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We propose a new strategy of shear flow turbulence control which is realized by the imposition in the plane Cou-ette flow of a specially designed, non-symmetric in span-wise direction seed velocity perturbations by a near wall volume... more
We propose a new strategy of shear flow turbulence control which is realized by the imposition in the plane Cou-ette flow of a specially designed, non-symmetric in span-wise direction seed velocity perturbations by a near wall volume forcing. The configuration of the imposed perturba-tions ensures a gain of shear flow energy and the breaking of turbulence spanwise reflection symmetry – generates span-wise mean flow. The latter changes the self-sustained dy-namics of turbulence and results in considerable reduction of its level and kinetic energy production. It has to empha-sized that the generated spanwise mean flow is a result of the intrinsic, nonlinear processes in the forced turbulence and not directly introduced in the system. A model, near-wall weak forcing is designed to impose in the flow the per-turbations with required statistics and characteristics. The efficiency of the proposed scheme has been demonstrated by direct numerical simulation (DNS) using the plane Cou-ette fl...
The energy transient growth mechanism of linear perturbations in plane constant shear flows is re-examined. Considering fluid particle dynamics and operating in terms of the pressure force, we focus on the physics of the energy exchange... more
The energy transient growth mechanism of linear perturbations in plane constant shear flows is re-examined. Considering fluid particle dynamics and operating in terms of the pressure force, we focus on the physics of the energy exchange between the base flow and a single Kelvin mode (i.e. plane waves or spatial Fourier harmonics of perturbations). The keystone of the energy exchange physics is the elastic reflection of the fluid particles from the maximum pressure plane of the Kelvin mode. An interplay of these physics with the shear flow kinematics quantitatively exactly describes the transient growth and, what is most important, the linear dynamics of the system allows to construct the dynamical equations that are identical to the Euler ones. The proposed mechanism is equally applicable to two-and three-dimensional (2D and 3D) perturbations and, thus, shows the universal nature of the transient growth physics in contrast to the widely accepted explanations, separating 2D (Orr mech...
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The general scheme for the construction of the general-relativistic model of the magnetically driven jet is suggested. The method is based on the usage of the 3 + 1 MHD formalism. It is shown that the critical points of the flow and the... more
The general scheme for the construction of the general-relativistic model of the magnetically driven jet is suggested. The method is based on the usage of the 3 + 1 MHD formalism. It is shown that the critical points of the flow and the explicit radial behavior of the physical variables may be derived through the jet “profile function”.
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It is found that velocity shear enables the extraction of kinetic energy from the background flow by Dust-Acoustic waves. It is also shown that the velocity shear leads to the appearance of a new mode of the dust particles collective... more
It is found that velocity shear enables the extraction of kinetic energy from the background flow by Dust-Acoustic waves. It is also shown that the velocity shear leads to the appearance of a new mode of the dust particles collective behaviour, called shear dust vortices.
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It is found that velocity shear enables the extraction of kinetic energy from the background flow by Dust-Acoustic waves. It is also shown that the velocity shear leads to the appearance of a new mode of the dust particles collective... more
It is found that velocity shear enables the extraction of kinetic energy from the background flow by Dust-Acoustic waves. It is also shown that the velocity shear leads to the appearance of a new mode of the dust particles collective behaviour, called shear dust vortices.
Research Interests:
Investigating the multi-point correlation (MPC) equations for the velocity and pressure fluctuations in the limit of homogeneous turbulence a new scaling symmetry has been discovered. Interesting enought this property is not shared with... more
Investigating the multi-point correlation (MPC) equations for the velocity and pressure fluctuations in the limit of homogeneous turbulence a new scaling symmetry has been discovered. Interesting enought this property is not shared with the Euler or Navier-Stokes equations from which the MPC equations have orginally emerged. This was first observed for parallel wall-bounded shear flows (see [2]) though there this property only holds true for the two-point equation. Hence, in a strict sense there it is broken for higher order correlation equations. Presently using this extended set of symmetry groups a much wider class of invariant solutions or turbulent scaling laws is derived for homogeneous and homogeneous-isotropic turbulence which is in stark contrast to the classical power law decay arising from Birkhoff’s or Loitsiansky’s integrals. In particular, we show that the experimentally observed specific scaling properties of fractal-generated turbulence (see [1, 4]) fall into this new class of solutions. Due to this specific grid a breaking of the classical scaling symmetries due to a wide range of scales acting on the flow is accomplished. This in particular leads to a constant integral and Taylor length scale downstream of the fractal grid and the exponential decay of the turbulent kinetic energy along the same axis. These particular properties can only be conceived from MPC equations using the new scaling symmetry. The latter new scaling law may have been the first clear indication towards the existence of the extended statistical scaling group. Though the latter is not obvious from the instantaneous Euler or Navier-Stokes equations it is directly implied.
