How turbulent convective fluctuations organize to form larger-scale structures in planetary atmospheres remains a question that eludes quantitative answers. The assumption this process is the result of an inverse cascade was suggested half century ago two-dimensional fluids, but its applicability atmospheric and oceanic flows heavily debated, hampering our understanding energy balance systems. We show using direct numerical simulations with spatial resolutions 12288

Geophysical and astrophysical fluid flows are typically driven by buoyancy strongly constrained at large scales planetary rotation. Rapidly rotating Rayleigh–Bénard convection (RRRBC) provides a paradigm for experiments direct numerical simulations (DNS) of such flows, but the accessible parameter space remains restricted to moderately fast rotation rates (Ekman numbers ${ {Ek}} \gtrsim 10^{-8}$ ), while realistic ${Ek}$ geo- applications orders magnitude smaller. On other hand, previously...

Abstract

We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we uncover a rich parameter space featuring four distinct branches of stationary solutions: large-scale vortices, hybrid states with embedded shielded vortices (SVs) either sign, two composed many similar SVs. Of the latter, first is dense vortex gas where all...

We study turbulent fluctuation-induced transitions between hurricane-like large-scale vortices and unidirectional jets in stochastically forced, viscously damped two-dimensional turbulence within an elongated periodic domain. Using direct numerical simulations of unprecedented duration, lasting up to 10000 viscous time units, we collect detailed statistical data on the lifetimes these metastable structures quantify impact domain aspect ratio, forcing scale, Reynolds number. also uncover...

Turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across broad spectrum length and time scales. While turbulence ubiquitous, from teacups to planetary atmospheres, oceans, stars, its manifestations can vary considerably different physical systems. For instance, three-dimensional turbulent flows display forward energy cascade large small scales, while in two-dimensional turbulence, cascades In given system, transition such...

In many geophysical and astrophysical flows, suppression of fluctuations along one direction the flow drives a quasi-2D upscale flux kinetic energy, leading to formation strong vortex condensates at largest scales. Recent studies have shown that transition towards this condensate state is hysteretic, giving rise limited bistable range in which both as well regular 3D can exist same parameter values. work, we use direct numerical simulations thin-layer investigate whether survives domain size...

A physically based analytic model ( λ model) is presented to describe the wind profile of tropical cyclones in terms pressure deficit and a single shape parameter ). To test model, an idealized full‐physics numerical employed provide wind‐profile samples also show influence environmental temperature properties initial vortices on cyclone size. It found that provides accurate fit azimuthal at top boundary layer. In simulations, size sensitive sea‐surface temperature, upper tropospheric vortex...

Transient dynamics are of large interest in many areas science. Here, a generalization basin stability (BS) is presented: constrained (CBS) that sensitive to various different types transients arising from finite size perturbations. CBS applied the paradigmatic Lorenz system for uncovering nonlinear precursory phenomena boundary crisis bifurcation. Further, used model Earth's carbon cycle as return time-dependent measure system's global attractor. Both case studies illustrate how CBS's...

We examine the steady state of turbulent flows in thin layers using direct numerical simulations. It is shown that when layer thickness smaller than a critical height, an inverse cascade arises which leads to formation condensate where most energy concentrated largest scale system. For second flow at becomes exactly two-dimensional. The amplitude studied as function and Reynolds number. Bi-stability intermittent bursts are found close two points. results interpreted based on mean-field...

Turbulent flows in a thin layer can develop an inverse energy cascade leading to spectral condensation of when the height is smaller than certain threshold. These condensates take form large-scale vortices physical space. Recently, evidence for bistability was found this system close critical height: depending on initial conditions, flow either condensate state with most two-dimensional (2-D) modes, or three-dimensional (3-D) small-scale modes. This bistable regime characterised by...

We study forced, rapidly rotating and stably stratified turbulence in an elongated domain using asymptotic expansion at simultaneously low Rossby number $\mathit {Ro}\ll 1$ large height compared with the energy injection scale, $h=H/\ell _{in}\gg . The resulting equations depend on parameter $\lambda =(h \mathit {Ro} )^{-1}$ Froude {Fr}$ An extensive set of direct numerical simulations (DNS) is performed to explore space $(\lambda,\mathit {Fr})$ show that a forward cascade occurs one region...

This paper presents a geometric microcanonical ensemble perspective on two-dimensional truncated Euler flows, which contain finite number of (Fourier) modes and conserve energy enstrophy. We explicitly perform phase space volume integrals over shells constant Two applications are considered. In the first part, we determine average spectrum for highly condensed flow configurations show that result is consistent with Kraichnan's canonical description, despite fact no thermodynamic limit...

