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John D. McCalpin

Abstract

Semi-Lagrangian advection schemes are known to be dissipative because of the interpolation required to estimate the values of the flow fields at each parcel's departure point. In this study, the amplification factors of first, second, third, and fourth-order Largrangian interpolation schemes are used to calculate the dissipative decay time scale and the resulting effective eddy viscocity as functions of wavelength and residual Courant number. The dissipation inherent in the semi-Lagrangian advection can then be compared to more traditional forms of dissipation, such as Laplacian of biharmonic eddy viscosity. The correspondence between semi-Lagrangian advection and more traditional Eulerian techniques is emphasized. The dependence of the dissipation on the time step and grid spacing is also discussed, with a view to selecting the discretionary parameters to meet conservation criteria.

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John D. McCalpin

Abstract

The phenomenon of Rossby wave generation by poleward propagating baroclinic coastal Kelvin waves is discussed in the low-frequency quasigeostrophic (QG) limit. The response of the system is divided into three frequency regimes: a low-frequency regime (longer than annual periods) for which the previously studied long-wave models are quite accurate, a high-frequency regime (semiannual or shorter) for which the Kelvin waves are coastally trapped (and thus of negligible importance to the interior), and an intermediate regime for which dispersive effects are important to the scattering process.

It is shown that the retention of the y dependence of the radius of deformation in a locally 1D, QG model is necessary and sufficient to describe the dominant energy flux out of the coastal waveguide for all three of these frequency regimes. This Rossby wave energy flux directly determines the interior Rossby wave amplitudes and modifies the evolution of the Kelvin wave amplitude along the coast.

The result of the application of a QG midlatitude β-plane model to this scattering process is contrasted with more accurate results from the locally 1D QG model and from a generalized QG model (which retains the linear variation of Coriolis force with latitude in all terms). A direct numerical simulation of the reduced-gravity shallow-water equations is used as a reference. It is shown that the traditional assumption of constant deformation radius in QG models causes O(1) errors in the Rossby wave response in the interior, and somewhat smaller errors in the prediction of the changes in the coastal Kelvin wave amplitude.

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John D. McCalpin

Abstract

The analytic theory of Cane and Gent on the reflection of low-frequency equatorial waves from arbitrary boundaries is applied to the reflection of long Rossby waves from realistic approximations to the western boundaries of the Atlantic, Pacific, and Indian oceans. The results show that low-frequency (annual period or longer), first meridional mode, first baroclinic mode reflection is close to that of straight north–south boundary in all three basins. However, increasing the frequency, meridional mode number, and/or vertical mode number causes drastic changes in the energy flux reflection coefficients. Corresponding to the general slope and complexity of the coastline, the effects are greatest for the Pacific Ocean and least for the Indian Ocean.

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John D. McCalpin

Abstract

The sensitivity of the time-averaged circulation of an oceanic double-gyre model to variations in the model's parameters and forcing is studied. Unresolved low-frequency variability in the solution leads to statistical uncertainty in the estimates of the time-averaged quantities. The authors utilize bootstrap analyses of a number of multicentury integrations of a reduced-gravity, quasigeostrophic, eddy-resolving ocean model to estimate these statistical uncertainties. An analysis is then presented of the sensitivity of the system to variations in the strength and asymmetry of the wind forcing and to variations in several other physical and numerical parameters of the system. The bootstrap results enable us to estimate error bounds on these sensitivities The physical measures of the system investigated include the means and variances of the total energy, the peak transport, the location of the separation point, and the penetration scale of the free jet.

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John D. McCalpin and Dale B. Haidvogel

Abstract

The low-frequency variability of the oceanic wind-driven circulation is investigated by use of a reduced-gravity, quasigeostrophic model with slight variations on the classic double-gyre wind forcing. Approximately 30 eddy-resolving simulations of 100–1000 years duration are analyzed to determine the types of low-frequency variability and to estimate statistical uncertainties in the results.

For parameters close to those leading to a stable antisymmetric solution, the system appears to have several preferred phenomenological regimes, each with distinct total energy levels. These states include a high-energy quasi-stable state; a low-energy, weakly penetrating state; and a state of intermediate energy and modest eddy/ring generation. The low-frequency variability of the model is strongly linked to the irregular transitions between these dynamical regimes.

For a central set of reference parameters, the behavior of the system is investigated for each period in which the total energy remains in certain ranges. The structure of the time-averaged streamfunction and eddy energy fields are observed to have remarkable repeatability from event to event for each state.

A parameter study documents the ways in which the probability distribution function of the total energy depends on the strength and asymmetry of the wind forcing field. As the parameters shift away from those leading to a steady antisymmetric solution, we find that increasing the asymmetry of the wind field or reducing the viscosity decreases the occurrences of the high-energy, quasi-stable state. The low-energy, weakly penetrating state is more robust and exists whenever there is both instability and a certain minimal asymmetry in the forcing. As the wind asymmetry is increased, the distributions shift smoothly (but rapidly) away from the higher-energy states, until only the low-energy state remains.

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