Exploiting self-organized criticality in strongly stratified turbulence

A multiscale reduced description of turbulent free shear flows in the presence of strong stabilizing density stratification is derived via asymptotic analysis of the Boussinesq equations in the simultaneous limits of small Froude and large Reynolds numbers. The analysis explicitly recognizes the occurrence of dynamics on disparate spatiotemporal scales, yielding simplified partial differential equations governing the coupled evolution of slow large-scale hydrostatic flows and fast small-scale isotropic instabilities and internal waves. The dynamics captured by the coupled reduced equations is illustrated in the context of two-dimensional strongly stratified Kolmogorov flow. A noteworthy feature of the reduced model is that the fluctuations are constrained to satisfy quasilinear (QL) dynamics about the comparably slowly varying large-scale fields. Crucially, this QL reduction is not invoked as an ad hoc closure approximation, but rather is derived in a physically relevant and mathematically consistent distinguished limit. Further analysis of the resulting slow–fast QL system shows how the amplitude of the fast stratified-shear instabilities is slaved to the slowly evolving mean fields to ensure the marginal stability of the latter. Physically, this marginal stability condition appears to be compatible with recent evidence of self-organized criticality in both observations and simulations of stratified turbulence. Algorithmically, the slaving of the fluctuation fields enables numerical simulations to be time-evolved strictly on the slow time scale of the hydrostatic flow. The reduced equations thus provide a solid mathematical foundation for future studies of three-dimensional strongly stratified turbulence in extreme parameter regimes of geophysical relevance and suggest avenues for new sub-grid-scale parametrizations.

Effects of the Control Parameters on the Stability of a Laminar Boundary Layer on a Porous Flat Plate

This work is devoted to the analysis of the linear temporal stability of a laminar dynamic boundary layer on a horizontal porous plane plate. The basic flow is assumed to be laminar and two-dimensional. The basic flow velocity profiles are obtained by numerically solving the Blasius equation using the Runge-Kutta method. The perturbations of these basic solutions are expressed in the form of three-dimensional Tollmien-Schlichting waves. The formulation of the stability problem leads to the Orr-Sommerfeld equation modified by the permeability parameter (Darcy number) and the small Reynolds number. This equation is given in a general form which can be applied to the Chebyshev domain and the boundary layer domain and solved numerically using the Chebyshev spectral collocation method. The marginal stability diagrams, the critical Reynolds numbers and the eigenvalue spectra are obtained for different values of the parameters which have modified the stability equation. Numerical solutions indicate the importance of the effect of these parameters on the flow stability characteristics.

Adaptive Critical Balance and Firehose Instability in an Expanding, Turbulent, Collisionless Plasma

Using a hybrid-kinetic particle-in-cell simulation, we study the evolution of an expanding, collisionless, magnetized plasma in which strong Alfvénic turbulence is persistently driven. Temperature anisotropy generated adiabatically by the plasma expansion (and consequent decrease in the mean magnetic-field strength) gradually reduces the effective elasticity of the field lines, causing reductions in the linear frequency and residual energy of the Alfvénic fluctuations. In response, these fluctuations modify their interactions and spatial anisotropy to maintain a scale-by-scale “critical balance” between their characteristic linear and nonlinear frequencies. Eventually the plasma becomes unstable to kinetic firehose instabilities, which excite rapidly growing magnetic fluctuations at ion-Larmor scales. The consequent pitch-angle scattering of particles maintains the temperature anisotropy near marginal stability, even as the turbulent plasma continues to expand. The resulting evolution of parallel and perpendicular temperatures does not satisfy double-adiabatic conservation laws, but is described accurately by a simple model that includes anomalous scattering. Our results have implications for understanding the complex interplay between macro- and microscale physics in various hot, dilute, astrophysical plasmas, and offer predictions concerning power spectra, residual energy, ion-Larmor-scale spectral breaks, and non-Maxwellian features in ion distribution functions that may be tested by measurements taken in high-beta regions of the solar wind.

Thermal adaptation of mRNA secondary structure: stability versus lability

Macromolecular function commonly involves rapidly reversible alterations in three-dimensional structure (conformation). To allow these essential conformational changes, macromolecules must possess higher order structures that are appropriately balanced between rigidity and flexibility. Because of the low stabilization free energies (marginal stabilities) of macromolecule conformations, temperature changes have strong effects on conformation and, thereby, on function. As is well known for proteins, during evolution, temperature-adaptive changes in sequence foster retention of optimal marginal stability at a species’ normal physiological temperatures. Here, we extend this type of analysis to messenger RNAs (mRNAs), a class of macromolecules for which the stability–lability balance has not been elucidated. We employ in silico methods to determine secondary structures and estimate changes in free energy of folding (ΔGfold) for 25 orthologous mRNAs that encode the enzyme cytosolic malate dehydrogenase in marine mollusks with adaptation temperatures spanning an almost 60 °C range. The change in free energy that occurs during formation of the ensemble of mRNA secondary structures is significantly correlated with adaptation temperature: ΔGfold values are all negative and their absolute values increase with adaptation temperature. A principal mechanism underlying these adaptations is a significant increase in synonymous guanine + cytosine substitutions with increasing temperature. These findings open up an avenue of exploration in molecular evolution and raise interesting questions about the interaction between temperature-adaptive changes in mRNA sequence and in the proteins they encode.

