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Title

Instability of Density Fronts in Layer and Continuously Stratified Models

Author

Yasushi Fukamachi, Nova Southeastern University

Defense Date

1992

Document Type

Dissertation - NSU Access Only

Degree Name

Ph.D. Oceanography/Marine Biology

Department

Oceanographic Center

First Advisor

Julian P. McCreary

Second Advisor

David B. Enfield

Third Advisor

Donald B. Olson

Fourth Advisor

Jeffrey A. Proehl

Fifth Advisor

Russell L. Snyder

Abstract

The instability of density fronts is investigated as a possible generation mechanism of the small-scale, wave-like patterns observed along upwelling fronts and filaments. Solutions are obtained using three different models: a linearized 1½-layer model, a nonlinear 1½-layer model, and a linearized continuously stratified model confined to the surface layer of the ocean. The front is specified in two different ways: vertically oriented isopycnals along with slab-like current in the layer model, and nearly vertical isopycnals associated with vertical shear in the continuously stratified model. The prescribed state used for both the linearized and nonlinear models consists of either a uniform or zonally sheared current in a layer of constant thickness that is geostrophically balanced by the horizontal temperature gradient within the layer.

In the layer model, an analytical solution is obtained to the linearized system. When the background current is balanced by the horizontal temperature gradient alone, this solution is unconditionally unstable. Energetic analyses of numerical solutions for both uniform and zonally sheared, background currents indicate that frontal instability, which utilizes the available potential energy associated with the horizontal temperature gradient within the layer, is responsible for the growth of the unstable waves. Interestingly, the unstable waves have negative energy due to the presence of the non-positive definite terms in the definition of the wave energy. A nonlinear solution for a zonally sheared, initial current simulates the observed wave-like patterns.

In the continuously stratified model, the unstable waves have positive energy and are generated by baroclinic instability. For a uniform background current, they are essentially the ageostrophic extensions of the Eady's baroclinic waves. For a zonally sheared current, they resemble the observed wave-like patterns, suggesting that the observed features are generated by ageostrophic baroclinic instability.

Although there are some differences between solutions in the layer and continuously stratified models, the layer system including vertically oriented isopycnals provides a reasonable alternative of the continuously stratified system. Moreover, the difference in wave energetics between the layer and continuously stratified models is likely an artifact of the different model formulations.

Comments

This work was supported by NSF grant OCE-89-12015 and by the ONR Coastal Sciences Program through grant N00014-90-J-1054 awarded to J. McCreary.

ORCID ID

D-1895-2012, 0000-0001-5798-9380

NSUWorks Citation

Yasushi Fukamachi. 1992. Instability of Density Fronts in Layer and Continuously Stratified Models. Doctoral dissertation. Nova Southeastern University. Retrieved from NSUWorks, Oceanographic Center. (64)
https://nsuworks.nova.edu/occ_stuetd/64.