Instabilities of fluid flows often generate turbulence. Using extensive direct numerical simulations, we study two-dimensional turbulence driven by a wavenumber-localised instability superposed on stochastic forcing, in contrast to previous studies state-independent forcing. As the contribution measured parameter $\gamma$ , increases, system undergoes two transitions. For below first threshold, regular large-scale vortex condensate forms. Above this shielded vortices (SVs) emerge within...

Abstract On–off intermittency occurs in nonequilibrium physical systems close to bifurcation points, and is characterised by an aperiodic switching between a large-amplitude ‘on’ state small-amplitude ‘off’ state. Lévy on–off recently introduced generalisation of multiplicative noise, which depends on stability parameter α skewness β . Here, we derive two novel results leveraging known exact the first-passage time statistics flights. First, compute anomalous critical exponents explicitly as...

We present an alternative form of intermittency, L\'evy on-off which arises from multiplicative $\ensuremath{\alpha}$-stable white noise close to instability threshold. study this problem in the linear and nonlinear regimes, both theoretically numerically, for case a pitchfork bifurcation with fluctuating growth rate. compute stationary distribution analytically numerically associated fractional Fokker-Planck equation Stratonovich interpretation. characterize system parameter space...

The transition from forward to inverse energy cascade in turbulent flows thin layers, varying the functional form of forcing and thickness layer, is investigated. As function becomes more three-dimensional, suppressed critical height ${h}_{c}$, where occurs, decreased.

The cubic-quintic Swift-Hohenberg equation (SH35) has been proposed as an order parameter description of several convective systems with reflection symmetry in the layer midplane, including binary fluid convection. We use numerical continuation, together extensive direct simulations (DNSs), to study SH35 additional nonvariational quadratic term model effects breaking midplane symmetry. structure leads propagation asymmetric spatially localized structures (LSs). An asymptotic prediction for...

Three-dimensional (3D) instabilities on a (potentially turbulent) two-dimensional (2D) flow are still incompletely understood, despite recent progress. Here, based known physical properties of such 3-D instabilities, we propose simple, energy-conserving model describing this situation. It consists 2D point-vortex coupled to localized 3D perturbations (ergophages), that ergophages can gain energy by altering vortex-vortex distances through an induced divergent velocity field, thus decreasing...

Geophysical and astrophysical fluid flows are typically driven by buoyancy strongly constrained at large scales planetary rotation. Rapidly rotating Rayleigh-B\'enard convection (RRRBC) provides a paradigm for experiments direct numerical simulations (DNS) of such flows, but the accessible parameter space remains restricted to moderately fast rotation rates (Ekman numbers $Ek \gtrsim 10^{-8}$), while realistic $Ek$ astro-/geophysical applications orders magnitude smaller. On other hand,...

Turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across broad spectrum length and time scales. While turbulence ubiquitous, from teacups to planetary atmospheres, oceans stars, its manifestations can vary considerably different physical systems. For instance, three-dimensional (3D) turbulent flows display forward energy cascade large small scales, while in two-dimensional (2D) turbulence, cascades In given system,...

Multiple stationary, localized structures were recently found for inclined porous medium convection with constant-temperature boundaries. We analyze traveling asymmetric, convective structures, consisting of 1 to 5 pulses, in a 2D layer fixed temperature at the bottom and an imperfectly conducting boundary top, such that midplane reflection symmetry is broken. Direct numerical simulations (DNS) are performed different Biot numbers top boundary. The drift velocity $c$ pulses measured values...

How turbulent convective fluctuations organise to form large-scale structures in planetary atmospheres remains a question that eludes quantitative answers. The assumption this process is the result of an inverse cascade was suggested half century ago two-dimensional fluids, but its applicability atmospheric and oceanic flows heavily debated, hampering our understanding energy balance systems. We show with direct numerical simulations spatial resolutions 122882 $\times$ 384 points rotating...

Convection is a ubiquitous process driving geophysical/astrophysical fluid flows, which are typically strongly constrained by planetary rotation on large scales. A celebrated model of such rapidly rotating Rayleigh-B\'enard convection, has been extensively studied in direct numerical simulations (DNS) and laboratory experiments, but the parameter values attainable state-of-the-art methods limited to moderately rapid (Ekman numbers $Ek\gtrsim10^{-8}$), while realistic $Ek$ significantly...