Publication Date:
2022-05-25
Description:
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution December 1996
Description:
The transformation of potential vorticity within and stability of nonlinear deep
western boundary currents in an idealized tropical ocean are studied using a shallowwater
model.
Observational evidence indicates that the potential vorticity of fluid parcels in
deep western boundary currents must change sign as they cross the equator, but this
evidence is otherwise unable to clarify the process. A series of numerical experiments
investigate this transformation in a rectangular basin straddling the equator. A mass
source located in the northwestern corner feeds fluid into the domain where it is
constrained to cross the equator to reach a distributed mass sink. Dissipation is
included as momentum diffusion. The Reynolds number, defined as the ratio of the
mass source per unit depth to the viscosity, determines the nature of the flow, and a
critical value, Rec, divides its possible behavior into two regimes. For Re 〈 Rec, the
flow is laminar and well described by linear theory. For Re just above the critical value,
the flow is time-dependent, with cyclonic eddies forming in the western boundary
current near the equator. For still larger Reynolds number, eddies of both signs
emerge and form a complicated, interacting network that extends into the basin several
deformation radii from the western boundary, as well as north and south of the equator.
The eddy field is established as the mechanism for potential vorticity transformation
in nonlinear cross-equatorial flow. The analysis of vorticity fluxes follows from
the flux-conservative form of the absolute vorticity equation. It is shown that the zonally
integrated meridional flux of vorticity across the equator using no slip boundary
conditions is virtually zero even in the strongly nonlinear limit suggesting that the eddies
are extremely efficient vorticity transfer agents. A decomposition of the vorticity
fluxes into components due to mean advection, eddy transport, and friction, reveals
the growth with Reynolds number of a turbulent boundary layer that exchanges vorticity
between the inertial portion of the boundary current and a frictional sub-layer
where modification is straightforward.
A linear stability analysis of the shallow-water system in the tropical ocean examines the initial formation of the eddy field. The formulation assumes that the basic
state is purely meridional and on a local f-plane. Realistic western boundary current
profiles undergo a horizontal shear instability that is partially stabilized by viscosity.
Calculations at several latitudes indicate that the instability is enhanced in the tropics
where the internal deformation radius is a maximum. The linear stability analysis predicts
a length scale of the disturbance, a location for its origin, and a critical Reynolds
number that agree well with numerical results.
Description:
Financial support for this research was provided by NSF grant number OCE-
9115915 and ONR ASSERT grant number N00014-94-1-0844.
Keywords:
Ocean currents
;
Ocean circulation
Repository Name:
Woods Hole Open Access Server
Type:
Thesis
Format:
application/pdf
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