Strong wave-mean-flow coupling in baroclinic acoustic streaming

The interaction of an acoustic wave with a stratified fluid can drive strong streaming flows owing to the baroclinic production of fluctuating vorticity, as recently demonstrated by Chini et al. (J. Fluid Mech., 744, 2014, pp. 329). In the present investigation, a set of wave/mean-flow interaction equations is derived that governs the coupled dynamics of a standing acoustic wave mode of characteristic (small) amplitude {\epsilon} and the streaming flow it drives in a thin channel with walls maintained at differing temperatures. Unlike classical Rayleigh streaming, the resulting mean flow arises at O({\epsilon}) rather than at O({\epsilon^2}). Consequently, fully two-way coupling between the waves and the mean flow is possible: the streaming is sufficiently strong to induce O(1) rearrangements of the imposed background temperature and density fields, which modifies the spatial structure and frequency of the acoustic mode on the streaming time scale. A novel Wentzel-Kramers-Brillouin-Jeffreys analysis is developed to average over the fast wave dynamics, enabling the coupled system to be integrated strictly on the slow time scale of the streaming flow. Analytical solutions of the reduced system are derived for weak wave forcing and are shown to reproduce results from prior direct numerical simulations (DNS) of the compressible Navier Stokes and heat equations with remarkable accuracy. Moreover, numerical simulations of the reduced system are performed in the regime of strong wave mean flow coupling for a fraction of the computational cost of the corresponding DNS. These simulations shed light on the potential for baroclinic acoustic streaming to be used as an effective means to enhance heat transfer.Comment: 29 pages, 7 figure

Regimes of stratified turbulence at low Prandtl number

Quantifying transport by strongly stratified turbulence in low Prandtl number ($Pr$) fluids is critically important for the development of better models for the structure and evolution of stellar interiors. Motivated by recent numerical simulations showing strongly anisotropic flows suggestive of scale-separated dynamics, we perform a multiscale asymptotic analysis of the governing equations. We find that, in all cases, the resulting slow-fast system naturally takes a quasilinear form. Our analysis also reveals the existence of several distinct dynamical regimes depending on the emergent buoyancy Reynolds and P\'eclet numbers, $Re_b = \alpha^2 Re$ and $Pe_b = Pr Re_b$, respectively, where $\alpha$ is the aspect ratio of the large-scale turbulent flow structures, and $Re$ is the outer scale Reynolds number. Scaling relationships relating the aspect ratio, the characteristic vertical velocity, and the strength of the stratification (measured by the Froude number $Fr$) naturally emerge from the analysis. When $Pe_b \ll \alpha$, the dynamics at all scales is dominated by buoyancy diffusion, and our results recover the scaling laws empirically obtained from direct numerical simulations by Cope et al. (2020). For $Pe_b \ge O(1)$, diffusion is negligible (or at least subdominant) at all scales and our results are consistent with those of Chini et al. (2022) for strongly stratified geophysical turbulence at $Pr = O(1)$.Finally, we have identified a new regime for $\alpha \ll Pe_b \ll 1$, in which slow, large scales are diffusive while fast, small scales are not. We conclude by presenting a map of parameter space that clearly indicates the transitions between isotropic turbulence, non-diffusive stratified turbulence, diffusive stratified turbulence and viscously-dominated flows.Comment: 25 pages, 1 figur

Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Benard convection

An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Benard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the "background field" variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Benard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents alpha and beta in the presumed Nu similar to (PrRa beta)-Ra-alpha scaling relation. The computations clearly show that for Ra <= 10(10) at fixed L = 2 root 2, Nu <= 0.106Pr(0)Ra(5/12), which indicates that molecular transport cannot generally be neglected in the "ultimate" high-Ra regime.NSF DMS-0928098 DMS-1515161 DMS-0927587 PHY-1205219Simons FoundationNSFONRInstitute for Computational Engineering and Sciences (ICES

A self-sustaining process theory for uniform momentum zones and internal shear layers in high Reynolds number shear flows

