An exact analysis of scalar transport in hydromagnetic flow between two parallel plates: a multi-scale approach

The present paper explores an analytical solution to study the two-dimensional concentration distribution of a solute in a conducting fluid flowing between two parallel plates in the presence of a transverse magnetic field. Mei’s homogenization technique is used to acquire the mean concentration distributions up to the second-order approximation and the transverse concentration distributions up to third order. An uneven form of the concentration cloud and the transverse variation of the concentration distribution in a hydromagnetic flow are illustrated for the initial stage. The rate of progress towards uniformity of a solute cloud seems much slower than that of normality. It is observed that the peak of the transverse mean concentration and transverse variation of the concentration distribution of the solute significantly decrease with the increase in the magnetic field for small dispersion times. This is because, with an increase in the magnetic field, the velocity profiles flatten at the central core region between the parallel plates. The research proposes a time scale of 10 δ 2 / D (where δ is half the distance between two parallel plates and D is the molecular diffusivity) to characterize the dispersion process to approach the transverse uniformity.

Influence of Freestream Turbulence Intensity on Bypass Transition Parameters in a Boundary Layer

An experimental investigation was carried out to study the turbulent flow behind passive grids in a subsonic wind tunnel. The enhanced level of turbulence was generated by five wicker metal grids with square meshes and different parameters (diameter of the grid rod d = 0.3 to 3 mm and the grid mesh size M = 1 to 30 mm). The velocity of the flow was measured by means of a one-dimensional hot-wire probe. For this purpose, skewness, kurtosis, and transverse variation of the velocity fluctuations were determined, obtaining knowledge of the degree of turbulence isotropy and homogeneity in the flow behind grids of variable geometry, for different incoming velocities U = 4, 6, 10, 15, 20 m/s. Approximately, the isotropic and homogeneous turbulence was obtained for x/M > 30. Next, several correlations for turbulence degeneration law were tested. Finally, as the main goal of the study, impact of turbulence intensity on bypass laminar–turbulent transition parameters (transition inception, shape parameter, and the length of the transition region) on a flat plate was investigated. Parameter ITum was created as an integral taken from the leading edge of the plate to the transition inception, divided by the distance from the leading edge to the transition inception, expressing in this way the averaged value of turbulence intensity.

Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe

Associated with Taylor’s classical analysis of scalar solute dispersion in the laminar flow of a solvent in a straight pipe, this work explores the approach towards transverse uniformity of concentration distribution. Mei’s homogenization technique is extended to find solutions for the concentration transport. Chatwin’s result for the approach to longitudinal normality is recovered in terms of the mean concentration over the cross-section. The asymmetrical structure of the concentration cloud and the transverse variation of the concentration distribution are concretely illustrated for the initial stage. The rate of approach to uniformity is shown to be much slower than that to normality. When the longitudinal normality of mean concentration is well established, the maximum transverse concentration difference remains near one-half of the centroid concentration of the cloud. A time scale up to$10 R^2/D$($R$is the radius of the pipe and$D$is the molecular diffusivity) is suggested to characterize the transition to transverse uniformity, in contrast to the time scale of$0.1 R^2/D$estimated by Taylor for the initial stage of dispersion, and that of$1.0 R^2/D$by Chatwin for longitudinal normality.

Dynamics of Rotating Shallow Gravity Currents Passing through a Channel. Part I: Observation of Transverse Structure

A detailed dataset describing a quasi-stationary bottom gravity current, approximately 10 m thick and 10 km wide, passing through a channel-like constriction in the western Baltic Sea is presented. The data include full-depth, synoptic, and highly resolved transects of stratification and turbulence parameters, as well as detailed velocity transects across the gravity current at different down-channel locations. The velocity data reveal a persistent transverse circulation, creating a characteristic wedge-shaped density structure in the interface. A strong asymmetry was also found in the interior of the gravity current, where the evolution of a dynamically significant transverse density gradient to the right of the down-channel flow was observed. Spectral analysis of the near-bottom velocities showed a surprisingly strong contribution to the bottom stress from low-frequency motions with periods up to 30 min that are possibly related to internal wave effects. Cross-channel transects of shear microstructure were used to investigate the transverse variation of local entrainment rates and bottom stresses. These data indicate that frictional control is essential for this class of gravity currents that are characterized by subcritical Froude numbers, small entrainment, strong rotational effects, and small thickness compared to the bottom Ekman layer.

Weakly nonlinear thermoacoustics for stacks with slowly varying pore cross-sections

A general theory of thermoacoustics is derived for arbitrary stack pores. Previous theoretical treatments of porous media are extended by considering arbitrarily shaped pores with the only restriction that the pore cross-sections vary slowly in the longitudinal direction. No boundary-layer approximation is necessary. Furthermore, the model allows temperature variations in the pore wall. By means of a systematic approach based on dimensional analysis and small parameter asymptotics, we derive a set of ordinary differential equations for the mean temperature and the acoustic pressure and velocity, where the equation for the mean temperature follows as a consistency condition of the assumed asymptotic expansion. The problem of determining the transverse variation is reduced to finding a Green's function for a modified Helmholtz equation and solving two additional integral equations. Similarly the derivation of streaming is reduced to finding a single Green's function for the Poisson equation on the desired geometry.