Dimensional transition in rotating turbulence

In this work we investigate, by means of direct numerical simulations, how rotation affects the bi-dimensionalization of a turbulent flow. We study a thin layer of fluid, forced by a two-dimensional forcing, within the framework of the "split cascade" in which the injected energy flows both to small scales (generating the direct cascade) and to large scale (to form the inverse cascade). It is shown that rotation reinforces the inverse cascade at the expense of the direct one, thus promoting bi-dimensionalization of the flow. This is achieved by a suppression of the enstrophy production at large scales. Nonetheless, we find that, in the range of rotation rates investigated, increasing the the vertical scale causes a reduction of the flux of the inverse cascade. Our results suggest that, even in rotating flows, the inverse cascade may eventually disappear when the vertical scale is sufficiently large with respect to the forcing scale

A new method for isolating turbulent states in transitional stratified plane Couette flow

We present a new adaptive control strategy to isolate and stabilize turbulent states in transitional, stably stratified plane Couette flow in which the gravitational acceleration (non-dimensionalized as the bulk Richardson number$Ri$) is adjusted in time to maintain the turbulent kinetic energy (TKE) of the flow. We demonstrate that applying this method at various stages of decaying stratified turbulence halts the decay process and allows a succession of intermediate turbulent states of decreasing energy to be isolated and stabilized. Once the energy of the initial flow becomes small enough, we identify a single minimal turbulent spot, and lower-energy states decay to laminar flow. Interestingly, the turbulent states which emerge from this process have very similar time-averaged$Ri$, but TKE levels different by an order of magnitude. The more energetic states consist of several turbulent spots, each qualitatively similar to the minimal turbulent spot. This suggests that the minimal turbulent spot may well be the lowest-energy turbulent state which forms a basic building block of stratified plane Couette flow. The fact that a minimal spot of turbulence can be stabilized, so that it neither decays nor grows, opens up exciting opportunities for further study of spatiotemporally intermittent stratified turbulence.The EPSRC grant EP/K034529/1 entitled ‘Mathematical Underpinnings of Stratified Turbulence’ is gratefully acknowledged for supporting the research presented here.This is the author accepted manuscript. The final version is available from Cambridge University Press via https://doi.org/10.1017/jfm.2016.62

Forcing-dependent dynamics and emergence of helicity in rotating turbulence

The effects of large-scale mechanical forcing on the dynamics of rotating turbulent flows are studied by means of direct numerical simulations, systematically varying the nature of the mechanical force in time. We find that the statistically stationary solutions of these flows depend on the nature of the forcing mechanism. Rapidly enough rotating flows with a forcing that has a persistent direction relative to the axis of rotation bifurcate from a non-helical state to a helical state despite the fact that the forcing is non-helical. We demonstrate that the nature of the mechanical force in time and the emergence of helicity have direct implications for the cascade dynamics of these flows, determining the anisotropy in the flow, the energy condensation at large scales and the power-law energy spectra that are consistent with previous findings and phenomenologies under strong and weak turbulence

Numerical studies in rotating and stratified turbulence

Although turbulence has been studied for more than five hundred years, a thorough understanding of turbulent flows is still missing. Nowadays computing power can offer an alternative tool, besides measurements and experiments, to give some insights into turbulent dynamics. In this thesis, numerical simulations are employed to study homogeneous and wall-bounded turbulence in rotating and stably stratified conditions, as encountered in geophysical flows where the rotation of the Earth as well as the vertical density variation influence the dynamics. In the context of homogeneous turbulence, we investigate how the transfer of energy among scales is affected by the presence of strong but finite rotation and stratification. Unlike geostrophic turbulence, we show that there is a forward energy cascade towards small scales which is initiated at the forcing scales. The contribution of this process to the general dynamic is secondary at large scales but becomes dominant at smaller scales where it leads to a shallowing of the energy spectrum, from k-3 to k-5/3. Two-point statistics show a good agreement with measurements in the atmosphere, suggesting that this process is an important mechanism for energy transfer in the atmosphere. Boundary layers subjected to system rotation around the wall-normal axis are usually referred to as Ekman layers and they can be seen as a model of the atmospheric and oceanic boundary layers developing at mid and high latitudes. We study the turbulent dynamics in Ekman layers by means of numerical simulations, focusing on the turbulent structures developing at moderately high Reynolds numbers. For neutrally stratified conditions, we show that there exists a turbulent helicity cascade in the logarithmic region. We focus on the effect of a stable stratification produced by a vertical positive temperature gradient. For moderate stratification, continuously turbulent regimes are produced which are in fair agreement with existing theories and models used in the context of atmospheric boundary layer dynamics. For larger degree of stratification, we show that laminar and turbulent motions coexist and displace along inclined patterns similar to what has been recently observed in other transitional flows.QC 20131210</p

