We present a new formulation of the incompressible Navier-Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation. The gauge freedom allows us to assign simple and speci...
A controlled quantum system possesses a search landscape defined by the observable value as a functional of the control field. Within the search landscape, there exist level sets of controls giving the same observable...
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We present new algorithms for computing the H∞ optimal performance for a class of single-input/single-output (SISO) infinite-dimensional systems. The algorithms here only require use of one or two fast Fourier transf...
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We reformulate the renormalization group (RNG) and the e{open}-expansion for derivation of turbulence models. The procedure is developed for the Navier-Stokes equations and the transport equations for the kinetic ener...
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We consider a few cases of homogeneous and isotropic turbulence differing by the mechanisms of turbulence generation. The advective terms in the Navier-Stokes and Burgers equations are similar. It is proposed that the...
We consider a few cases of homogeneous and isotropic turbulence differing by the mechanisms of turbulence generation. The advective terms in the Navier-Stokes and Burgers equations are similar. It is proposed that the longitudinal structure functions Sn(r) in homogeneous and isotropic three-dimensional turbulence are governed by a one-dimensional (1D) equation of motion, resembling the 1D Burgers equation, with the strongly nonlocal pressure contributions accounted for by Galilean invariance-breaking terms. The resulting equations, not involving parameters taken from experimental data, give both scaling exponents and amplitudes of the structure functions in an excellent agreement with experimental data. The derived probability density function P(Δu,r)≠P(−Δu,r), but P(Δu,r)=P(−Δu,−r), in accord with the symmetry properties of the Navier-Stokes equations. With decrease of the displacement r, the probability density, which cannot be represented in a scale-invariant form, shows smooth variation from the Gaussian at the large scales to close-to-exponential function, thus demonstrating onset of small-scale intermittency. It is shown that accounting for the subdominant contributions to the structure functions Sn(r)∝rξn is crucial for a derivation of the amplitudes of the moments of the velocity difference.
The Kolmogorov relation for the third-order moments of the velocity differences is generalized for the case of statistically steady turbulence and applied to the Bénard convection problem. The predicted temperatu...
The Kolmogorov relation for the third-order moments of the velocity differences is generalized for the case of statistically steady turbulence and applied to the Bénard convection problem. The predicted temperature and velocity spectra are ET≊k−7/5 and E≊k−11/5, respectively. At the smaller scales, in the dissipation range of the temperature fluctuations, the Kolmogorov range where most of the energy is dissipated is predicted. The new set of scaling exponents, which can be observed in the experiments in the small-aspect-ratio convection cells, is derived.
Direct numerical simulations with up to 10242 resolution are performed to study statistical properties of the inverse energy cascade in stationary homogeneous two-dimensional turbulence driven by small-scale Gaussian ...
Direct numerical simulations with up to 10242 resolution are performed to study statistical properties of the inverse energy cascade in stationary homogeneous two-dimensional turbulence driven by small-scale Gaussian white-in-time noise. The energy spectra for the inverse energy cascade deviate strongly from the expected k−5/3 law and are close (somewhat flatter) to k−3. The reason for the deviation is traced to the emergence of strong vortices distributed over all scales. Statistical properties of the vortices are explored.
A simple fluctuation argument A la Landau suggests why probability density functions of velocity gradients of turbulent velocity fields are often found to have a close to exponential tail. The detailed functional form...
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A simple fluctuation argument A la Landau suggests why probability density functions of velocity gradients of turbulent velocity fields are often found to have a close to exponential tail. The detailed functional form depends on the assumptions made concerning the intermittency.
Intermittency effects in turbulence are discussed from a dynamical point of view. A two-fluid model is developed to describe quantitatively the non-gaussian statistics of turbulence at small scales. With a self-simila...
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Intermittency effects in turbulence are discussed from a dynamical point of view. A two-fluid model is developed to describe quantitatively the non-gaussian statistics of turbulence at small scales. With a self-similarity argument, the model gives rise to the entire set of inertial range scaling exponents for normalized velocity structure functions. The results are in excellent agreement with experimental and numerical measurements. The model suggests a physical mechanism of intermittency, namely the self-interaction of turbulence structures.
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