Energy cascades in rapidly rotating and stratified turbulence within elongated domains

We study forced, rapidly rotating and stably stratified turbulence in an elongated domain using an asymptotic expansion at simultaneously low Rossby number $\mathit {Ro}\ll 1$ and large domain height compared with the energy injection scale, $h=H/\ell _{in}\gg 1$ . The resulting equations depend on the parameter $\lambda =(h \mathit {Ro} )^{-1}$ and the Froude number $\mathit {Fr}$ . An extensive set of direct numerical simulations (DNS) is performed to explore the parameter space $(\lambda,\mathit {Fr})$ . We show that a forward energy cascade occurs in one region of this space, and a split energy cascade outside it. At weak stratification (large $\mathit {Fr}$ ), an inverse cascade is observed for sufficiently large $\lambda$ . At strong stratification (small $\mathit {Fr}$ ) the flow becomes approximately hydrostatic and an inverse cascade is always observed. For both weak and strong stratification, we present theoretical arguments supporting the observed energy cascade phenomenology. Our results shed light on an asymptotic region in the phase diagram of rotating and stratified turbulence, which is difficult to attain by brute-force DNS.

Energy Spectra of Ensemble of Nonlinear Capillary Waves on a Fluid

The problem of spectral description of the nonlinear capillary waves on the fluid surface is discussed. Usually, three-wave nonlinear interactions are considered as a major factor determined by the energy spectrum of these waves in the kinetic wave turbulent regime. We demonstrate that four-wave interactions should be taken into account. In this case, there are two possible scenarios for the transfer of energy over the wave spectrum: kinetic and dynamic. The first is described by the averaged stochastic interaction of waves using the kinetic equation, while the second is described by dynamic equations written for discrete modes. In this article, we compare the time scales, spectral shapes, and other properties of both energy cascades, allowing them to be identified in an experiment.

Active Turbulence

Active fluids exhibit spontaneous flows with complex spatiotemporal structure, which have been observed in bacterial suspensions, sperm cells, cytoskeletal suspensions, self-propelled colloids, and cell tissues. Despite occurring in the absence of inertia, chaotic active flows are reminiscent of inertial turbulence, and hence they are known as active turbulence. Here, we survey the field, providing a unified perspective over different classes of active turbulence. To this end, we divide our review in sections for systems with either polar or nematic order, and with or without momentum conservation (wet or dry). Comparing to inertial turbulence, we highlight the emergence of power-law scaling with either universal or nonuniversal exponents. We also contrast scenarios for the transition from steady to chaotic flows, and we discuss the absence of energy cascades. We link this feature to both the existence of intrinsic length scales and the self-organized nature of energy injection in active turbulence, which are fundamental differences with inertial turbulence. We close by outlining the emerging picture, remaining challenges, and future directions. Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 13 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Energy Sources Generation and Energy Cascades along the Kuroshio East of Taiwan Island and the East China Sea

There are multi-spatial-scale ocean dynamic processes in the western boundary current region, so the budget of energy source and sink in the Kuroshio Current area can describe the oceanic energy cycle and transformation more accurately. The slope of the one-dimensional spectral energy density varies between −5/3 and −3 in the wavenumber range of 0.02–0.1 cpkm, indicating an inverse energy cascade in the Kuroshio of Taiwan Island and the East China Sea. According to the steady-state energy evolution, an energy source must be present. The locations of energy sources were identified using the spectral energy transfer calculated by 24 years of Ocean General Circulation Model for the Earth Simulator (OFES) data. At the sea surface, the kinetic energy (KE) sources are mainly within 23.2°–25.6° Nand 28°–29° N at less than 0.02 cpkm and within 23.2°–25° N and 26°–30° N at 0.02–0.1 cpkm. The available potential energy (APE) sources are mainly within 22°–28° N and 28.6°–30° N at less than 0.02 cpkm and within22.6°–24.6° N, 25.4°–28° N and 29.2°–30° N at 0.02–0.1 cpkm. Beneath the sea surface, the energy sources are mainly above 400 m depth. Wind stress and density differences are primarily responsible for the KE and APE sources, respectively. Once an energy source is formed, to maintain a steady state, energy cascades (mainly inverse cascades by calculating spectral energy flux) will be engendered. By calculating the energy flux at 600 m depth, KE changes from inflow (sink) to outflow (source), and the conversion depth of source and sink is 380 m. However, outflow of the APE behaves as the source.