Research Interests:
The Lie group or symmetry approach applied to turbulence as developed by Oberlack [1] is used to derive new scaling laws for various statistical quantities of a zero pressure gradient (ZPG) turbulent boundary layer flow. For this purpose... more
The Lie group or symmetry approach applied to turbulence as developed by Oberlack [1] is used to derive new scaling laws for various statistical quantities of a zero pressure gradient (ZPG) turbulent boundary layer flow. For this purpose the approach was applied to the two-point correlation (TPC) equations to find their symmetry groups and thereof to derive invariant solutions (scaling laws). For the verification of these new scaling laws three direct numerical simulations (DNS) at Reθ = 810, 2240, 2500 were performed using a spectral method with up to 538 million grid points.
The general scheme for the construction of the general-relativistic model of the magnetically driven jet is suggested. The method is based on the usage of the 3+1 mhd formalism. It is shown that the critical points of the flow and the... more
The general scheme for the construction of the general-relativistic model of the magnetically driven jet is suggested. The method is based on the usage of the 3+1 mhd formalism. It is shown that the critical points of the flow and the explicit radial behavior of the physical variables may be derived through the jet ``profile function".
Research Interests:
Research Interests:
Recent studies of nonmodal phenomena in two-component plasma flows revealed that the velocity shear induces a number of new effects both in electrostatic and magnetized shear flows. It can be expected that dusty plasmas also host... more
Recent studies of nonmodal phenomena in two-component plasma flows revealed that the velocity shear induces a number of new effects both in electrostatic and magnetized shear flows. It can be expected that dusty plasmas also host shear-modified and shear-induced modes of collective behavior, which may be found by means of the nonmodal approach and which are inaccessible by means of the standard normal mode analysis. In this paper, considering the simple electrostatic dusty plasma case, a general mathematical formalism is developed for studying how velocity shear affects the evolution of dust-acoustic waves (DAWs) and ion-acoustic waves (IAWs). In the limiting (very low-frequency) case when Boltzmann distributions are used both for the electrons and the ions it is found that the velocity shear enables the extraction of kinetic energy of the background flow by the dust-acoustic waves. It is also shown that the velocity shear leads to the appearance of a new collective mode of the dust particles-shear dust vortices. In the general case it is demonstrated that the velocity shear couples DAWs and IAWs and under suitable conditions may cause their mutual transformation into each other. The flow also sustains shear ion-dust vortices-nonperiodic patterns, which may eventually acquire oscillating features and generate both DAWs and IAWs. The inverse regime, which is called evanescence of acoustic waves, can also occur: the initial blend of DAWs and IAWs can fade away degenerating into the nonperiodic, evanescent perturbation.
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Background of three dimensional hydrodynamic/vortical fluctuations in a stochastically forced, laminar, incompressible, plane Couette flow is simulated by direct numerical simulations (DNS). It was found that the fluctuating field has... more
Background of three dimensional hydrodynamic/vortical fluctuations in a stochastically forced, laminar, incompressible, plane Couette flow is simulated by direct numerical simulations (DNS). It was found that the fluctuating field has well pronounced peculiarities: (i) The hydrodynamic fluctuations exhibits non–exponential, transient growth; (ii) Streamwise non–constant fluctuations with the characteristic length scale of the order of the channel width are predominant in the fluctuating spectrum; (iii) Existence of coherent structures in the fluctuating background; (iv) Stochastic forcing breaks the spanwise reflection symmetry (inherent to the linear and full Navier–stokes equations in a case of the Couette flow) and inputs an asymmetry on dynamical processes. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Recent studies of nonmodal phenomena in two-component plasma flows revealed that the velocity shear induces a number of new effects both in electrostatic and magnetized shear flows. It can be expected that dusty plasmas also host... more
Recent studies of nonmodal phenomena in two-component plasma flows revealed that the velocity shear induces a number of new effects both in electrostatic and magnetized shear flows. It can be expected that dusty plasmas also host shear-modified and shear-induced modes of collective behavior, which may be found by means of the nonmodal approach and which are inaccessible by means of
Research Interests:
Research Interests:
Research Interests:
Lie group analysis is used to derive new scaling laws (exponential laws) for ZPG turbulent boundary layer flow. A new scaling group was found in the two-point correlation equations. DNS of such a flow was performed at Re θ = 2240 using a... more
Lie group analysis is used to derive new scaling laws (exponential laws) for ZPG turbulent boundary layer flow. A new scaling group was found in the two-point correlation equations. DNS of such a flow was performed at Re θ = 2240 using a spectral method with up to 160 million grid points. The results of the numerical simulations are compared with the new scaling laws and good agreement is achieved.
