Potential Vorticity in the Ocean: Ertel and Rossby Approaches with Estimates for the Lofoten Vortex

Abstract The potential vorticity (PV) in the ocean is considered, including the history of the term. Various aspects and basic formulas used to calculate the PV in practice are discussed; the conditions for the fulfillment of its conservation law are considered. Two approaches to the PV are consider...
Ausführliche Beschreibung

Abstract The potential vorticity (PV) in the ocean is considered, including the history of the term. Various aspects and basic formulas used to calculate the PV in practice are discussed; the conditions for the fulfillment of its conservation law are considered. Two approaches to the PV are considered: by Ertel and by Rossby. To illustrate the main conclusions, we estimate the PV for the quasi-permanent anticyclonic Lofoten vortex in the Norwegian Sea. We use the data of GLORYS12V1 global oceanic reanalysis for calculations of the PV. The PV by Ertel is ascertained to be a kinematic characteristic. It determines the vortex core, where its typical values are zero, while they can attain %$ - 1.0 \times {{10}^{{ - 10}}}%$ $ m^{–1} %$ s^{–1} $ at the core-periphery, where isopycnic lines thicken. The vertical and horizontal sections of the relative and potential vorticities are constructed. It is found that the horizontal components mainly contribute to the PV, while vertical components are much less significant. In contrast to the PV by Ertel, the PV by Rossby is a dynamic characteristic in the quasi-geostrophic approximation. The main contributor to it is the relative vorticity, which characterizes the rotation of particles. The volumetric PV characterizes the vortex power. The PV maximum is –1.3 × $ 10^{–5} $ $ s^{–1} $ and corresponds to a level of 500 m; the PV does not exceed 1.0 × $ 10^{–5} $ $ s^{–1} $ below 1000 m, and it is ~0.5 × $ 10^{–5} $ $ s^{–1} $ at a level of 3000 m. The volumetric PV for the Lofoten vortex is –9.82 × $ 10^{6} $ $ s^{–1} $. It is –2.28 × $ 10^{8} $ $ s^{–1} $ in the core (up to 1000 m). Ausführliche Beschreibung