Fossil Two-Dimensional Turbulence in the Ocean

Abstract

Turbulence in the stratified ocean is constrained at large vertical scales by buoyancy forces, leaving remnant internal waves and temperature and salinity fluctuations, termed fossil turbulence, that persist after the flow is no longer actively turbulent (with inertial-force dominated eddies) at the scales of the fluctuations. Most patches of ocean temperature microstructure are fossil turbulence (no longer turbulent) at the largest scales, and moving as buoyancy-dominated internal waves with embedded active turbulent motions (if any) only at smaller scales. Larger scale two-dimensional turbulent motions may grow in the horizontal until contrained by Coriolis forces to form eddy-like Coriolis-inertial “waves” with embedded, smaller scale, active 2-D and 3-D turbulence. The remnant horizontal fluctuations in the scalar and vorticity fields that persist after the fluid motions are no longer active 2-D turbulence at the scale of the fluctuations are termed fossil 2-D turbulence. By preserving the largest scales L _wo of the previous active 2-D turbulence the 2-D fossils preserve information about the dissipation rate ε₀ that existed when fossilization of the 2-D turbulence began assuming L _w0 = C _Ω L _{Ω 0}, where L _{Ω 0} = (ε ₀/f ³)^1/2 is the Coriolis-inertial (or Hopfinger) length scale at fossilization, f is the Coriolis parameter 2Ω sin Φ, Ω is the rotation rate, Φ is the latitude and C _Ω is a universal constant of order 1.