nonlinear western boundary current flow near a corner

Cited by 6 publications

References 23 publications

On The Parametric Model of Western Boundary Outflow

On The Parametric Model of Western Boundary Outflow

On the Abel Equation of the Second Kind with Sinusoidal Forcing

Wavefields forced by long obstacles on a beta-plane

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