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.

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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

Towards Resolving Natural Shock Oscillation and Mitigation of Altitude Excitation in a Transonic Fan

Navier-Stokes Simulations of Vertical Sloshing with Time-Periodic Excitation

The statistical relationship between vortex tubes and vortex sheets in turbulent wall-bounded flow is analyzed by means of conditional averaging of DNS fields. The results support strong association between the two types of coherent structures, and indicate that vortex tubes are produced upon roll-up of vortex sheets (as in the hairpin vortex paradigm), or interact causing the ejection of near-wall vorticity, or generate sheets of streamwise vorticity through a rubbing effect caused by the no-slip condition.

On the Relationship Between Vortex Tubes and Sheets in Wall-Bounded Flows

In the present paper the dynamics of the coupling process of compressible vortex pairs is analyzed by means of extensive numerical simulations. The objective of the study is to determine the influence both of the initial vortex structure and of the compressibility. Different initial vortex structures have been considered and their influence on the vorticity dynamics has been assessed. The numerical simulations show that free vortex evolution produces vortex dipoles whose structure depends upon the initial vortex structure and on the vortex Mach number. In the presence of shock — vortex pair interaction the coupling process obeys a either a two- or three- stage mechanism dependending upon the shock strength, and nonlinear couples are formed.

Sergio Pirozzoli

Papers

Towards Resolving Natural Shock Oscillation and Mitigation of Altitude Excitation in a Transonic Fan

Navier-Stokes Simulations of Vertical Sloshing with Time-Periodic Excitation

On the Relationship Between Vortex Tubes and Sheets in Wall-Bounded Flows

Numerical Simulations of the Coupling Process of Compressible Vortices

Turbulence Spectra in Natural and Forced Convection