Intermittency Scaling for Mixing and Dissipation in Rotating Stratified Turbulence at the Edge of Instability

Many issues pioneered by Jackson Herring deal with how nonlinear interactions shape atmospheric dynamics. In this context, we analyze new direct numerical simulations of rotating stratified flows with a large-scale forcing, which is either random or quasi-geostrophic (QG). Runs were performed at a moderate Reynolds number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> and up to 1646 turn-over times in one case. We found intermittent fluctuations of the vertical velocity <i>w</i> and temperature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula> in a narrow domain of parameters as for decaying flows. Preliminary results indicate that parabolic relations between normalized third- and fourth-order moments of the buoyancy flux <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∝</mo><mfenced separators="" open="⟨" close="⟩"><mi>w</mi><mi>θ</mi></mfenced></mrow></semantics></math></inline-formula> and of the energy dissipation emerge in this domain, including for passive and active scalars, with or without rotation. These are reminiscent of (but not identical to) previous findings for other variables and systems such as oceanic and atmospheric flows, climate re-analysis data, fusion plasmas, the Solar Wind, or galaxies. For QG forcing, sharp scaling transitions take place once the Ozmidov length scale <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ℓ</mi><mrow><mi>O</mi><mi>z</mi></mrow></msub></semantics></math></inline-formula> is resolved—<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ℓ</mi><mrow><mi>O</mi><mi>z</mi></mrow></msub></semantics></math></inline-formula> being the scale after which a turbulent Kolmogorov energy spectrum likely recovers at high <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula>.