An official website of the United States government
The mean state of the atmosphere and ocean is set through a balance between external forcing (radiation, winds, heat and freshwater fluxes) and the emergent turbulence, which transfers energy to dissipative structures. The forcing gives rise to jets in the atmosphere and currents in the ocean, which spontaneously develop turbulent eddies through the baroclinic instability. A critical step in the development of a theory of climate is to properly include the eddy-induced turbulent transport of properties like heat, moisture, and carbon. In the linear stages, baroclinic instability generates flow structures at the Rossby deformation radius, a length scale of order 1,000 km in the atmosphere and 100 km in the ocean, smaller than the planetary scale and the typical extent of ocean basins, respectively. There is, therefore, a separation of scales between the large-scale gradient of properties like temperature and the smaller eddies that advect it randomly, inducing effective diffusion. Numerical solutions show that such scale separation remains in the strongly nonlinear turbulent regime, provided there is sufficient drag at the bottom of the atmosphere and ocean. We compute the scaling laws governing the eddy-driven transport associated with baroclinic turbulence. First, we provide a theoretical underpinning for empirical scaling laws reported in previous studies, for different formulations of the bottom drag law. Second, these scaling laws are shown to provide an important first step toward an accurate local closure to predict the impact of baroclinic turbulence in setting the large-scale temperature profiles in the atmosphere and ocean.
more »
« less
Predicting the Slowing of Stellar Differential Rotation by Instability-driven Turbulence
Abstract Differentially rotating stars and planets transport angular momentum (AM) internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the axisymmetric Goldreich–Schubert–Fricke instability at the stellar equator with radial differential rotation. This instability arises when fast thermal diffusion eliminates the stabilizing effects of buoyancy forces in a system where a stabilizing entropy gradient dominates over the destabilizing AM gradient. Our turbulence closure invokes a dominant three-wave coupling between pairs of linearly unstable eigenmodes and a near-zero frequency, viscously damped eigenmode that features latitudinal jets. We derive turbulent transport rates of momentum and heat and provide them in analytic forms. Such formulae, free of tunable model parameters, are tested against direct numerical simulations; the comparison shows good agreement. They improve upon prior quasi-linear or “parasitic saturation” models containing a free parameter. Given model correspondences, we also extend this theory to heat and compositional transport for axisymmetric thermohaline-instability-driven turbulence in certain regimes.
more »
« less
- Award ID(s):
- 2409206
- PAR ID:
- 10587310
- Publisher / Repository:
- American Astronomical Society
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 966
- Issue:
- 2
- ISSN:
- 0004-637X
- Page Range / eLocation ID:
- 195
- Subject(s) / Keyword(s):
- Astrophysical fluid dynamics, Solar differential rotation, Stellar rotation, Stellar interiors, Hydrodynamics, Extrasolar gaseous giant planets
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Visco-resistive magnetohydrodynamic turbulence, driven by a two-dimensional unstable shear layer that is maintained by an imposed body force, is examined by decomposing it into dissipationless linear eigenmodes of the initial profiles. The down-gradient momentum flux, as expected, originates from the large-scale instability. However, continual up-gradient momentum transport by large-scale linearly stable but nonlinearly excited eigenmodes is identified, and found to nearly cancel the down-gradient transport by unstable modes. The stable modes effectuate this by depleting the large-scale turbulent fluctuations via energy transfer to the mean flow. This establishes a physical mechanism underlying the long-known observation that coherent vortices formed from nonlinear saturation of the instability reduce turbulent transport and fluctuations, as such vortices are composed of both the stable and unstable modes, which are nearly equal in their amplitudes. The impact of magnetic fields on the nonlinearly excited stable modes is then quantified. Even when imposing a strong magnetic field that almost completely suppresses the instability, the up-gradient transport by the stable modes is at least two-thirds of the down-gradient transport by the unstable modes, whereas for weaker fields, this fraction reaches up to 98% . These effects are persistent with variations in magnetic Prandtl number and forcing strength. Finally, continuum modes are shown to be energetically less important, but essential for capturing the magnetic fluctuations and Maxwell stress. A simple analytical scaling law is derived for their saturated turbulent amplitudes. It predicts the fall-off rate as the inverse of the Fourier wavenumber, a property which is confirmed in numerical simulations.more » « less
