Instability of Navier slip flow of liquidsInstabilité des écoulements glissant de liquides.

We investigate the stability problem related to the basic slip flows of liquids in plane microchannels by using the Navier slip concept. We found that if the Navier slip parameter ($N_s$) equals 0.06, the critical Reynolds number (${\mathit{Re}}_{\mathrm{cr}}$) becomes 213.6. There are short-wave instabilities, however, when we further increase $N_s$ to 0.07 or 0.08. ${\mathit{Re}}_{\mathrm{cr}}$ becomes 132.9 for $N_s=0.08$ if we neglect the short-wave instability. To cite this article: A.K.-H. Chu, C. R. Mecanique 332 (2004).     

Numerical verification of the weak turbulent model for swell evolution

The purpose of this article is to numerically verify the theory of weak turbulence. We have performed numerical simulations of an ensemble of nonlinearly interacting free gravity waves (a swell) by two different methods: by solving the primordial dynamical equations describing the potential flow of an ideal fluid with a free surface, and by solving the kinetic Hasselmann equation, describing the wave ensemble in the framework of the theory of weak turbulence. In both cases we have observed effects predicted by this theory: frequency downshift, angular spreading and formation of a Zakharov–Filonenko spectrum $I_{\omega }\sim {\omega }^{\mathrm{-4}}$. To achieve quantitative coincidence of the results obtained by different methods, we have to augment the Hasselmann kinetic equation by an empirical dissipation term $S_{\mathrm{diss}}$ modeling the coherent effects of white-capping. Using the standard dissipation terms from the operational wave predicting model (WAM) leads to a significant improvement on short times, but does not resolve the discrepancy completely, leaving the question about the optimal choice of $S_{\mathrm{diss}}$ open. In the long run, WAM dissipative terms essentially overestimate dissipation.     

Scaling of the near-wall layer beneath turbulent separated flow

This paper is a continuation of an earlier paper [P.E. Hancock, Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows, Eur. J. Mech. B Fluids 24 (2005) 425–438] in which it is proposed that each Reynolds stress has its own velocity scale. Two of these, $u_{\tau }^{\prime }$ and $w_{\tau }^{\prime }$, are directly related by definition to the r.m.s. of the wall-shear-stress fluctuations (${\tau }_x$ and ${\tau }_z$) in the streamwise and transverse directions. They are also velocity scales for the true dissipation of the turbulent kinetic energy and the Kolmogorov velocity and length scales at the surface. From asymptotic considerations it is shown that the other two scales are related to averages involving instantaneous gradients of wall-shear-stress fluctuations. The measurements, made using pulsed-wire anemometry into the viscous sublayer, show that $u_{\tau }^{\prime }$ and $w_{\tau }^{\prime }$ are also the velocity scales for the respective streamwise and transverse fourth-order velocity moments, together with the viscous velocity scale ($\nu /y$). Normalised, the fourth-order moments show an inner-layer-like behaviour independent of both position and direction, like that seen in the second-order moments [P.E. Hancock, Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows, Eur. J. Mech. B Fluids 24 (2005) 425–438]. However, not surprisingly, the third order moments exhibit an effect of mean shear, seen in the skewing of the probability distributions. Though not measured directly, the measurements imply the behaviour of the averaged products of fluctuations in wall-shear-stress and wall-pressure-gradient ($\overline{{\tau }_x\partial p/\partial x}$ and $\overline{{\tau }_z\partial p/\partial z}$). Normalised, they also are independent of position and direction. Some of the results presented apply more generally to the near-wall region beneath turbulent flow.