This article was accepted into the corpus but its outbound wikilinks were never NER-processed — typical at the deepest BFS hop or when the run's entity cap was reached. No expansion funnel to show.
| Ekman number | |
|---|---|
| Name | Ekman number |
| Quantity | ratio of viscous to Coriolis forces |
Ekman number The Ekman number is a dimensionless parameter that quantifies the relative importance of viscous forces to Coriolis forces in rotating flows. It appears in the study of boundary layers, geophysical fluid dynamics, oceanography, atmospheric science, planetary science, and engineering where rotation influences momentum transport. The Ekman number helps characterize regimes in which rotation dominates viscous dissipation versus those in which viscosity controls flow structure.
The Ekman number is defined as the ratio of viscous forces to Coriolis forces in a rotating frame and thereby indicates whether rotation-induced effects such as Ekman spirals, boundary layers, and Taylor columns will be prominent. In contexts such as Atlantic Ocean, Pacific Ocean, Southern Ocean, Arctic Ocean, and Indian Ocean dynamics, low Ekman numbers imply strong rotational constraint and quasi-geostrophic balance, whereas high Ekman numbers indicate viscous-dominated flows found near Mississippi River delta, Rio de la Plata, and industrial rotating machinery like gas turbine bearings. In planetary settings including Earth, Mars, Venus, Jupiter, Saturn, and Titan, Ekman number helps diagnose atmospheric and interior dynamics relative to effects studied in Coriolis force contexts such as the Coriolis effect and Taylor–Proudman theorem.
Ekman number is typically expressed as Ek = ν / (2 Ω L^2) or variants Ek = ν / (Ω L^2), where ν is kinematic viscosity, Ω is angular rotation rate, and L is a characteristic length scale used in analyses of flows around features like Gulf Stream, Kuroshio Current, Icelandic Low, Aleutian Low, and structures in continental shelf regions. This form connects to nondimensionalization procedures used in studies by institutions such as National Oceanic and Atmospheric Administration, Woods Hole Oceanographic Institution, Scripps Institution of Oceanography, Max Planck Institute for Meteorology, and British Antarctic Survey.
Ekman number is central to modeling oceanic boundary layers beneath features such as Ekman layer-related upwelling along the Peruvian coast, wind-driven circulation in the Mediterranean Sea, and coastal currents adjacent to Cape Horn and Cape of Good Hope. It informs atmospheric boundary layer studies over Amazon Rainforest, Sahara Desert, and polar regions like Antarctic Peninsula. In engineering, Ekman number considerations appear in rotating equipment design at Rolls-Royce and General Electric, in laboratory rotating tank experiments at MIT, Caltech, and University of Cambridge, and in planetary mission planning by organizations such as NASA and European Space Agency.
Derivation begins from the Navier–Stokes equations in a rotating frame employed in analyses by authors associated with Imperial College London, Princeton University, University of Oxford, Columbia University, and University of Washington. Non-dimensionalization with velocity scale U and length L yields nondimensional momentum balance terms including viscous term (ν U/L^2) and Coriolis term (Ω U), whose ratio defines Ekman number. This procedure parallels derivations of other parameters like Rossby number, Reynolds number, and Prandtl number used in canonical works by researchers at Lamont–Doherty Earth Observatory, Jet Propulsion Laboratory, and National Aeronautics and Space Administration.
Typical Ekman numbers vary widely: in large-scale ocean gyres such as the North Atlantic Gyre and North Pacific Gyre Ek ≪ 1, often 10^(-8)–10^(-4); in laboratory rotating tanks and experiments at University of California, Berkeley or University of Exeter Ek ~ 10^(-6)–10^(-2); in planetary cores like Earth's core or Mercury flows Ek can be extremely small, 10^(-15)–10^(-9); in engineering rotors and seals associated with Siemens and ABB operations Ek may approach O(1). These scalings interact with other nondimensional parameters in systems such as El Niño–Southern Oscillation and mesoscale eddies in the Gulf Stream.
Laboratory measurements of Ekman-layer phenomena have been conducted in rotating tank experiments at facilities including Scripps Institution of Oceanography, Leeds University, and CNRS laboratories, using techniques developed in studies of Taylor–Couette flow and von Kármán flow. Numerical estimation uses computational fluid dynamics codes from groups at Stanford University, Lawrence Livermore National Laboratory, Los Alamos National Laboratory, and open-source projects like MITgcm and ROMS, resolving viscous and Coriolis terms to compute Ekman number diagnostics in simulations of Atlantic Meridional Overturning Circulation and Arctic sea ice dynamics.
Ekman number links to and is compared with dimensionless numbers including Reynolds number, Rossby number, Prandtl number, Ekman layer depth scales (related to Burger number), and parameters used in planetary fluid studies such as the Elsasser number and Magnetic Reynolds number. Understanding combinations of these parameters is crucial in frameworks developed by research groups at University of Cambridge (UK), Caltech, ETH Zurich, University of Tokyo, and University of British Columbia.
Category:Dimensionless numbers