The background of three dimensional (3D) hydrodynamic/vortical fluctuations in a stochastically forced, laminar and incompressible plane Couette flow is simulated numerically. It was found that the fluctuating background in the flow has... more
The background of three dimensional (3D) hydrodynamic/vortical fluctuations in a stochastically forced, laminar and incompressible plane Couette flow is simulated numerically. It was found that the fluctuating background in the flow has the following characteristics: The hydrodynamic fluctuations show the nonexponential, transient growth; an anisotropy of the fluctuating velocity field increases with the shear rate; existence of the streamwise structural regularities (coherent structures) with the characteristic length-scale of the order of a channel width; appearance of the nonzero velocity cross-correlations; Symmetry breaking of the spanwise reflection of the dynamical processes due to the stochastic forcing.
Investigating the multi-point correlation (MPC) equations for the velocity and pressure fluctuations in the limit of homogeneous turbulence a new scaling symmetry has been discovered. Interesting enought this property is not shared with... more
Investigating the multi-point correlation (MPC) equations for the velocity and pressure fluctuations in the limit of homogeneous turbulence a new scaling symmetry has been discovered. Interesting enought this property is not shared with the Euler or Navier-Stokes equations from which the MPC equations have orginally emerged. This was first observed for parallel wall-bounded shear flows in [1]. Presently using this extended set of symmetry groups a much wider class of invariant solutions or turbulent scaling laws is derived for the decay of homogeneous-isotropic turbulence which is in stark contrast to the classical power law decay. In particular, we show that the experimentally observed specific scaling properties of fractal-generated turbulence i.e. a constant integral and Taylor length scale and the exponential decay of the turbulent kinetic energy (see [2, 3]) fall into this new class of solutions. The latter new scaling law may have been the first clear indication towards the existence of the extended statistical scaling group.
Research Interests:
The Lie group, or symmetry approach, developed by Oberlack (see e.g. Oberlack [26] and references therein) is used to derive new scaling laws for various quantities of a zero pressure gradient turbulent boundary layer flow. The approach... more
The Lie group, or symmetry approach, developed by Oberlack (see e.g. Oberlack [26] and references therein) is used to derive new scaling laws for various quantities of a zero pressure gradient turbulent boundary layer flow. The approach unifies and extends the work done by Oberlack for the mean velocity of stationary parallel turbulent shear flows. From the two-point correlation (TPC) equations the knowledge of the symmetries allows us to derive a variety of invariant solutions (scaling laws) for turbulent flows, one of which is the new exponential mean velocity profile that is found in the mid-wake region of flat-plate boundary layers. Further, a third scaling group was found in the TPC equations for the one-dimensional turbulent boundary layer. This is in contrast to the Navier–Stokes and Euler equations, which have one and two scaling groups, respectively. The present focus is on the exponential law in the outer region of turbulent boundary layer corresponding new scaling laws for one- and two-point correlation functions. A direct numerical simulation (DNS) of a flat plate turbulent boundary layer with zero pressure gradient was performed at two different Reynolds numbers Reθ=750,2240. The Navier–Stokes equations were numerically solved using a spectral method with up to 140 million grid points. The results of the numerical simulations are compared with the new scaling laws. TPC functions are presented. The numerical simulation shows good agreement with the theoretical results, however only for a limited range of applicability.
