Emergence of optimal disturbances in a stratified turbulent shear flow under the stochastic forcing

Large-scale inclined organized structures in stably stratified turbulent shear flows were revealed in the numerical simulation and indirectly confirmed by the field measurements in the stable atmospheric boundary layer. Spatial scales and forms of these structures coincide with those of the optimal disturbances of a simplified linear model. In this paper, we clarify the relation between the organized structures and the optimal disturbances, analyzing a time series of turbulent fields obtained by the RANS model with eddy viscosity/diffusivity and stochastic forcing generating the small-scale turbulence.

Optimal energy growth in stably stratified turbulent Couette flow

<p>In this report, we will try to explain the emergence of large-scale organized structures in stably stratified turbulent flows using optimal disturbances of the mean turbulent flow. These structures have been recently obtained in numerical simulations of turbulent stably stratified flows [1] (Ekman layer, LES) and [2] (plane Couette flow, DNS and LES) and indirectly confirmed by field measurements in the stable boundary layer of the atmosphere [1, 2]. In instantaneous temperature fields they manifest themselves as irregular inclined thin layers with large gradients (fronts), spaced from each other by distances comparable to the height of the entire turbulent layer, and separated by regions with weak stratification.</p><p>Optimal disturbances of a stably stratified turbulent plane Couette flow are investigated in a wide range of Reynolds and Richardson numbers. These disturbances were computed based on a simplified linearized system of equations in which turbulent Reynolds stresses and heat fluxes were approximated by isotropic viscosity and diffusion with coefficients obtained from DNS results. It was shown [3] that the spatial scales and configurations of the inclined structures extracted from DNS data coincide with the ones obtained from optimal disturbances of the mean turbulent flow.</p><p>Critical value of the stability parameter is found starting from which the optimal disturbances resemble inclined structures. The physical mechanisms that determine the evolution, energetics and spatial configuration of these optimal disturbances are discussed. The effects due to the presence of stable stratification are highlighted.</p><p>Numerical experiments with optimal disturbances were supported by the RSF (grant No. 17-71-20149). Direct numerical simulation of stratified turbulent Couette flow was supported by the RFBR (grant No. 20-05-00776).</p><p>References:</p><p>[1] P.P. Sullivan, J.C. Weil, E.G. Patton, H.J. Jonker, D.V. Mironov. Turbulent winds and temperature fronts in large-eddy simulations of the stable atmospheric boundary layer // J. Atmos. Sci., 2016, V. 73, P. 1815-1840.</p><p>[2] A.V. Glazunov, E.V. Mortikov, K.V. Barskov, E.V. Kadantsev, S.S. Zilitinkevich. Layered structure of stably stratified turbulent shear flows // Izv. Atmos. Ocean. Phys., 2019, V. 55, P. 312–323.</p><p>[3] G.V. Zasko, A.V. Glazunov, E.V. Mortikov, Yu.M. Nechepurenko. Large-scale structures in stratified turbulent Couette flow and optimal disturbances // Russ. J. Num. Anal. Math. Model., 2010, V. 35, P. 35–53.</p>

Output tracking control for TRMS based on time receding optimal observation of disturbances

The paper presents an approach to design the adaptive output tracking controller for disturbed Twin Rotor Multi-Input Multi-Output System (TRMS) by using a time receding observer of functional disturbances for compensative control purpose, without using conventional methods as a neural network. To do this, first the disturbed Euler-Lagrange model of TRMS is converted to an equivalent bilinear form. And then, secondly an optimal disturbances estimator for this disturbed bilinear system is constructed based on time receding minimizing their effect. The complete output tracking controller for TRMS is created then by combining an exact linearization controller with the proposed disturbances estimation mechanism. Simulation results show that the here suggested controller meet completely the expected output tracking performances.

Large organized structures in stably stratified turbulent shear flows.

<p>We analyzed the data of the numerical simulation of stably stratified turbulent shear flows. It is shown that, along with chaotic turbulence, the flows contain large organized structures. In the temperature field, these structures appear as inclined layers with weakly stable stratification, separated by very thin layers with large temperature gradients. The existence of such layered structures in nature is indirectly confirmed by the analysis of field measurements. An increase of the turbulent Prandtl number with increasing gradient Richardson number was fixed in simulation data. The hypothesis is proposed that physical mechanism for maintaining of turbulence in supercritically stable stratification is connected with the revealed  structures. It is shown that the spatial scales and the shapes of the identified organized structures can be explained using the calculation of  optimal disturbances for the simplified linear model.</p><p>This study was supported by the Russian Foundation for Basic Research (grants nos. 18-05-60126,  20-05-00776) and by Academy of Finland project ClimEco no. 314 798/799 (2018-2020).</p>

Large-scale structures in stratified turbulent Couette flow and optimal disturbances

Direct numerical simulation data of a stratified turbulent Couette flow contains two types of organized structures: rolls arising at neutral and close to neutral stratifications, and layered structures which manifest themselves as static stability increases. It is shown that both types of structures have spatial scales and forms that coincide with the scales and forms of the optimal disturbances of the simplified linear model of the Couette flow with the same Richardson numbers.

Optimal disturbances of stably stratified turbulent Couette flow

Direct numerical simulation data of a stably stratified turbulent Couette flow contains two types of organized structures: the rolls that arise at neutral and close to neutral stratification, and the layered structures, which manifest themselves as the static stability increases. It is shown that both types of structures have spatial scales and forms that coincide with the scales and forms of the corresponding optimal disturbances of the simplified linear model of the Couette flow with the same Richardson numbers.