scholarly journals Invariant manifolds in stratified turbulence

2019 ◽  
Vol 4 (5) ◽  
Author(s):  
N. E. Sujovolsky ◽  
G. B. Mindlin ◽  
P. D. Mininni
Keyword(s):  
Invariant Manifolds ◽  
Stratified Turbulence

Flow structures and kinetic-potential exchange in forced rotating stratified turbulence

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Tianyi Li ◽  
Minping Wan ◽  
Jianchun Wang ◽  
Shiyi Chen
Keyword(s):  
Flow Structures ◽  
Stratified Turbulence

scholarly journals Turbulent thermal diffusion in strongly stratified turbulence: Theory and experiments

2017 ◽  
Vol 2 (6) ◽  
Author(s):  
G. Amir ◽  
N. Bar ◽  
A. Eidelman ◽  
T. Elperin ◽  
N. Kleeorin ◽  
...  
Keyword(s):  
Thermal Diffusion ◽  
Turbulence Theory ◽  
Stratified Turbulence ◽  
Theory And Experiments

scholarly journals Correlation between Buoyancy Flux, Dissipation and Potential Vorticity in Rotating Stratified Turbulence

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 157
Author(s):  
Duane Rosenberg ◽  
Annick Pouquet ◽  
Raffaele Marino
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Potential Vorticity ◽  
Isotropic Turbulence ◽  
Joint Probability ◽  
Buoyancy Flux ◽  
Turbulent Regime ◽  
Stratified Turbulence ◽  
Low Dissipation ◽  
Linear And Nonlinear

We study in this paper the correlation between the buoyancy flux, the efficiency of energy dissipation and the linear and nonlinear components of potential vorticity, PV, a point-wise invariant of the Boussinesq equations, contrasting the three identified regimes of rotating stratified turbulence, namely wave-dominated, wave–eddy interactions and eddy-dominated. After recalling some of the main novel features of these flows compared to homogeneous isotropic turbulence, we specifically analyze three direct numerical simulations in the absence of forcing and performed on grids of 10243 points, one in each of these physical regimes. We focus in particular on the link between the point-wise buoyancy flux and the amount of kinetic energy dissipation and of linear and nonlinear PV. For flows dominated by waves, we find that the highest joint probability is for minimal kinetic energy dissipation (compared to the buoyancy flux), low dissipation efficiency and low nonlinear PV, whereas for flows dominated by nonlinear eddies, the highest correlation between dissipation and buoyancy flux occurs for weak flux and high localized nonlinear PV. We also show that the nonlinear potential vorticity is strongly correlated with high dissipation efficiency in the turbulent regime, corresponding to intermittent events, as observed in the atmosphere and oceans.

scholarly journals Turbulent fluxes of entropy and internal energy in temperature stratified flows

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
I. Rogachevskii ◽  
N. Kleeorin
Keyword(s):  
Mach Number ◽  
Internal Energy ◽  
Turbulent Flux ◽  
Stratified Flows ◽  
Fluid Temperature ◽  
Stratified Turbulence ◽  
Convective Flux ◽  
Low Mach Number ◽  
Linear Approach ◽  
The Mean

We derive equations for the mean entropy and the mean internal energy in low-Mach-number temperature stratified turbulence (i.e. for turbulent convection or stably stratified turbulence), and show that turbulent flux of entropy is given by$\boldsymbol{F}_{s}=\overline{{\it\rho}}\,\overline{\boldsymbol{u}s}$, where$\overline{{\it\rho}}$is the mean fluid density,$s$is fluctuation of entropy and overbars denote averaging over an ensemble of turbulent velocity fields,$\boldsymbol{u}$. We demonstrate that the turbulent flux of entropy is different from the turbulent convective flux,$\boldsymbol{F}_{c}=\overline{T}\,\overline{{\it\rho}}\,\overline{\boldsymbol{u}s}$, of the fluid internal energy, where$\overline{T}$is the mean fluid temperature. This turbulent convective flux is well-known in the astrophysical and geophysical literature, and it cannot be used as a turbulent flux in the equation for the mean entropy. This result is exact for low-Mach-number temperature stratified turbulence and is independent of the model used. We also derive equations for the velocity–entropy correlation,$\overline{\boldsymbol{u}s}$, in the limits of small and large Péclet numbers, using the quasi-linear approach and the spectral${\it\tau}$approximation, respectively. This study is important in view of different applications to astrophysical and geophysical temperature stratified turbulence.