Analysis of Energy Sources along the Kuroshio in the East of Taiwan Island and East China Sea

<p>The locations and generation mechanisms of energy sources in the Kuroshio were analyzed. The slope of the one-dimensional spectral energy density varies between -5/3 and -3 in the wavenumber range of 0.03-0.1 cpkm (wavelengths of approximately 209 to 63 km, respectively), indicating an inverse energy cascade in the Kuroshio; according to the steady-state energy evolution, an energy source which occurs at scale smaller than Rhines scale must be present. By analyzing the wavenumber-frequency spectrum, the period of higher kinetic energy (KE) is about 89-209 days and spatial scale is less than 0.03 cpkm. The locations of energy sources were identified with using the spectral energy transfer calculated by altimetry and model data. At the sea surface, the KE sources are mainly within 23.2°-25.2°N and 28°-30°N at less than 0.03 cpkm and 23.2°-23.6°N and 26°-30°N at 0.03-0.1 cpkm. The available potential energy (APE) sources are mainly within 22.2°-28°N and 28.6°-30°N at less than 0.03 cpkm and 29.2°-30°N at 0.03-0.1 cpkm. Wind stress and density differences (including buoyancy flux, temperature flux and salinity flux) are primarily responsible for the KE and APE sources, respectively. Beneath the sea surface, the energy sources are mainly above 400 m depth, and buoyancy flux plays a major role in the generation of energy sources. The energy cycle process can be summarized as follows: once an energy source is formed, to maintain a steady state, energy cascades (mainly inverse cascades) will be engendered.</p><p> </p>

Influence of the Distortion of Vertical Wavenumber Spectra on Estimates of Turbulent Dissipation using the Finescale Parameterization: Eikonal Calculations

The finescale parameterization, formulated on the basis of a weak nonlinear wave–wave interaction theory, is widely used to estimate the turbulent dissipation rate, ε. However, this parameterization has previously been found to overestimate ε in the Antarctic Circumpolar Current (ACC) region. One possible reason for this overestimation is that vertical wavenumber spectra of internal wave energy are distorted from the canonical Garrett-Munk spectrum and have a spectral “hump” at low vertical wavenumbers. Such distorted vertical wavenumber spectra were also observed in other mesoscale eddy-rich regions. In this study, using eikonal simulations, in which internal wave energy cascades are evaluated in the frequency-wavenumber space, we examine how the distortion of vertical wavenumber spectra impacts on the accuracy of the finescale parameterization. It is shown that the finescale parameterization overestimates ε for distorted spectra with a low-vertical-wavenumber hump because it incorrectly takes into account the breaking of these low-vertical-wavenumber internal waves. This issue is exacerbated by estimating internal wave energy spectral levels from the low-wavenumber band rather than from the high-wavenumber band, which is often contaminated by noise in observations. Thus, in order to accurately estimate the distribution of ε in eddy-rich regions like the ACC, high-vertical-wavenumber spectral information free from noise contamination is indispensable.

Examining instabilities due to driven scalars in AdS

We extend the study of the non-linear perturbative theory of weakly turbulent energy cascades in AdSd+1 to include solutions of driven systems, i.e. those with time-dependent sources on the AdS boundary. This necessitates the activation of non-normalizable modes in the linear solution for the massive bulk scalar field, which couple to the metric and normalizable scalar modes. We determine analytic expressions for secular terms in the renormalization flow equations mass values $$ {m}_{BF}^2<{m}^2\le 0 $$ m BF 2 < m 2 ≤ 0 , and for various driving functions. Finally, we numerically evaluate these sources for d = 4 and discuss what role these driven solutions play in the perturbative stability of AdS.