Interaction Length Scale Research Articles

Axisymmetric flow past a slender body of finite length

The axisymmetric laminar boundary layer on a finite slender body of revolution whose radius scales with the boundary-layer thickness is studied theoretically with the aim of establishing the flow properties near the trailing tip of the body. It is found that, in contrast to the case of two-dimensional flow, the axisymmetric boundary layer does not simply set up an arbitrary velocity profile at the onset of the trailing tip: instead it develops a rather involved and interesting multilayer structure dependent on the trailing-tip shape, which we take to be of the form (1 - x ) n . Because of the unusual nature of the boundary layer at the onset of the trailing tip, we expect that the viscous-inviscid interaction, which comes into play within a short length scale near the tip, is also of a rather novel form. The interaction length scale depends significantly on the range of the index n of the body shape. It is concluded that interactive cases for body shapes with 1/4 < n < ⅓ might be studied next in future work, since for n in this range the wall layer thickness and the body radius are comparable in size and so the interactive flow is not quasi-planar.

Viscous Stabilization of Gravity Wave Critical Level Flows

Abstract A criterion for the viscous stabilization of gravity wave critical level flow is derived to be Z¼≤ 2.5 Zr where Z¼is the vertical thickness of the unstable region in the vicinity of a gravity wave critical level calculated with an inviscid linear theory and Zy is the viscous length scale for gravity wave critical level interaction. The stability implications of this criterion are examined for gravity wave critical level flows in the laboratory, the atmospheric planetary boundary layer, the upper atmosphere and the ocean thermocline region. Laboratory flows, where no turbulence in the vicinity of a gravity wave critical level was observed, are found to meet our criterion for stability. Applying this criterion to atmospheric boundary layer flows implies that no such regions of instability should be observed in the fully developed turbulent convective region, but such turbulent regions should exist in stably stratified cases. Using observed gravity wave parameters for the upper atmosphere the stabil...