Geometrical effects on western intensification of wind-driven ocean currents: The rotated-channel Stommel model, coastal orientation, and curvature

- Theoretical and numerical revisiting of steady state western boundary jets (Gulf Stream, etc.).
- New theorem that describes how coastal orientations thickens a western boundary layer.
- Matched asymptotics analysis of the effects of curving coastlines.
- Introduces a simple rotated channel model to analyze western boundary currents.
- Numerical solutions in disk, parabolic, squircle-bounded and other complex ocean shapes.

We revisit early models of steady western boundary currents [Gulf Stream, Kuroshio, etc.] to explore the role of irregular coastlines on jets, both to advance the research frontier and to illuminate for education. In the framework of a steady-state, quasigeostrophic model with viscosity, bottom friction and nonlinearity, we prove that rotating a straight coastline, initially parallel to the meridians, significantly thickens the western boundary layer. We analyze an infinitely long, straight channel with arbitrary orientation and bottom friction using an exact solution and singular perturbation theory, and show that the model, though simpler than Stommel's, nevertheless captures both the western boundary jet (“Gulf Stream”) and the “orientation effect”. In the rest of the article, we restrict attention to the Stommel flow (that is, linear and inviscid except for bottom friction) and apply matched asymptotic expansions, radial basis function, Fourier-Chebyshev and Chebyshev-Chebyshev pseudospectral methods to explore the effects of coastal geometry in a variety of non-rectangular domains bounded by a circle, parabolas and squircles. Although our oceans are unabashedly idealized, the narrow spikes, broad jets and stationary points vividly illustrate the power and complexity of coastal control of western boundary layers.