Research Interests: Applied Mathematics, Lie Groups, DNS, Numerical Simulation, Turbulent boundary layer, and 16 moreClassical Physics, Spectral method, Turbulent Flow, Shear Flow, Navier Stokes, Euler Lagrange Equation, Lie Group, Boundary Layer, Scaling Law, Velocity Profile, Direct Numerical Simulation (DNS), Point Group Symmetry, Reynolds Number, Pressure Gradient, One Dimensional Turbulence, and Correlation function
Direct numerical simulations (DNS) of a vibrating grid turbulence at two different Reynolds numbers (based on an amplitude and frequency of the grid) Re = 500, 1000 are presented. The evolution of a turbulent/non-turbulent interface was... more
Direct numerical simulations (DNS) of a vibrating grid turbulence at two different Reynolds numbers (based on an amplitude and frequency of the grid) Re = 500, 1000 are presented. The evolution of a turbulent/non-turbulent interface was detected and compared to the theoretical results obtained in the paper [1] using Lie group analysis of the governing equations. Good agreement was found between DNS and theory. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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Direct numerical simulation of the turbulence generated at a grid vibrating normally to itself using spectral code [1] is presented. Due to zero mean shear there is no production of turbulence apart from the grid. Action of the grid is... more
Direct numerical simulation of the turbulence generated at a grid vibrating normally to itself using spectral code [1] is presented. Due to zero mean shear there is no production of turbulence apart from the grid. Action of the grid is mimiced by the function implemented in the middle of the simulation box:f_i (x_1 ,x_2 ) = {n^2 S}/2left{ {left| {{δ _{i3} }/4\cos left( {{2π }/Mx_1 } right)\cos left. {left( {{2π }/Mx_2 } right)} right|} right.sin (nt) + {β _i }/4} right}, where M is the mesh size, S/2 - amplitude or stroke of the grid, n - frequency. β i are random numbers with uniform distribution. The simulations were performed for the following parameters: x 1, x 2 ∈ [-π; π], x 3 ∈ [-2π; 2π]; Re = nS 2/? = 1000; S/M = 2; Numerical grid: 128 × 128 × 256.
Research Interests:
High resolution direct numerical simulation data of turbulent boundary layers are analyzed by means of wavelets. The developed anisotropic wavelet transform reinterpolates the data in the wall normal direction, originally given on a... more
High resolution direct numerical simulation data of turbulent boundary layers are analyzed by means of wavelets. The developed anisotropic wavelet transform reinterpolates the data in the wall normal direction, originally given on a Chebychev grid, onto an adapted dyadic grid. The contructed wavelet bases accounts for the anisotropy of the flow by using different scales in the wall normal direction and in the planes parallel to the wall. Therewith the vorticity field is decomposed into coherent and incoherent contributions. It is shown that few wavelet coefficients retain the coherent structures of the flow, while the majority of the coefficients corresponds to a structurless noise like background flow. Scale and direction dependent statistics in wavelet space quantify the properties of the total, coherent and incoherent flows as a function of the wall distance.
Research Interests:
Lie group approach is used to derive new scaling laws for zero-pressure gradient turbulent boundary layer flow. A direct numerical simulation of the flow at Reynolds number Reθ = 2240 was performed for the verify theoretical results.... more
Lie group approach is used to derive new scaling laws for zero-pressure gradient turbulent boundary layer flow. A direct numerical simulation of the flow at Reynolds number Reθ = 2240 was performed for the verify theoretical results. Navier-Stokes equations were numerically solved using spectral method with up to 160 million grid points. The numerical simulation shows validity of the theoretical results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Research Interests:
A more complete understanding of transition to turbulence in a Poiseuille flow rotating about the streamwise axis is sought by studying the stability of the flow. Using the classical theory of modal analysis, the stability characteristics... more
A more complete understanding of transition to turbulence in a Poiseuille flow rotating about the streamwise axis is sought by studying the stability of the flow. Using the classical theory of modal analysis, the stability characteristics of this flow setup are investigated. We find that the addition of the Coriolis force significantly increases the growth rates achieved compared to the non-rotating channel flow until a certain point, after which the high Rossby numbers stabilize the flow. Given the non-normality of the equations governing the flow, we investigate the transient energy growth. We show that the energetic growth can be, as in the non-rotating case, of the order of O(10^3) and that the maximal growth is caused by disturbances nearly perpendicular to the main flow. The maximal growth is achieved by crosswise perturbations until the point of alpha transition, after which the maximal growth is created by an oblique disturbance. The induced crosswise double-S velocity profile found in previous investigations is explained by the optimal initial disturbances leading to this maximal growth.