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The stability of spiral flow between rotating and sliding cylinders is considered. In the limit of narrow gap, a’ modified’ energy theory is constructed. This theory exploits the consequences of assuming the existence of a preferred spiral direction along which disturbances do not vary. The flow is also analyzed from the viewpoint of linearized theory. Both problems depend strongly on the sign of Rayleigh's discriminant, – 2Ωζ. Here Ω is the component of angular velocity, and ζ is the component of total vorticity of the basic flow in the direction perpendicular to the spiral ribbons on which the disturbance is constant. When the discriminant is negative, there is evidently no instability to infinitesimal disturbances, and the spiral disturbance whose energy increases at the smallest R is a roll whose axis is perpendicular to the stream. This restores and generalizes Orr's non-linear results for disturbances having a preferred spiral direction. When the discriminant is positive, the critical disturbances of linear theory and the modified energy theory are spiral vortices. The differences between the energy and linear limits can be made smaller in the restricted class of disturbances with coincidence achieved for axisymmetric disturbances in the rotating cylinder problem in the limit of narrow gap. For the sliding-rotating case, the critical disturbance of the linear theory appears as a periodic wave in a co-ordinate system fixed on the outer cylinder. This wave has a dimensionless frequency equal to - ½ a sin (χ-ψ), where a is the wave-number, χ is the angle between the pipe axis and the direction of motion of the inner cylinder relative to the outer one, and ψ is the disturbance spiral angle.Instability limits, frequencies and wave-numbers are computed numerically when the cylinder gap is not narrow. These are in even closer agreement with Ludwieg's experimental results than the approximate results which were given in part 1.

Abstract-Computer industry has adopted multi-threaded and multi-core architectures as the clock rate increase stalled in early 2000's. However, because of the lack of compilers and other related software technologies, most of the generalpurpose applications today still cannot take advantage of such architectures to improve their performance. Thread-level speculation (TLS) has been proposed as a way of using these multi-threaded architectures to parallelize general-purpose applications. Both simultaneous multithreading (SMT) and chip multiprocessors (CMP) have been extended to implement TLS. While the characteristics of SMT and CMP have been widely studied under multi-programmed and parallel workloads, their behavior under TLS workload is not well understood. The TLS workload due to speculative nature of the threads which could potentially be rollbacked and due to variable degree of parallelism available in applications, exhibits unique characteristics which makes it different from other workloads. In this paper, we present a detailed study of the performance, power consumption and thermal effect of these multithreaded architectures against that of a Superscalar with equal chip area. A wide spectrum of design choices and tradeoffs are also studied using commonly used simulation techniques. We show that the SMT based TLS architecture performs about 21% better than the best CMP based configuration while it suffers about 16% power overhead. In terms of Energy-Delay-Squared product (ED 2 ), SMT based TLS performs about 26% better than the best CMP based TLS configuration and 11% better than the superscalar architecture. But the SMT based TLS configuration, causes more thermal stress than the CMP based TLS architectures.