Comparing vorticity and curvature Rossby numbers.

Area of Science:

• Ocean dynamics
• Fluid mechanics
• Geophysical fluid dynamics

Background:

• Assessing the nonlinear term's significance relative to the Coriolis term in ocean momentum equations is vital.
• The bulk Rossby number is insufficient for point-by-point nonlinearity assessment, necessitating the pointwise Rossby number.

Purpose of the Study:

• To compare the accuracy of two approximate formulations of the pointwise Rossby number: the vorticity Rossby number and the curvature Rossby number.
• To determine which formulation is more suitable for diagnosing nonlinearity in ocean circulation.

Main Methods:

• Theoretical analysis of the Rossby number formulations.
• Data analysis of oceanic flows.

Main Results:

• The vorticity Rossby number overestimates oceanic flow nonlinearity by neglecting kinetic energy spatial variations.
• The curvature Rossby number inherently includes kinetic energy considerations, proving more accurate.

Conclusions:

• The curvature Rossby number is a more accurate and useful metric for diagnosing and understanding nonlinearity in ocean circulation.
• This improved understanding aids in better modeling and prediction of ocean dynamics.