Third-order structure functions in rotating and stratified turbulence: a comparison between numerical, analytical and observational results

International audienceFirst, we review analytical and observational studies on third-order structure functions including velocity and buoyancy increments in rotating and stratified turbulence and discuss how these functions can be used in order to estimate the flux of energy through different scales in a turbulent cascade. In particular, we suggest that the negative third-order velocity–temperature–temperature structure function that was measured by Lindborg & Cho (Phys. Rev. Lett., vol. 85, 2000, p. 5663) using stratospheric aircraft data may be used in order to estimate the downscale flux of available potential energy (APE) through the mesoscales. Then, we calculate third-order structure functions from idealized simulations of forced stratified and rotating turbulence and compare with mesoscale results from the lower stratosphere. In the range of scales with a downscale energy cascade of kinetic energy (KE) and APE we find that the third-order structure functions display a negative linear dependence on separation distance $r$, in agreement with observation and supporting the interpretation of the stratospheric data as evidence of a downscale energy cascade. The spectral flux of APE can be estimated from the relevant third-order structure function. However, while the sign of the spectral flux of KE is correctly predicted by using the longitudinal third-order structure functions, its magnitude is overestimated by a factor of two. We also evaluate the third-order velocity structure functions that are not parity invariant and therefore display a cyclonic–anticyclonic asymmetry. In agreement with the results from the stratosphere, we find that these functions have an approximate $r^2$-dependence, with strong dominance of cyclonic motions

Research data supporting "A new method for isolating turbulent states in transitional stratified plane Couette flow"

This dataset contains HDF5 files with three-dimensional flow fields from several key times in the reported model simulations. The initial condition is provided, and the code is open access, allowing the full time-dependent model simulations to be reproduced. In addition, several 3D fields from the subsequent model evolution are included which were used to make figures in the published manuscript. The HDF5 file format is self-describing with header metadata and is readable in a wide variety of available software packages.EPSRC [EP/K034529/1

Numerical study of the stabilisation of boundary-layer disturbances by finite amplitude streaks

Well-resolved large-eddy simulations of passive control of the laminar-turbulent transition process in flat-plate boundary-layer flows are presented. A specific passive control mechanism is studied, namely the modulation of the laminar boundary-layer profile by a periodic array of steady boundary-layer streaks. This has been shown experimentally to stabilise the exponential growth of Tollmien-Schlichting (TS) waves and delay transition to turbulence. Here we examine the effect of the steady modulations on the amplification of different types of disturbances such as TS-waves, stochastic noise and free-stream turbulence. In our numerical simulations, the streaks are forced at the inflow as optimal solutions to the linear parabolic stability equations (PSE), whereas the additional disturbances are excited via volume forcing active within the computational domain. The simulation results show, in agreement with experimental and theoretical studies, significant damping of unstable two-dimensional TS-waves of various frequencies when introduced into a modulated base flow: The damping characteristics are mainly dependent on the streak amplitude. A new phenomenon is also identified which is characterised by the strong amplification via nonlinear interactions of the second spanwise harmonic of the streak when the streak amplitude is comparable to the TS amplitude. Furthermore, we demonstrate that control by streaks can be effective also in case of stochastic two-dimensional noise. However, as soon as a significant three-dimensionality is dominant, as in e.g. oblique or bypass transition, control by streaks leads often to premature transition. Visualisations of the flow fields are used to highlight the different vortical structures and their interactions that are relevant to the various transition scenarios and the corresponding control by streamwise streak