The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

An introduction to heat transfer


 The spectral ratio between horizontal and vertical components (H/V ratio) of microtremors measured at the ground surface has been used to estimate fundamental periods and amplification factors of a site, although this technique lacks theoretical background. The aim of this article is to formulate the H/V technique in terms of the characteristics of Rayleigh and Love waves, and to contribute to improve the technique. The improvement includes use of not only peaks but also troughs in the H/V ratio for reliable estimation of the period and use of a newly proposed smoothing function for better estimation of the amplification factor. The formulation leads to a simple formula for the amplification factor expressed with the H/V ratio. With microtremor data measured at 546 junior high schools in 23 wards of Tokyo, the improved technique is applied to mapping site periods and amplification factors in the area.

Ground Motion Characteristics Estimated from Spectral Ratio between Horizontal and Verticcl Components of Mietremors.

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

/pdf/the-structure-of-turbulent-shear-flow-2yf3szhaqb.pdf

The Structure of Turbulent Shear Flow

A direct numerical simulation of incompressible channel flow at a friction Reynolds number ( ) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Karman constant . There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits dependence over a short range in wavenumber . Further, consistent with previous experimental observations, when these spectra are multiplied by (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the range.

Direct numerical simulation of turbulent channel flow up to

Natural Grid Stretching for Dns of Compressible Wall-Bounded Flows

The present research is aimed at understanding the subtle (and not yet fully understood) relationship between the complex nonlinear dynamics of fluid turbulence and Kolmogorov power-law scaling in wavenumber space. Time evolution is often overlooked in DNS of turbulent flows, hence investigation of a suitably simple minimal flow unit (MFU) can help to understand the passage from a vortical-dominated stage to a turbulent stage having all the ingredients of turbulent flows. In particular, we aim at clarifying the physical phenomena associated with the formation of a finite-time singularity (FTS) in the Euler equations and of Kolmogorov’s k−5∕3 scaling in the Navier–Stokes equations. For that purpose, high-resolution simulations of the Euler and Navier–Stokes detection are carried out and analyzed by means of state-of-the-art detection techniques to isolate the contribution of tube-like and sheet-like structures. Equipping the MFU with passive scalars (relevant in turbulent combustion) further helps understanding why passive scalar spectra have a different behavior than the velocity field spectra close to the FTS, but they also attain a k−5∕3 power spectrum at subsequent times, in the presence of finite viscosity. By adding a passive vector (relevant in MHD flows), dynamical differences with respect to the vorticity field can also be established.

Sergio Pirozzoli

Papers

Natural Grid Stretching for Dns of Compressible Wall-Bounded Flows

A Minimal Flow Unit for Turbulence, Combustion, and Astrophysics