Background Shear Flow Research Articles

Shear flow generation by Reynolds stress and suppression of resistive g modes

Suppression of resistive g-mode turbulence by background shear flow generated from a small external flow source and amplified by the fluctuation-induced Reynolds stress is demonstrated and analyzed. The model leads to a paradigm for the low-to-high (L–H) confinement mode transition. To demonstrate the L–H transition model, single-helicity nonlinear fluid simulations using the vorticity equation for the electrostatic potential, the pressure fluctuation equation, and the background poloidal flow equation are used in the sheared slab configuration. The relative efficiency of the external flow and the Reynolds stress for producing shear flow depends on the poloidal flow damping parameter ν, which is given by neoclassical theory. For large ν, the external flow is a dominant contribution to the total background poloidal shear flow and its strength predicted by the neoclassical theory is not enough to suppress the turbulence significantly. In contrast, for small ν, it is shown that the fluctuations drive a Reynolds stress that becomes large and suddenly, at some critical point in time, shear flow much larger than the external flow is generated and leads to an abrupt, order unity reduction of the turbulent transport just like that of the L–H transition in tokamak experiments. It is also found that, even in the case of no external flow, the shear flow generation due to the Reynolds stress occurs through the nonlinear interaction of the resistive g modes and reduces the transport. To supplement the numerical solutions, the Landau equation for the mode amplitude of the resistive g mode is derived, taking into account the fluctuation-induced shear flow and the opposite action of the Reynolds stress in the resistive g turbulence compared with the classical shear flow Kelvin–Helmholtz (KH) driven turbulence is analyzed.

Modons in Shear Flow

Abstract Modons in shear flow are computed as equilibrium solutions of the equivalent barotropic vorticity equation using a numerical Newton–Kantorovich iterative technique with double Fourier spectral expansion. The model is given a first guess of an exact prototype modon with a small shear flow imposed, then iterated to an equilibrium solution. Continuation (small-step extrapolation of the shear amplitude) is used to produce examples of modons embedded in moderate amplitude background shear flows. It is found that in the presence of symmetric shear, the modon is strengthened relative to the prototype. The best-fit phase speed for this case is significantly greater than the Doppler-shifted speed. Nonsymmetric shear strengthens the poles selectively: positive shear strengthens the low while weakening the high. The diagnosed functional relationship between the streamfunction in the traveling reference frame and the vorticity appears linear for all types of shear studied. The modons in symmetric shear are s...

The stability of filamentary vorticity in two-dimensional geophysical vortex-dynamics models

The linear stability of filaments or strips of ‘potential’ vorticity in a background shear flow is investigated for a class of two-dimensional, inviscid, non-divergent models having a linear inversion relation between stream function and potential vorticity. In general, the potential vorticity is not simply the Laplacian of the stream function – the case which has received the greatest attention historically. More general inversion relationships between stream function and potential vorticity are geophysically motivated and give an impression of how certain classic results, such as the stability of strips of vorticity, hold under more general circumstances.In all models, a strip of potential vorticity is unstable in the absence of a background shear flow. Imposing a shear flow that reverses the total shear across the strip, however, brings about stability, independent of the Green-function inversion operator that links the stream function to the potential vorticity. But, if the Green-function inversion operator has a sufficiently short interaction range, the strip can also be stabilized by shear having the same sense as the shear of the strip. Such stabilization by ‘co-operative’ shear does not occur when the inversion operator is the inverse Laplacian. Nonlinear calculations presented show that there is only slight disruption to the strip for substantially less adverse shear than necessary for linear stability, while for co-operative shear, there is major disruption to the strip. It is significant that the potential vorticity of the imposed flow necessary to create shear of a given value increases dramatically as the interaction range of the inversion operator decreases, making shear stabilization increasingly less likely. This implies an increased propensity for filaments to ‘roll-up’ into small vortices as the interaction range decreases, a finding consistent with many numerical calculations performed using the quasi-geostrophic model.