scholarly journals Fast and slow invariant manifolds in chemical kinetics

2013 ◽  
Vol 65 (10) ◽  
pp. 1502-1515 ◽  
Author(s):  
V. Bykov ◽  
V. Gol’dshtein
Keyword(s):  
Chemical Kinetics ◽  
Invariant Manifolds

Local Mass Conservation and Velocity Splitting in PV-Based Balanced Models. Part II: Numerical Results

2007 ◽  
Vol 64 (6) ◽  
pp. 1794-1810 ◽  
Author(s):  
Ali R. Mohebalhojeh ◽  
Michael E. McIntyre
Keyword(s):  
Potential Vorticity ◽  
Wave Speed ◽  
Invariant Manifolds ◽  
Mass Conservation ◽  
Flow Speed ◽  
Local Mass ◽  
Potential Vorticity Inversion ◽  
Divergence Equation ◽  
Local Mass Conservation ◽  
Derivatives Of

The effects of enforcing local mass conservation on the accuracy of non-Hamiltonian potential-vorticity- based balanced models (PBMs) are examined numerically for a set of chaotic shallow-water f-plane vortical flows in a doubly periodic square domain. The flows are spawned by an unstable jet and all have domain-maximum Froude and Rossby numbers Fr ∼0.5 and Ro ∼1, far from the usual asymptotic limits Ro → 0, Fr → 0, with Fr defined in the standard way as flow speed over gravity wave speed. The PBMs considered are the plain and hyperbalance PBMs defined in Part I. More precisely, they are the plain-δδ, plain-γγ, and plain-δγ PBMs and the corresponding hyperbalance PBMs, of various orders, where “order” is related to the number of time derivatives of the divergence equation used in defining balance and potential-vorticity inversion. For brevity the corresponding hyperbalance PBMs are called the hyper-δδ, hyper-γγ, and hyper-δγ PBMs, respectively. As proved in Part I, except for the leading-order plain-γγ each plain PBM violates local mass conservation. Each hyperbalance PBM results from enforcing local mass conservation on the corresponding plain PBM. The process of thus deriving a hyperbalance PBM from a plain PBM is referred to for brevity as plain-to-hyper conversion. The question is whether such conversion degrades the accuracy, as conjectured by McIntyre and Norton. Cumulative accuracy is tested by running each PBM alongside a suitably initialized primitive equation (PE) model for up to 30 days, corresponding to many vortex rotations. The accuracy is sensitively measured by the smallness of the ratio ϵ = ||QPBM − QPE||2/||QPE||2, where QPBM and QPE denote the potential vorticity fields of the PBM and the PEs, respectively, and || ||2 is the L2 norm. At 30 days the most accurate PBMs have ϵ ≈ 10−2 with PV fields hardly distinguishable visually from those of the PEs, even down to tiny details. Most accurate is defined by minimizing ϵ over all orders and truncation types δδ, γγ, and δγ. Contrary to McIntyre and Norton’s conjecture, the minimal ϵ values did not differ systematically or significantly between plain and hyperbalance PBMs. The smallness of ϵ suggests that the slow manifolds defined by the balance relations of the most accurate PBMs, both plain and hyperbalance, are astonishingly close to being invariant manifolds of the PEs, at least throughout those parts of phase space for which Ro ≲ 1 and Fr ≲ 0.5. As another way of quantifying the departures from such invariance, that is, of quantifying the fuzziness of the PEs’ slow quasimanifold, initialization experiments starting at days 1, 2, . . . 10 were carried out in which attention was focused on the amplitudes of inertia–gravity waves representing the imbalance arising in 1-day PE runs. With balance defined by the most accurate PBMs, and imbalance by departures therefrom, the results of the initialization experiments suggest a negative correlation between early imbalance and late cumulative error ϵ. In such near-optimal conditions the imbalance seems to be acting like weak background noise producing an effect analogous to so-called stochastic resonance, in that a slight increase in noise level brings PE behavior closer to the balanced behavior defined by the most accurate PBMs when measured cumulatively over 30 days.

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