A linear stability analysis of two-layer moist convection with a saturation interface

The linear convective instability of a mixture of dry air, water vapour and liquid water, with a stable unsaturated layer residing on an unstable saturated layer, is studied. It may serve as a prototype model for understanding the instability that causes mixing at the top of stratocumulus cloud or fog. Such a cloud-clear air interface is modelled as an infinitely thin saturation interface where radiative and evaporative cooling take place. The interface position is determined by the Clausius–Clapeyron equation, and can undulate with the evolution of moisture and temperature. In the small-amplitude regime two physical mechanisms are revealed. First, the interface undulation leads to the undulation of the cooling source, which destabilizes the system by superposing a vertical dipole heating anomaly on the convective cell. Second, the evolution of the moisture field induces non-uniform evaporation at the interface, which stabilizes the system by introducing a stronger evaporative cooling in the ascending region and vice versa in the descending region. These two mechanisms are competing, and their relative contribution to the instability is quantified by theoretically estimating their relative contribution to buoyancy flux tendency. When there is only evaporative cooling, the two mechanisms break even, and the marginal stability curve remains the same as the classic two-layer Rayleigh–Bénard convection with a fixed cooling source.

Predicting the Dimits shift through reduced mode tertiary instability analysis in a strongly driven gyrokinetic fluid limit

The tertiary instability is believed to be important for governing magnetised plasma turbulence under conditions of strong zonal flow generation, near marginal stability. In this work, we investigate its role for a collisionless strongly driven fluid model, self-consistently derived as a limit of gyrokinetics. It is found that a region of absolute stability above the linear threshold exists, beyond which significant nonlinear transport rapidly develops. Characteristically, this range exhibits a complex pattern of transient zonal evolution before a stable profile can arise. Nevertheless, the Dimits transition itself is found to coincide with a tertiary instability threshold, so long as linear effects are included. Through a simple and readily extendable procedure, tracing its origin to St-Onge (J. Plasma Phys., vol. 83, issue 05, 2017, 905830504), the stabilising effect of the typical zonal profile can be approximated, and the accompanying reduced mode estimate is found to be in good agreement with nonlinear simulations.

Linear Stability of a Steady Convective Flow between Permeable Cylinders

Linear stability analysis of a steady convective flow in a tall vertical annulus caused by nonlinear heat sources is conducted in the paper. Heat sources are generated as a result of a chemical reaction. The effect of radial cross-flow through permeable porous walls of the annulus is analyzed. The problem is relevant to biomass thermal conversion. The base flow solution is obtained by solving nonlinear boundary value problem. Linear stability analysis is performed, using collocation method. The calculations show that radial inward or outward flow has a stabilizing effect on the flow, while the increase in the Frank–Kamenetskii parameter (proportional to the intensity of the chemical reaction) destabilizes the flow. The increase in the Reynolds number based on the radial velocity leads to the appearance of the second minimum on the marginal stability curves. The rate of increase in the critical Grashof number with respect to the Reynolds number is different for inward and outward radial flows.

Steady-state and nonlinear stability analysis for the feasibility of different fluids in a supercritical natural circulation loop

A numerical model for a supercritical natural circulation loop is developed to examine the flow instabilities by nonlinear stability analysis. The supercritical natural circulation loop is a loop geometry, which is driven by natural circulation with supercritical fluids as a coolant. A mathematical formulation is developed to study the steady-state and transient solution procedure for supercritical natural circulation loop. This mathematical model is then used to perform various parametric studies with different supercritical fluids (water, [Formula: see text], R134a, ammonia, R22, propane, and isobutane). The behavior of all the fluids is analyzed on identical geometrical and operating conditions. A comprehensive numerical study of the nonlinear stability analysis is presented with particular emphasis on the feasibility of various fluids in a natural circulation loop environment. The 50% increment in loop diameter and height increased the stable operating zones and shifted the marginal stability boundary upward respectively by approximately three times and 25–40% of the previous value. However, further increase in diameter and height reduces the increment of stable operating zones; hence the marginal stability boundary shifts upward marginally than the previous value. Furthermore, the marginal stability boundaries are generated to identify the stable and unstable zones for the available geometrical and operating conditions.