Many exact coherent states (ECS) arising in wall-bounded shear flows have an asymptotic structure at extreme Reynolds number Re in which the effective Reynolds number governing the streak and roll dynamics is O(1). Consequently, these viscous ECS are not suitable candidates for quasi-coherent structures away from the wall that necessarily are inviscid in the mean. Specifically, viscous ECS cannot account for the singular nature of the inertial domain, where the flow self-organizes into uniform momentum zones (UMZs) separated by internal shear layers and the instantaneous streamwise velocity develops a staircase-like profile. In this investigation, a large-Re asymptotic analysis is performed to explore the potential for a three-dimensional, short streamwise- and spanwise-wavelength instability of the embedded shear layers to sustain a spatially-distributed array of much larger-scale, effectively inviscid streamwise roll motions. In contrast to other self-sustaining process theories, the rolls are sufficiently strong to differentially homogenize the background shear flow, thereby providing a mechanistic explanation for the formation and maintenance of UMZs and interlaced shear layers that respects the leading-order balance structure of the mean dynamics

Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions

We investigate the structure of strongly nonlinear Rayleigh–Bénard convection cells in the asymptotic limit of large Rayleigh number and fixed, moderate Prandtl number. Unlike the flows analyzed in prior theoretical studies of infinite Prandtl number convection, our cellular solutions exhibit dynamically inviscid constant-vorticity cores. By solving an integral equation for the cell-edge temperature distribution, we are able to predict, as a function of cell aspect ratio, the value of the core vorticity, details of the flow within the thin boundary layers and rising/falling plumes adjacent to the edges of the convection cell, and, in particular, the bulk heat flux through the layer. The results of our asymptotic analysis are corroborated using full pseudospectral numerical simulations and confirm that the heat flux is maximized for convection cells that are roughly square in cross section

AMI observations of northern supernova remnants at 14-18 GHz

We present observations between 14.2 and 17.9 GHz of 12 reported supernova remnants (SNRs) made with the Arcminute Microkelvin Imager Small Array (AMI SA). In conjunction with data from the literature at lower radio frequencies, we determine spectra of these objects. For well-studied SNRs (Cas A, Tycho's SNR, 3C58 and the Crab Nebula), the results are in good agreement with spectra based on previous results. For the less well-studied remnants the AMI SA observations provide higher-frequency radio observations than previously available, and better constrain their radio spectra. The AMI SA results confirm a spectral turnover at ~11 GHz for the filled-centre remnant G74.9+1.2. We also see a possible steepening of the spectrum of the filled-centre remnant G54.1+0.3 within the AMI SA frequency band compared with lower frequencies. We confirm that G84.9+0.5, which had previously been identified as a SNR, is rather an HII region and has a flat radio spectrum.Comment: 12 pages, 24 figures, accepted MNRA

The Arabidopsis thaliana F-box gene HAWAIIAN SKIRT is a new player in the microRNA pathway

In Arabidopsis, the F-box HAWAIIAN SKIRT (HWS) protein is important for organ growth. Loss of function of HWS exhibits pleiotropic phenotypes including sepal fusion. To dissect the HWS role, we EMS-mutagenized hws-1 seeds and screened for mutations that suppress hws-1 associated phenotypes. We identified shs-2 and shs-3 (suppressor of hws-2 and 3) mutants in which the sepal fusion phenotype of hws-1 was suppressed. shs-2 and shs-3 (renamed hst-23/hws-1 and hst-24/hws-1) carry transition mutations that result in premature terminations in the plant homolog of Exportin-5 HASTY (HST), known to be important in miRNA biogenesis, function and transport. Genetic crosses between hws-1 and mutant lines for genes in the miRNA pathway, also suppress the phenotypes associated with HWS loss of function, corroborating epistatic relations between the miRNA pathway genes and HWS. In agreement with these data, accumulation of miRNA is modified in HWS loss or gain of function mutants. Our data propose HWS as a new player in the miRNA pathway, important for plant growth