Irreversiblity in Bacterial Turbulence: Insights from the Mean-Bacterial-Velocity Model

Venkata, Kiran, Kolluru; Gupta, Anupam; and, Akhilesh Kumar Verma; Pandit, Rahul

doi:10.48550/arxiv.2201.12722

Cited by 4 publications

(6 citation statements)

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“…Therefore, to make our con- jecture robust, we perform an additional self-consistency check by observing that the scaling forms of E(k) and τ eff for α α c implies a scale-dependent flux |Π(k)| ∼ k 3/8 . (The lack of constant fluxes in such systems, unlike inertial turbulence, has been observed in previous studies [17,18] as well, although its precise form remained unobserved.) While scaling measurements of flux are less clean than for energy spectra, we find (Fig.…”

mentioning

confidence: 70%

“…( 1), multiplying the resultant equation with u (k) (which is the complex-conjugate of u(k)) and taking the shell-sum as in Eq. ( 5) gives the energy spectrum equation [17,18] as…”

Section: Appendix A: Direct Numerical Simulationsmentioning

confidence: 99%

“…rms /2 [17,18]. The assumption of a scale-independent τ eff is reasonable when δ 0: Larger scales carry less energy and their role in distorting small scales is marginal.…”

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confidence: 99%

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Intermittency, fluctuations and maximal chaos in an emergent universal state of active turbulence

Mukherjee¹,

Singh²,

James³

et al. 2022

Preprint

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A hydrodynamic model of active, low Reynolds number suspensions, shows the emergence of an asymptotic state with a universal spectral scaling and non-Gaussian (intermittent) fluctuations in the velocity field. Such states arise when these systems are pushed beyond a critical level of activity and show features akin to high Reynolds number, inertial turbulence. We provide compelling numerical and analytical evidence for the existence of such a transition at a critical value of activity and further show that the maximally chaotic states are tied to this transition.

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mentioning

confidence: 70%

“…( 1), multiplying the resultant equation with u (k) (which is the complex-conjugate of u(k)) and taking the shell-sum as in Eq. ( 5) gives the energy spectrum equation [17,18] as…”

Section: Appendix A: Direct Numerical Simulationsmentioning

confidence: 99%

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Intermittency, fluctuations and maximal chaos in an emergent universal state of active turbulence

Mukherjee¹,

Singh²,

James³

et al. 2022

Preprint

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“…The next step is to ignore the first term 4 . Given that Re ν is the dominant term, we write (C. 19) in the simplified form…”

Section: Discussionmentioning

confidence: 99%

An analytical and computational study of the incompressible Toner-Tu Equations

Gibbon¹,

Venkata²,

Padhan³

et al. 2022

Preprint

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We consider the incompressible Toner-Tu (ITT) partial differential equations (PDEs), which are an important example of a set of active-fluid PDEs. They share many properties with the Navier-Stokes equations (NSEs) but there are also important differences. The NSEs are usually considered either in the decaying or the additively forced cases, whereas the ITT equations have no additive forcing, but instead have a linear, activity term αu (with u the velocity field), which pumps energy into the system; they also have a negative u|u| 2 -term that stabilizes growth and provides a platform for either frozen or statistically steady states. These differences make the ITT equations an intriguing candidate for study using a combination of PDE analysis and pseudospectral direct numerical simulations (DNSs). In the d = 2 case, we have established global regularity of solutions. We have also shown the existence of bounded hierarchies of weighted, time-averaged norms of both higher derivatives and higher moments of the velocity field. For d = 3 there are equivalent bounded hierarchies for Leray-type weak solutions. We present results for these norms from our DNSs in both d = 2 and d = 3, and contrast them with their counterparts for the d = 3 NSEs.

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“…Step The next step is to ignore the first term. 5 Given that Re ν is the dominant term, we write (C. 19) in the simplified form (C.23) 5 The term with the negative exponent of H n on the RHS of (C. 19) is only out of control if H n temporarily becomes very small. In principle, this could be dealt with by adding a constant term to H n to provide the platform of a lower bound.…”

Section: Appendix C Proofs In the D = 3 Casementioning

confidence: 99%