اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA hierarchy of energy- and flux-budget (EFB) turbulence closure models for stably stratified geophysical flows
390
0
0.0
(
0
)
تأليف
S.S. Zilitinkevich
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper we advance physical background of the energy- and flux-budget turbulence closure based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, and a new relaxation equation for the turbulent dissipation time-scale. The closure is designed for stratified geophysical flows from neutral to very stable and accounts for the Earth rotation. In accordance to modern experimental evidence, the closure implies maintaining of turbulence by the velocity shear at any gradient Richardson number Ri, and distinguishes between the two principally different regimes: strong turbulence at Ri << 1 typical of boundary-layer flows and characterised by the practically constant turbulent Prandtl number; and weak turbulence at Ri > 1 typical of the free atmosphere or deep ocean, where the turbulent Prandtl number asymptotically linearly increases with increasing Ri (which implies very strong suppression of the heat transfer compared to the momentum transfer). For use in different applications, the closure is formulated at different levels of complexity, from the local algebraic model relevant to the steady-state regime of turbulence to a hierarchy of non-local closures including simpler down-gradient models, presented in terms of the eddy-viscosity and eddy-conductivity, and general non-gradient model based on prognostic equations for all basic parameters of turbulence including turbulent fluxes.
قيم البحث
اقرأ أيضاً
The energy and flux budget (EFB) closure theory for a passive scalar (non-buoyant and non-inertial particles or gaseous admixtures) is developed for stably stratified turbulence. The physical background of the EFB turbulence closures is based on the
budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, as well as the turbulent flux of particles. The EFB turbulence closure is designed for stratified geophysical flows from neutral to very stable stratification and it implies that turbulence is maintained by the velocity shear at any stratification. In a steady-state, expressions for the turbulent flux of passive scalar and the anisotropic non-symmetric turbulent diffusion tensor are derived, and universal flux Richardson number dependencies of the components of this tensor are obtained. The diagonal component in the vertical direction of the turbulent diffusion tensor is suppressed by strong stratification, while the diagonal components in the horizontal directions are not suppressed, and they are dominant in comparison with the other components of turbulent diffusion tensor. This implies that any initially created strongly inhomogeneous particle cloud is evolved into a thin pancake in horizontal plane with very slow increase of its thickness in the vertical direction. The turbulent Schmidt number increases linearly with the gradient Richardson number. Considering the applications of these results to the atmospheric boundary-layer turbulence, the theoretical relationships are derived which allow to determine the turbulent diffusion tensor as a function of the vertical coordinate measured in the units of the local Obukhov length scale. The obtained relations are potentially useful in modelling applications of particle dispersion in the atmospheric boundary-layer turbulence and free atmosphere turbulence.
We have advanced the energy and flux budget (EFB) turbulence closure theory that takes into account a two-way coupling between internal gravity waves (IGW) and the shear-free stably stratified turbulence. This theory is based on the budget equation f
or the total (kinetic plus potential) energy of IGW, the budget equations for the kinetic and potential energies of fluid turbulence, and turbulent fluxes of potential temperature for waves and fluid flow. The waves emitted at a certain level, propagate upward, and the losses of wave energy cause the production of turbulence energy. We demonstrate that due to the nonlinear effects more intensive waves produce more strong turbulence, and this, in turns, results in strong damping of IGW. As a result, the penetration length of more intensive waves is shorter than that of less intensive IGW. The anisotropy of the turbulence produced by less intensive IGW is stronger than that caused by more intensive waves. The low amplitude IGW produce turbulence consisting up to 90 % of turbulent potential energy. This resembles the properties of the observed high altitude tropospheric strongly anisotropic (nearly two-dimensional) turbulence.
We observe the emergence of strong vertical drafts in direct numerical simulations of the Boussinesq equations in a range of parameters of geophysical interest. These structures, which appear intermittently in space and time, generate turbulence and
enhance kinetic and potential energy dissipation, providing an explanation for the observed variability of the local energy dissipation in the ocean and the modulation of its probability distribution function. We show how, due to the extreme drafts, in runs with Froude numbers observable in oceans, roughly $10%$ of the domain flow can account for up to $50%$ of the total volume dissipation, consistently with recent estimates based on oceanic models.
Stably stratified layers are present in stellar interiors (radiative zones) as well as planetary interiors - recent observations and theoretical studies of the Earths magnetic field seem to indicate the presence of a thin, stably stratified layer at
the top of the liquid outer core. We present direct numerical simulations of this region, which is modelled as an axisymmetric spherical Couette flow for a stably stratified fluid embedded in a dipolar magnetic field. For strong magnetic fields, a super-rotating shear layer, rotating nearly 30% faster than the imposed rotation rate difference between the inner convective dynamo region and the outer boundary, is generated in the stably stratified region. In the Earth context, and contrary to what was previously believed, we show that this super-rotation may extend towards the Earth magnetostrophic regime if the density stratification is sufficiently large. The corresponding differential rotation triggers magnetohydrodynamic instabilities and waves in the stratified region, which feature growth rates comparable to the observed timescale for geomagnetic secular variations and jerks. In the stellar context, we perform a linear analysis which shows that similar instabilities are likely to arise, and we argue that it may play a role in explaining the observed magnetic dichotomy among intermediate-mass stars.
In this study, the stability dependence of turbulent Prandtl number ($Pr_t$) is quantified via a novel and simple analytical approach. Based on the variance and flux budget equations, a hybrid length scale formulation is first proposed and its functi
onal relationships to well-known length scales are established. Next, the ratios of these length scales are utilized to derive an explicit relationship between $Pr_t$ and gradient Richardson number. In addition, theoretical predictions are made for several key turbulence variables (e.g., dissipation rates, normalized fluxes). The results from our proposed approach are compared against other competing formulations as well as published datasets. Overall, the agreement between the different approaches is rather good despite their different theoretical foundations and assumptions.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
