Beyond Coherent Structures

Duration: 1 hour 8 mins

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Description:	Javier Jimenez, Universidad Politécnica de Madrid 7 January 2022 – 13:00 to 14:00


Created:	2022-01-10 16:02
Collection:	Mathematical aspects of turbulence: where do we stand?
Publisher:	Isaac Newton Institute
Copyright:	Javier Jimenez
Language:	eng (English)


Abstract:	Much of what we know about interscale transfer in turbulence is due to Kolmogorov (for energy), or to Townsend (for momentum in shear flows). We also have a reasonably good understanding of the viscous vortices at the small-scale end of the energy cascade, and a (less definite) one that the energy input at the large-scale end of the momentum cascade is a linear process, in the sense that the fluctuations extract their energy from the mean shear. While we know little about the geometry of the flow in the inertial range, and it is doubtful that the concept of shape applies to it, the dissipative vortices and the production mechanism have definite shapes and dimensions, leading to the concept of coherent structures. These are good representations of shear flows. They evolve under their own dynamics to a first approximation, and account for most of the dissipation and of the energy production. Some of these dynamics are well understood: shear instabilities, lift-up, Orr bursts, the self-sustaining cycle, etc. They will be briefly reviewed, with emphasis on what is universal and what is particular about them. But we will also argue that a representation in terms of structures is incomplete. In the first place, their description as self-contained dynamical systems begs the question of how are they initiated? Secondly, turbulence is clearly not a fully linear process, and the effect of nonlinearity is poorly understood: what limits linear growth? How do the different scales interact? We will argue that a further level of description is required in which the causal connection of the different coherent processes is explicitly addressed, and that current computers are beginning to make such an analysis possible.

Abstract:

Much of what we know about interscale transfer in turbulence is due to Kolmogorov (for energy), or to Townsend (for momentum in shear flows). We also have a reasonably good understanding of the viscous vortices at the small-scale end of the energy cascade, and a (less definite) one that the energy input at the large-scale end of the momentum cascade is a linear process, in the sense that the fluctuations extract their energy from the mean shear.
While we know little about the geometry of the flow in the inertial range, and it is doubtful that the concept of shape applies to it, the dissipative vortices and the production mechanism have definite shapes and dimensions, leading to the concept of coherent structures. These are good representations of shear flows. They evolve under their own dynamics to a first approximation, and account for most of the dissipation and of the energy production. Some of these dynamics are well understood: shear instabilities, lift-up, Orr bursts, the self-sustaining cycle, etc. They will be briefly reviewed, with emphasis on what is universal and what is particular about them.
But we will also argue that a representation in terms of structures is incomplete. In the first place, their description as self-contained dynamical systems begs the question of how are they initiated? Secondly, turbulence is clearly not a fully linear process, and the effect of nonlinearity is poorly understood: what limits linear growth? How do the different scales interact? We will argue that a further level of description is required in which the causal connection of the different coherent processes is explicitly addressed, and that current computers are beginning to make such an analysis possible.

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