For steady two-dimensional flows with a single eddy (i.e. nested closed streamlines), Prandtl (1905) and Batchelor (1956) proposed that in the limit of vanishing viscosity vorticity is constant an inner region separated from boundary layer. In this paper, by constructing higher order approximate solutions Navier-Stokes equations establishing validity layer expansion, we give rigorous proof exis...

The linear marginal instability of an axisymmetric magnetohydrodynamics Taylor-Couette flow of infinite vertical extension is considered. We are only interested in those vertical wave numbers for which the characteristic Reynolds number is minimum. For hydrodynamically unstable flows minimum Reynolds numbers exist even without a magnetic field, but there are also solutions with smaller characte...

Temperature transformation does not collapse data, but the resulting wall model accurately predicts temperatures in high-speed boundary layer flows. Here we explain why this is so. The insights gained lead to a new turbulent Prandtl number formulation and more accurate models.

Let the viscosity ε → 0 $\varepsilon \rightarrow 0$ for 2D steady Navier-Stokes equations in region ≤ x L $0\le x\le L$ and y < ∞ y<\infty$ with no slip boundary conditions at = $y=0$ . For 1 $L<<1$ , we justify validity of Prandtl layer expansion scaled layers, including celebrated Blasius layer. Our uniform estimates are achieved through a fixed-point scheme: u v ⟶ DNS − $$\begin{equation*} \...

This study is a linear stability analysis of the flows induced by ultrasound acoustic waves (Eckart streaming) within an infinite horizontal fluid layer heated from below. We first investigate the dependence of the instability threshold on the normalized acoustic beam width H(b) for an isothermal fluid layer. The critical curve, given by the critical values of the acoustic streaming parameter, ...

An experimental investigation was carried out to determine heat transfer coefficients for natural convection from a heated horizontal wire. The heating is provided by electrical current, and the temperature of the wire is determined from the measurement of its resistance. The experiments are performed in three different convective environments: air, water, and oil. Prandtl number ranged between...