Published on September 14, 2023
–
Updated on September 28, 2024
Dates
on the September 19, 2023
10:30 am
Location
Observatoire de la Côte d'Azur - NEF
Dissipation in turbulence in the presence of waves, and its intermittency scaling in rotating stratified flows.
Fluids and plasmas with large Reynolds numbers need a way to dissipate energy, beyond
particle acceleration at small scales. Turbulence offers a clear possibility through nonlin-
ear couplings and the systematic formation of strong localized gradients, for instance in
the form of current, vorticity and shear structures. Moreover, the dissipation occurring
in such flows can actually be determined through the use of exact laws derived from, e.g.,
energy and helicity conservation, as is the case for the solar wind and the magnetosphere.
Why and how dissipation takes place physically in hydrodynamics, magnetohydrody-
namics and in other complex nonlinear systems as in the atmosphere, the ocean, the
solar wind, the sun, the interstellar medium and beyond, is briefly presented, starting
from basic considerations. The role of waves – such as those due to gravity, rotation or
magnetic fields – is then analyzed in this context in terms of one governing parameter,
namely the ratio of the wave period to the (turbulent) eddy turn-over time. It is shown
that the spatially localized dissipation in such systems can be, in some cases and by some
measure, stronger than for homogeneous isotropic turbulence. This is associated with
the occurence of non-Gaussian probability distribution functions for velocity gradients,
as well as for the vertical velocity itself in rotating stratified turbulent flows (RST).
The intermittency which characterizes these systems is analyzed in more detail for RST
through the joint behavior of normalized third and fourth-order moments, namely the
skewness S and kurtosis K, for various fields [1]. Parabolic scaling for K(S) is observed
in some cases. It is similar to (but different from) previous results for a variety of fields
and systems, including the atmospheric boundary layer, climate re-analysis data, fusion
plasmas, the solar wind, as well as in galaxies. For quasi-geostrophic (quasi-2D) forcing,
a sharp scaling transition takes place once the Ozmidov length scale ℓOz is larger than
the dissipation scale– ℓOz being the scale after which a turbulent Kolmogorov isotropic
energy spectrum may recover at high Reynolds and buoyancy Reynolds numbers.
[1] A. Pouquet, D. Rosenberg, R. Marino and P. Mininni: Intermittency scaling for mixing and
dissipation in rotating stratified turbulence at the edge of instability. Atmosphere, Special Issue
in the honor of Jack Herring†. Under revision, August 2023.
particle acceleration at small scales. Turbulence offers a clear possibility through nonlin-
ear couplings and the systematic formation of strong localized gradients, for instance in
the form of current, vorticity and shear structures. Moreover, the dissipation occurring
in such flows can actually be determined through the use of exact laws derived from, e.g.,
energy and helicity conservation, as is the case for the solar wind and the magnetosphere.
Why and how dissipation takes place physically in hydrodynamics, magnetohydrody-
namics and in other complex nonlinear systems as in the atmosphere, the ocean, the
solar wind, the sun, the interstellar medium and beyond, is briefly presented, starting
from basic considerations. The role of waves – such as those due to gravity, rotation or
magnetic fields – is then analyzed in this context in terms of one governing parameter,
namely the ratio of the wave period to the (turbulent) eddy turn-over time. It is shown
that the spatially localized dissipation in such systems can be, in some cases and by some
measure, stronger than for homogeneous isotropic turbulence. This is associated with
the occurence of non-Gaussian probability distribution functions for velocity gradients,
as well as for the vertical velocity itself in rotating stratified turbulent flows (RST).
The intermittency which characterizes these systems is analyzed in more detail for RST
through the joint behavior of normalized third and fourth-order moments, namely the
skewness S and kurtosis K, for various fields [1]. Parabolic scaling for K(S) is observed
in some cases. It is similar to (but different from) previous results for a variety of fields
and systems, including the atmospheric boundary layer, climate re-analysis data, fusion
plasmas, the solar wind, as well as in galaxies. For quasi-geostrophic (quasi-2D) forcing,
a sharp scaling transition takes place once the Ozmidov length scale ℓOz is larger than
the dissipation scale– ℓOz being the scale after which a turbulent Kolmogorov isotropic
energy spectrum may recover at high Reynolds and buoyancy Reynolds numbers.
[1] A. Pouquet, D. Rosenberg, R. Marino and P. Mininni: Intermittency scaling for mixing and
dissipation in rotating stratified turbulence at the edge of instability. Atmosphere, Special Issue
in the honor of Jack Herring†. Under revision, August 2023.