G S Dwarakanath
Articles written in Proceedings – Section A
Volume 71 Issue 3 March 1970 pp 119-140
The paper deals with the structure of collisionless shocks arising from turbulent wave-particle interactions. The conditions under which wave-particle interaction effects could become significant leading to growing waves and a shock are discussed. Using the Mott-Smith expression for the zero-order distribution functions for the ions within the shock, the dielectric constant as well as the integral representing the wave-particle interaction term in the Lenard-Balescu equation are evaluated for a collisionless plasma. An expression is given for the ion distribution function within the shock.
It is shown that the component of the pressure tensor perpendicular to the direction of flow of the plasma leads to a new kind of viscosity term arising from the interaction of the particles with the growing waves and this provides a dissipative mechanism to account for the conversion of the kinetic energy of the incoming plasma into the thermal energy of the hot ionised gas behind the shock.
Volume 74 Issue 3 September 1971 pp 115-132
The structure of strong shock waves in monatomic gases is studied using the Fokker-Planck model to represent the particle collisions and the Mott-Smith distribution to describe the distribution function within the shock front. The differential equation governing the variation of the density within the shock is derived by using the variational principle. The thickness of the shock front is evaluated numerically for various monatomic gases for Mach numbers varying from 2 to 20, and besides, the variation of the shock thickness with viscosity is also studied for different gases. Several parameters of physical interest within the shock, such as density, temperature and mean velocity of flow are evaluated numerically and detailed curves showing their variation within the shock are presented for different Mach numbers. It is found that the temperature rises very steeply, reaches a maximum within a distance less than half the thickness of the shock and then diminishes slowly to attain its asymptotic downstream values. The variation of the mean velocity is slow for weak shocks, but for higher Mach numbers, the mean velocity diminishes steeply and reaches the downstream values within half the thickness of the shock.