Volume 87, Issue 5
May 1978, pages 85-160
pp 85-105 May 1978
A general analysis of the Hamilton-Jacobi form of dynamics motivated by phase space methods and classical transformation theory is presented. The connection between constants of motion, symmetries, and the Hamilton-Jacobi equation is described.
pp 107-112 May 1978
In an effort to shed further light upon the nature of “supersonic” disturbances as distinct from that of ‘subsonic’ disturbances in parallel compressible flows, this paper makes an investigation of the stability characteristics of the surface waves generated in a liquid layer adjacent to a high-speed gas-stream. It turns out that the nature of the surface waves generated in the liquid layer depends markedly upon the type of disturbances present in the high-speed gas-stream. For the case of ‘subsonic’ disturbances it is shown that the energy transfer from the gas stream to the surface waves is contributed predominantly by the Fourier component of the normal gas-pressure force-field in phase with the slope of the wavy surface. For the case of ‘supersonic’ disturbances, this energy transfer is shown to be predominantly due to the component of the pressure-field in phase with the surface-wave displacement and is related to the presence of travelling periodic waves in the gas-stream—this energy transfer is shown to promote always the growth of the surface waves.
pp 113-123 May 1978
The effect of surface mass transfer velocities having normal, principal and transverse direction components (‘vectored’ suction and injection) on the steady, laminar, compressible boundary layer at a three-dimensional stagnation point has been investigated both for nodal and saddle points of attachment. The similarity solutions of the boundary layer equations were obtained numerically by the method of parametric differentiation. The principal and transverse direction surface mass transfer velocities significantly affect the skin friction (both in the principal and transverse directions) and the heat transfer. Also the inadequacy of assuming a linear viscosity-temperature relation at low-wall temperatures is shown.
pp 125-136 May 1978
The wave propagation at large distances from a source of disturbance (isolated harmonic electric charge or body force of fixed frequency) in an infinite piezoelectric medium belonging to classes (6), (6 m m) or ceramic (α m) and (6 2 2) is discussed by means of asymptotic evaluation (at large distances) of Fourier integrals. Numerical results are given for the (6 m m) crystal class using the constants of cadmium selenide crystal.
pp 137-145 May 1978
The magneto-elastic torsional wave in a bar under initial stress is studied. Most of the equations have been formulated on Biot’s incremental deformation theory and the initial stress has been taken in the form of uniform tension. Two cases have been considered: first when the material of the rod is homogeneous and second when it is non-homogeneous. In both the cases frequency equations for the wave have been calculated
pp 147-160 May 1978
The steady flow in a parallel plate channel rotating with an angular velocity Ω and bounded below by a permeable bed is analysed under the effect of buoyancy force. On the porous bed the boundary condition of Beavers and Joseph is applied and an exact solution of the governing equations is found. The solution in dimensionless form contains four parameters: The permeability parameterσ2, the Grashof numberG, the rotation parameterK2 and a dimensionless constantα. The effects of these parameters, specially,σ2, G andK2, on the slip velocities and velocity distributions are studied. For largeK2, there arise thin boundary layers on the walls of the channel.