Forced Linear Shear Flows with Rotation: Rotating Couette–Poiseuille Flow, Its Stability, and Astrophysical Implications

We explore the effect of forcing on the linear shear flow or plane Couette flow, which is also the background flow in the very small region of the Keplerian accretion disk. We show that depending on the strength of forcing and boundary conditions suitable for the systems under consideration, the background plane shear flow, and hence the accretion disk velocity profile, is modified into parabolic flow, which is a plane Poiseuille flow or Couette–Poiseuille flow, depending on the frame of reference. In the presence of rotation, the plane Poiseuille flow becomes unstable at a smaller Reynolds number under pure vertical as well as three-dimensional perturbations. Hence, while rotation stabilizes the plane Couette flow, the same destabilizes the plane Poiseuille flow faster and hence the forced local accretion disk. Depending on the various factors, when the local linear shear flow becomes a Poiseuille flow in the shearing box due to the presence of extra force, the flow becomes unstable even for Keplerian rotation, and hence turbulence will ensue. This helps to resolve the long-standing problem of subcritical transition to turbulence in hydrodynamic accretion disks and the laboratory plane Couette flow.

Parasitic Capillary Waves on Small-Amplitude Gravity Waves with a Linear Shear Current

This paper describes a numerical investigation of ripples generated on the front face of deep-water gravity waves progressing on a vertically sheared current with the linearly changing horizontal velocity distribution, namely parasitic capillary waves with a linear shear current. A method of fully nonlinear computation using conformal mapping of the flow domain onto the lower half of a complex plane enables us to obtain highly accurate solutions for this phenomenon with the wide range of parameters. Numerical examples demonstrated that, in the presence of a linear shear current, the curvature of surface of underlying gravity waves depends on the shear strength, the wave energy can be transferred from gravity waves to capillary waves and parasitic capillary waves can be generated even if the wave amplitude is very small. In addition, it is shown that an approximate model valid for small-amplitude gravity waves in a linear shear current can reasonably well reproduce the generation of parasitic capillary waves.

Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current

We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear current. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive the modal equations from the formulation for plane waves tangent to the ring wave, which opens a way to obtaining important characteristics of the ring waves (group speed, wave action conservation law) and to constructing more general ‘hybrid solutions’ consisting of a part of a ring wave and two tangent plane waves. The modal equations constitute a new spectral problem, and are analysed for a number of examples of surface ring waves in a homogeneous fluid and internal ring waves in a stratified fluid. Detailed analysis is developed for the case of a two-layered fluid with a linear shear current where we study their wavefronts and two-dimensional modal structure. Comparisons are made between the modal functions (i.e. eigenfunctions of the relevant spectral problems) for the surface waves in homogeneous and two-layered fluids, as well as the interfacial waves described exactly and in the rigid-lid approximation. We also analyse the wavefronts of surface and interfacial waves for a large family of power-law upper-layer currents, which can be used to model wind generated currents, river inflows and exchange flows in straits. Global and local measures of the deformation of wavefronts are introduced and evaluated.

Design of Gust Wind Tunnel With Unsteady and Shear Main-Flows

Micro air vehicles (MAVs) have been developed for many fields. The MAVs usually receive strong impact from a velocity change in time or space, and facilities for aerodynamic experiments of MAVs under a gusty environment have been required. The present study has developed a gust wind tunnel to generate unsteady and non-uniform flows. We developed a small wind tunnel with eight multi-fans and a shutter mechanism at the upstream of the test section. We controlled the outputs of the fans independently and obtained a linear shear layer with an error of 5 percent. The velocity gradient of the shear layer was from 5 to 8 s−1. The shutter mechanisms provided a longitudinal gust with the velocity change from 2 m/s to 10 m/s within 0.3 seconds.

Wind inflow observation from load harmonics: initial steps towards a field validation

A previously published wind sensing method is applied to an experimental dataset obtained from a 3.5 MW turbine. The method is based on a load-wind model that correlates once-per-revolution blade load harmonics to rotor-equivalent shears and wind directions. Loads measured during turbine operation are used to estimate online – through the load-wind model – the inflow at the rotor disk, thereby turning the whole turbine into a sort of generalized anemometer. The experimental dataset consists of synchronous measurements of loads, from blade-mounted strain gages, and of the inflow, obtained from a nearby met mast. As the mast reaches only to hub height, a second independent method is used to extend the met-mast-measured shear above hub height to cover the entire rotor disk. Part of the dataset is first used to identify the load-wind model, and then the performance of the wind observer is characterized with the rest of the data. Although the experimental setup falls short of providing a thorough validation of the method, it still allows for a realistic practical demonstration of some of its main features. Results indicate a good quality of the estimated linear shear both in terms of 1 and 10 min averages and of resolved time histories, with mean average errors around 0.04. A similarly accuracy is found in the estimation of the yaw misalignment, with mean errors typically below 3∘.