-
Abstract This study investigates how Langmuir turbulence (LT) driven by Stokes drift shear affects the heated ocean surface boundary layer (OSBL) based on turbulence-resolving large-eddy simulations (LES) and assesses an analytic vertical mixing parameterization based on a simplified second-moment closure (SMC) approach. Diurnal solar heating forces OSBL shoaling to generate a diurnal warm layer (DWL) in which heat and momentum are trapped. Without LT, relatively weak turbulent mixing results in a near-surface jet that is associated with enhanced turbulent kinetic energy (TKE) production of shear-driven turbulence (ST), which approximately balances TKE dissipation rates. Conversely, LT maintains strong mixing, delaying the DWL formation and preventing the TKE dissipation enhancement by generating a less sheared jet. However, sufficiently strong heating destroys TKE to ultimately reduce mixing and to create more sheared jets, which effectively shifts the LT to an ST-dominated regime. A second-moment turbulence budget analysis suggests that 1) the near-surface OSBL responds rapidly to the surface forcing, 2) Stokes drift impacts heat and momentum budgets in profoundly different ways, and 3) buoyancy terms are to leading order negligible. Building on these findings and introducing a physics-based mixing length, we develop a simplified SMC model that can be solved for near-surface expressions for key turbulent variables and mixing coefficients in terms of known variables. For ST, these expressions are consistent with the Monin–Obukhov similarity theory. For LT, these expressions reveal a fundamental dependence of turbulent variables on Stokes drift shear.more » « less
-
Abstract A high-resolution fourth-order Padé scheme is used to simulate locally isothermal 3D disk turbulence driven by the vertical shear instability (VSI) using 268.4 M points. In the early nonlinear period of axisymmetric VSI, angular momentum transport by vertical jets creates correlatedN-shaped radial profiles of perturbation vertical and azimuthal velocity. This implies dominance of positive perturbation vertical vorticity layers and a recently discovered angular momentum staircase with respect to radius (r). These features are present in 3D in a weaker form. The 3D flow consists of vertically and azimuthally coherent turbulent shear layers containing small vortices with all three vorticity components active. Previously observed large persistent vortices in the interior of the domain driven by the Rossby wave instability are absent. We speculate that this is due to a weaker angular momentum staircase in 3D in the present simulations compared to a previous simulation. The turbulent viscosity parameterα(r) increases linearly withr. At intermediate resolution, the value ofα(r) at midradius is close to that of a previous simulation. The specific kinetic energy spectrum with respect to radial wavenumber has a power-law region with exponent −1.84, close to the value −2 expected for shear layers. The spectrum with respect to azimuthal wavenumber has a −5/3 region and lacks a −5 region reported in an earlier study. Finally, it is found that axisymmetric VSI has artifacts at late times, including a very strong angular momentum staircase, which in 3D is present weakly in the disk’s upper layers.more » « less
-
ABSTRACT Active Galactic Nuclei (AGN) are believed to provide the energy that prevents runaway cooling of gas in the cores of galaxy clusters. However, how this energy is transported and thermalized throughout the Intracluster Medium (ICM) remains unclear. In recent work, we showed that streaming cosmic rays (CRs) destabilize sound waves in dilute ICM plasmas. Here, we show that CR streaming in the presence of gravity also destabilizes a pressure-balanced wave. We term this new instability the CR buoyancy instability (CRBI). In stark contrast to standard results without CRs, the pressure-balanced mode is highly compressible at short wavelengths due to CR streaming. Maximal growth rates are of order (pc/pg)β1/2ωff, where pc/pg is the ratio of CR pressure to thermal gas pressure, β is the ratio of thermal to magnetic pressure, and ωff is the free-fall frequency. The CRBI operates alongside buoyancy instabilities driven by background heat fluxes, i.e. the heat-flux-driven buoyancy instability (HBI) and the magneto-thermal instability (MTI). When the thermal mean free path lmfp is ≪ the gas scale height H, the HBI/MTI set the growth rate on large scales, while the CRBI sets the growth rate on small scales. Conversely, when lmfp ∼ H and (pc/pg)β1/2 ≳ 1, CRBI growth rates exceed HBI/MTI growth rates even on large scales. Our results suggest that CR-driven instabilities may be partially responsible for the sound waves/weak shocks and turbulence observed in galaxy clusters. CR-driven instabilities generated near radio bubbles may also play an important role redistributing AGN energy throughout clusters.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3847/1538-4357/ad38c3
