arXiv subjects

Tatsuya Yasuda

Publications and source records attributed to Tatsuya Yasuda.

5 recordsLinked to original sources

arXiv2024

Stabilising nonlinear travelling waves in pipe flow using time-delayed feedback

We demonstrate the first successful non-invasive stabilisation of nonlinear travelling waves in a straight cylindrical pipe using time-delayed feedback control (TDF) working in various symmetry subspaces. By using an approximate linear stability analysis and by analysing the frequency domain effect of the control using transfer functions, we find that solutions with well separated unstable eigenfrequencies can have narrow windows of stabilising time-delays. To mitigate this issue we employ a "multiple time-delayed feedback" (MTDF) approach, where several control terms are included to attenuate a broad range of unstable eigenfrequencies. We implement a gradient descent method to dynamically adjust the gain functions in order to reduce the need for tuning a high dimensional parameter space. This results in a novel control method where the properties of the target state are not needed in advance and speculative guesses can result in robust stabilisation. This enables travelling waves to be stabilised from generic turbulent states and unknown travelling waves to be obtained in highly symmetric subspaces.

physics.flu-dyn↗

arXiv2022

Stabilisation of exact coherent structures in two-dimensional turbulence using time-delayed feedback

Time-delayed feedback control, attributed to Pyragas (1992 Physics Letters 170(6) 421-428), is a method known to stabilise periodic orbits in low dimensional chaotic dynamical systems. A system of the form $\dot{\mathbf{x}}(t)=f(\mathbf{x})$ has an additional term $G(\mathbf{x}(t)-\mathbf{x}(t-T))$ introduced where $G$ is some `gain matrix' and $T$ a time delay. The form of the delay term is such that it will vanish for any orbit of period $T,$ therefore making it also an orbit of the uncontrolled system. This non-invasive feature makes the method attractive for stabilising exact coherent structures in fluid turbulence. Here we begin by validating the method for the basic flow in Kolmogorov flow; a two-dimensional incompressible Navier-Stokes flow with a sinusoidal body force. The linear predictions for stabilisation are well captured by direct numerical simulation. By applying an adaptive method to adjust the streamwise translation of the delay, a known travelling wave solution is able to be stabilised up to relatively high Reynolds number. We discover that the famous `odd-number' limitation of this time-delayed feedback method can be overcome in the fluid problem by using the symmetries of the system. This leads to the discovery of 8 additional exact coherent structures which can be stabilised with this approach. This means that certain unstable exact coherent structures can be obtained by simply time-stepping a modified set of equations, thus circumventing the usual convergence algorithms.

physics.flu-dyn↗

arXiv2018

Spatio-temporal intermittency of the turbulent energy cascade

In incompressible and periodic statistically stationary turbulence, exchanges of turbulent energy across scales and space are characterised by very intense and intermittent spatio-temporal fluctuations around zero of the time-derivative term, the spatial turbulent transport of fluctuating energy, and the pressure-velocity term. These fluctuations are correlated with each other and with the intense intermittent fluctuations of the interscale energy transfer rate. These correlations are caused by the sweeping effect, the link between non-linearity and non-locality, and also relate to geometrical alignments between the two-point fluctuating pressure force difference and the two-point fluctuating velocity difference in the case of the correlation between the interscale transfer rate and the pressure-velocity term. All these processes are absent from the spatio-temporal average picture of the turbulence cascade in statistically stationary and homogeneous turbulence.

physics.flu-dyn↗

arXiv2018

Periodic orbits in Large Eddy Simulation of Box Turbulence

We describe and compare two time-periodic flows embedded in Large Eddy Simulation (LES) of turbulence in a three-dimensional, periodic domain subject to constant external forcing. One of these flows models the regeneration of large-scale structures that was observed in this geometry by Yasuda et al. ({\sl Fluid Dyn. Res.} {\bf 46}, 061413, 2014), who used a smaller LES filter length and thus obtained a greater separation of scales of coherent motion. We speculate on the feasibility of modelling the regenerative dynamics with time-periodic solutions in such a flow, which may require novel techniques to deal with the extreme ill-conditioning of the associated boundary value problems.

physics.flu-dyn↗

arXiv2017

Transitions in large eddy simulation of box turbulence

One promising decomposition of turbulent dynamics is that into building blocks such as equilibrium and periodic solutions and orbits connecting these. While the numerical approximation of such building blocks is feasible for flows in small domains and at low Reynolds numbers, computations in developed turbulence are currently out of reach because of the large number of degrees of freedom necessary to represent Navier-Stokes flow on all relevant spatial scales. We mitigate this problem by applying large eddy simulation (LES), which aims to model, rather than resolve, motion on scales below the filter length, which is fixed by a model parameter. By considering a periodic spatial domain, we avoid complications that arise in LES modelling in the presence of boundary layers. We consider the motion of an LES fluid subject to a constant body force of the Taylor-Green type as the separation between the forcing length scale and the filter length is increased. In particular, we discuss the transition from laminar to weakly turbulent motion, regulated by simple invariant solution, on a grid of $32^3$ points.

physics.flu-dyn↗