Showing papers by "E. A. Kuznetsov published in 2019"
TL;DR: In this paper, it was shown that the maximum value of the rotor field at the stage of quasi-shocks formation increases exponentially in time, while the thickness l(t) of the maximum area in the transverse direction to the vector B decreases in time also exponentially.
Abstract: The vorticity rotor field B = curlω (divorticity) for freely decaying two-dimensional hydrodynamic turbulence due to a tendency to breaking is concentrated near the lines corresponding to the position of the vorticity quasi-shocks. The maximum value of the divorticity Bmax at the stage of quasi-shocks formation increases exponentially in time, while the thickness l(t) of the maximum area in the transverse direction to the vector B decreases in time also exponentially. It is numerically shown that Bmax(t) depends on the thickness according to the power law Bmax(t) ∼ l−α(t), where α = 2/3. This behavior indicates in favor of folding for the divergence-free vector field of the divorticity.
4 citations
TL;DR: In this paper, the authors study the statistical correlation functions for the three-dimensional hydrodynamic turbulence onset when the dynamics is dominated by the pancake-like high-vorticity structures.
Abstract: We study the statistical correlation functions for the three-dimensional hydrodynamic turbulence onset when the dynamics is dominated by the pancake-like high-vorticity structures. With extensive numerical simulations, we systematically examine the two-points structure functions (moments) of velocity. We observe formation of the power-law scaling for both the longitudinal and the transversal moments in the same interval of scales as for the energy spectrum. The scaling exponents for the velocity structure functions demonstrate the same key properties as for the stationary turbulence case. In particular, the exponents depend on the order of the moment non-trivially, indicating the intermittency and the anomalous scaling, and the longitudinal exponents turn out to be slightly larger than the transversal ones. When the energy spectrum has power-law scaling close to the Kolmogorov’s one, the longitudinal third-order moment shows close to linear scaling with the distance, in line with the Kolmogorov’s 4/5-law despite the strong anisotropy.
3 citations
12 Feb 2019
TL;DR: In this paper, the formation of coherent vortical structures in the form of thin pancakes is studied for three-dimensional flows at the high Reynolds regime when, in the leading order, the development of such structures can be described within the 3D Euler equations for ideal incompressible fluids.
Abstract: The formation of the coherent vortical structures in the form of thin pancakes is studied for three-dimensional flows at the high Reynolds regime when, in the leading order, the development of such structures can be described within the 3D Euler equations for ideal incompressible fluids. Numerically and analytically on the base of the vortex line representation we show that compression of such structures and respectively increase of their amplitudes are possible due to the compressibility of the continuously distributed vortex lines. It is demonstrated that this growth can be considered as analog of breaking for the divergence-free vorticity field. At high amplitudes this process has a self-similar behavior connected the maximal vorticity and the pancake width by the Kolmogorov type relation ωmax ∝ l-2/3. The role of such structures in the Kolmogorov spectrum formation is also discussed.
1 citations
1 citations
TL;DR: In this paper, the authors study the statistical correlation functions for the three-dimensional hydrodynamic turbulence onset when the dynamics is dominated by the pancake-like high-vorticity structures.
Abstract: We study the statistical correlation functions for the three-dimensional hydrodynamic turbulence onset when the dynamics is dominated by the pancake-like high-vorticity structures. With extensive numerical simulations, we systematically examine the two-points structure functions (moments) of velocity. We observe formation of the power-law scaling for both the longitudinal and the transversal moments in the same interval of scales as for the energy spectrum. The scaling exponents for the velocity structure functions demonstrate the same key properties as for the stationary turbulence case. In particular, the exponents depend on the order of the moment non-trivially, indicating the intermittency and the anomalous scaling, and the longitudinal exponents turn out to be slightly larger than the transversal ones. When the energy spectrum has power-law scaling close to the Kolmogorov's one, the longitudinal third-order moment shows close to linear scaling with the distance, in line with the Kolmogorov's 4/5-law despite the strong anisotropy.