Laboratory, numerical, and oceanic fossil turbulence in rotating and stratified flows

Abstract

Turbulent eddy motions are produced, and characterized, by inertial‐vortex forces. Growth of the energy, or Obukhov, scale L₀ is constrained by buoyancy and Coriolis forces at the stratified fossil Ozmidov L_R0 and rotational fossil Hopfinger L_Ω0 length scales, and constrained at all scales by viscous, buoyancy, and Coriolis forces at sizes proportional to the stratified fossil Kolmogorov L_KF and rotational fossil Kolmogorov L_Kƒ length scales, respectively. Universal constants of proportionality between turbulence wavelengths and these fossil turbulence length scales at their respective buoyant‐inertial, Coriolis‐inertial, buoyant‐inertial‐viscous, and Coriolis‐inertial‐viscous transitions are inferred from available laboratory, numerical, and field studies. It is important to distinguish between turbulence, which entrains, and these nonturbulent, or fossil turbulence, internal waves, Coriolis‐inertial eddies, and viscous flow regimes, which are nonlinear remnants of turbulence but do not entrain and have other properties different from turbulence. Hydrodynamic phase diagrams based on the universal constants of transition may be used to classify microstructure and mesostructure as actively turbulent, active‐fossil, fossil, or nonturbulent. One advantage of making these distinctions is to avoid undersampling errors from data sets consisting only of fossil turbulence microstructure and mesostructure. This may improve the reliability of dissipation methods used for estimating average heat, mass, and momentum fluxes in the ocean and atmosphere from microstructure and mesostructure data.