arXiv subjects

S. Kurien

Publications and source records attributed to S. Kurien.

3 recordsLinked to original sources

arXiv2007

Kuzmin-Osledets Formulations of Compressible Euler Equations

Kuzmin-Oseledets formulations of compressible Euler equations case are considered. Exact results and physical interpretations are given. One such exact result for the compressible barotropic case is the potential helicity Lagrange invariant. In recognition of the fundamental physical implications of this Lagrange invariant clarified here, this invariant is shown to hold for compressible non-barotropic cases as well upon using a stronger gauge condition. Symmetry restoration taking place at the Lagrangian level in the Kuzmin-Oseledets formulation is pointed out. The Kuzmin-Oseledets formulation in the compressible barotropic case is shown to admit an exact solution that physically describes a density wave on a steady irrotational flow with the Kuzmin-Oseledets velocity q growing monotonically with it and hence specifying some information about the fluid impulse that is needed to set up the flow in question.

physics.flu-dyn↗

arXiv2007

A study of the Navier-Stokes-alpha model for two-dimensional turbulence

For wavenumbers k such that k * alpha > 1, corresponding to spatial scales smaller than alpha, there are three candidate power laws for the energy spectrum of the Navier-Stokes-alpha model, corresponding to three possible dynamical eddy turnover time scales in the model equations: one from the smoothed field, the second from the rough field and the third from a special combination of the two. Using two-dimensional turbulence as a test case, we measure the scaling of the spectra from high-resolution simulations of the Navier-Stokes-alpha model, in the limit as alpha goes to infinity. We show that the energy spectrum of the smoothed velocity field scales as k^{-7} in the direct enstrophy cascade regime, consistent with dynamics dominated by the time scale of the rough velocity field.

physics.flu-dyn↗

arXiv2004

Anomalous scaling of low-order structure functions of turbulent velocity

It is now believed that the scaling exponents of moments of velocity increments are anomalous, or that the departures from Kolmogorov's (1941) self-similar scaling increase nonlinearly with the increasing order of the moment. This appears to be true whether one considers velocity increments themselves or their absolute values. However, moments of order lower than 2 of the absolute values of velocity increments have not been investigated thoroughly for anomaly. Here, we discuss the importance of the scaling of non-integer moments of order between +2 and -1, and obtain them from direct numerical simulations at moderate Reynolds numbers (Taylor microscale Reynolds numbers $R_λ\le$ 450) and experimental data at high Reynolds numbers ($R_λ\approx$ 10,000). The relative difference between the measured exponents and Kolmogorov's prediction increases as the moment order decreases towards -1, thus showing that the anomaly that is manifest in high-order moments is present in low-order moments as well. This conclusion provides a motivation for seeking a theory of anomalous scaling as the order of the moment vanishes. Such a theory does not have to consider rare events--which may be affected by non-universal features such as shear--and so may be regarded as advantageous to consider and develop.

nlin.CD↗