On the dynamics of near-wall turbulence

A model of the dynamic physical processes that occur in the near-wall region of a turbulent flow at high Reynolds numbers is described. The hairpin vortex is postulated to be the basic flow structure of the turbulent boundary layer. It is argued that the central features of the near-wall flow can be explained in terms of how asymmetric hairpin vortices interact with the background shear flow, with each other, and with the surface layer near the wall. The physical process that leads to the regeneration of new hairpin vortices near the surface is described, as well as the processes of evolution of such vortices to larger-scale motions farther from the surface. The model is supported by recent important developments in the theory of unsteady surface-layer separation and a number of ‘kernel' experiments which serve to elucidate the basic fluid mechanics phenomena believed to be relevant to the turbulent boundary layer. Explanations for the kinematical behaviour observed in direct numerical simulations of low Reynolds number boundary-layer and channel flows are given. An important aspect of the model is that it has been formulated to be consistent with accepted rational mechanics concepts that are known to provide a proper mathematical description of high Reynolds number flow.

Simple Dynamical Models of Neptune's Great Dark Spot

The large amplitude oscillations of the shape of Neptune's Great Dark Spot are well reproduced by simple dynamical models of an isolated vortex embedded in a background shear flow. From the time series of the aspect ratio and inclination of the vortex values are estimated for the background shear and the mean vorticity of the Great Dark Spot, and a lower bound is placed on the value of the Rossby deformation radius. These models imply the existence of a planetary-scale zone of deterministic chaotic advection in the atmosphere of Neptune.

Stationary Drift-Rossby Vortices in Shear Flows

Stationary vortex solutions of the Charney-Hasegawa-Mima equation describing planetary Rossby waves and plasma drift waves are analyzed for background flow with velocity shear. The solutions are obtained by Larichev-Reznik's method that divides the entire plane into two regions by a circle on which the internal and external solutions of linear equations are connected. The boundary conditions on the circle are satisfied correctly by adding a vorticity-free flow to the external background shear flow. Explicit flow patterns, dipolar, tripolar and quadrupolar, are given for several kinds of the background shear flows; the monopolar vortex like the Jovian Red Spot could not be obtained by this method. Another method is given, to derive a nonlinear equation for the stream function when the equilibrium density profile and shear flow in a plasma are prescribed.

Chaotic Lagrangian trajectories around an elliptical vortex patch embedded in a constant and uniform background shear flow

The Lagrangian flow around a Kida vortex [J. Phys. Soc. Jpn. 50, 3517 (1981)], an elliptical two-dimensional vortex patch embedded in a uniform and constant background shear, is described by a nonintegrable two-degree-of-freedom Hamiltonian. For small values of shear, there exist large chaotic zones surrounding the vortex, often much larger than the vortex itself and extremely close to its boundary. Motion within the vortex is integrable. Implications for two-dimensional turbulence are discussed.

Resonant wave interactions in a stratified shear flow

Resonant interactions between triads of internal gravity waves propagating in a shear flow are considered for the case when the stratification and the background shear flow vary slowly with respect to typical wavelengths. If ωn, kn(n = 1, 2, 3) are the local frequencies and wavenumbers respectively then the resonance conditions are that ω1 + ω2 + ω3 = 0 and k1 + k2 + k3 = 0. If the medium is only weakly inhomogeneous, then there is a strong resonance and to leading order the resonance conditions are satisfied globally. The equations governing the wave amplitudes are then well known, and have been extensively discussed in the literature. However, if the medium is strongly inhomogeneous, then there is a weak resonance and the resonance conditions can only be satisfied locally on certain space-time resonance surfaces. The equations governing the wave amplitudes in this case are derived, and discussed briefly. Then the results are applied to a study of the hierarchy of wave interactions which can occur near a critical level, with the aim of determining to what extent a critical layer can reflect wave energy.