The energy flux number and three types of planetary dynamo

It is proposed that the existence and nature of a planetary dynamo can be characterized by a dimensionless number Φ ≡ F e R /ϱλ 2 ω, called the energy flux number, where F e is the energy flux available for dynamo generation, R is the core radius (or thickness of the dynamo generating region), ϱ is the fluid density, λ is the magnetic diffusivity and ω is the angular velocity. For Φ ≲ 1, there is no dynamo. For 1 ≲ Φ ≲ 10 2.5 there is an “energy‐limited dynamo”, in which F e is insufficient to enable the dynamo to reach the dynamically desirable state A ≡ B 2 /8πϱλω ∼ 1, where B is a typical field amplitude (in Gauss). For 10 2.5 ≲ Φ ≲ 10 5 , there is a dynamically determined dynamo (Λ ∼ 1) in which the magnetic Reynolds number of turbulent eddies is small. For Φ ≳ 10 5 , there is a turbulent dynamo. Probable planetary examples of these three dynamo states are Mercury (Φ ∼ 10 2 ‐10 3 ), Earth (Φ ∼ 10 4 ) and Jupiter (Φ ∼ 10 11 ), respectively.