Background Shear Research Articles

Multi-Scale Localized Perturbation Method in OpenFOAM

A modified set of governing differential equations for geophysical fluid flows is derived. All of the simulation fields are decomposed into a nominal large-scale background state and a small-scale perturbation from this background, and the new system is closed by the assumption that the perturbation is one-way coupled to the background. The decomposition method, termed the multi-scale localized perturbation method (MSLPM), is then applied to the governing equations of stratified fluid flows, implemented in OpenFOAM, and exercised in order to simulate the interaction of a vertically-varying background shear flow with an axisymmetric perturbation in a turbulent ocean environment. The results demonstrate that the MSLPM can be useful in visualizing the evolution of a perturbation within a complex background while retaining the complex physics that are associated with the original governing equations. The simulation setup may also be simplified under the MSLPM framework. Further applications of the MSLPM, especially to multi-scale simulations that encompass a large range of spatial and temporal scales, may be beneficial for researchers.

Analytical Approximations of Dispersion Relations for Internal Gravity Waves Equation with Shear Flows

The problem of internal gravity waves fields in a stratified medium of finite depth is considered for model distributions of background shear currents. For the analytical solution of the problem, a constant distribution of the buoyancy frequency and various linear dependences of the background shear current on depth were used. The dispersion dependences are obtained, which are expressed in terms of the modified Bessel function of the imaginary index. Under the Miles–Howard stability condition and large Richardson numbers, the Debye asymptotics of the modified Bessel function of the imaginary index were used to construct analytical solutions. The dispersion equation is solved using the proposed analytical approximation. The properties of the dispersion equation are studied and the main analytical characteristics of the dispersion curves are investigated depending on the parameters of background shear flows.

Synergy of Experimental Rock Mechanics, Seismology, and Geodynamics Reveals Still Elusive Upper Mantle Rheology

AbstractWe present a novel geodynamic approach that can potentially tighten existing constraints on mantle rheology. This new approach, which we call probabilistic geodynamic modeling, is applied here to the rheology of the upper mantle. We combine the numerical modeling of plate‐driven corner flow and the seismic observation of radial anisotropy, aiming to reduce substantial uncertainties associated with experimentally derived flow laws, but our results also highlight the complex competition among different deformation mechanisms under mantle conditions. Despite the remaining rheological uncertainty, our study suggests that significant background shear flow is required near the lithosphere‐asthenosphere boundary to explain the strong radial anisotropy observed at 100–200 km depth underneath the Pacific plate, and the plausible nature of this background flow is characterized using our new probabilistic approach. Our analysis also provides a new insight into the asthenospheric water content and the grain size distribution in the upper mantle, but these results are also subject to nontrivial nonuniqueness. The merit of our probabilistic approach lies in its ability to assess the extent of such nonuniqueness, and we demonstrate this by quantifying the robustness of some of our results.

Investigation of the Internal Tides in the Northwest Pacific Ocean Considering the Background Circulation and Stratification

AbstractA global ocean circulation and tide model with nonuniform resolution is used in this work to resolve the ocean circulation globally as well as mesoscale eddies and internal tides regionally. Focusing on the northwest Pacific Ocean (NWP, 0°–35°N, 105°–150°E), a realistic experiment is conducted to simulate internal tides considering the background circulation and stratification. To investigate the influence of a background field on the generation and propagation of internal tides, idealized cases with horizontally homogeneous stratification and zero surface fluxes are also implemented for comparison. By comparing the realistic cases with idealized ones, the astronomical tidal forcing is found to be the dominant factor influencing the internal tide conversion rate magnitude, whereas the stratification acts as a secondary factor. However, stratification deviations in different areas can lead to an error exceeding 30% in the local internal tide energy conversion rate, indicating the necessity of a realistic stratification setting for simulating the entire NWP. The background shear is found to refract propagating diurnal internal tides by changing the effective Coriolis frequencies and phase speeds, while the Doppler-shifting effect is remarkable for introducing biases to semidiurnal results. In addition, nonlinear baroclinic tide energy equations considering the background circulation and stratification are derived and diagnosed in this work. The mean flow–baroclinic tide interaction and nonlinear energy flux are the most significant nonlinear terms in the derived equations, and nonlinearity is estimated to contribute approximately 5% of the total internal tide energy in the greater Luzon Strait area.

Interfacial solitons propagating through a background shear current

Nonlinear internal solitary waves (ISWs) propagating through a two-layer stratified system, in the presence of a shear background current, are theoretically investigated. We implement a new version of the Miyata–Choi–Camassa model with mobile layers (MCC-ML), by considering an asymptotic, uniform velocity distribution for each layer. To investigate the typical geophysical flow conditions observed in the coastal oceans, we focused on theoretical predictions for a density ratio between the two layers set to 0.99. A rigid-lid at the top of the theoretical domain is considered since it represents a good approximation under the Boussinesq condition. By varying the ratio of the undisturbed layer thickness from 0.1 to 10, we considered ISWs with both positive and negative polarities, when the background fluid is at rest. For increasing velocity differences between the two layers, ISWs tend to broaden (steepen) when the background velocities assume the same (opposite) direction of those induced by the wave. We show that the polarity conversion can be easily predicted since it directly depends on both stratification features and ambient velocities. The shear current affects also the wave celerity: for increasing background shear, upstream-propagating solitons reach a critical condition for which the wave celerity is equal to zero. We found that this occurrence is associated with a well-defined value of the wave amplitude. For even larger background shears, the waves are observed to change their direction of propagation. By linear analysis, we finally obtained the limiting background shear current for which the MCC-ML model does not provide any solution.

Turbulent filament properties in L and H-mode regime in the RFX-mod operating as a tokamak

The dynamics of turbulent filaments in L and ELM-free H-mode in the RFX-mod device operating as a tokamak is discussed in the present work. L-H transition and sustained H-mode have been achieved in the RFX-mod with the aid of an external electrode biasing (Spolaore et al 2017 Nucl. Fusion 57 116039). Through advanced statistical techniques, turbulent filaments are detected and tracked from the edge to the scrape-off layer (SOL) in a two-dimension floating potential map (measured with a 2D array of Langmuir probes) related with extreme events of a fixed ion saturation current signal in the SOL. While in L-mode filaments travel almost freely, their motion becomes restricted to the near SOL during the induced biasing H-mode. In this region, the background shear decorrelation time becomes shorter than the convective filament time, favouring its suppression. However, the experimental observation of a nearly ‘trapped’ monopole potential points out the possible role of the vortex selection mechanism. The sign and magnitude of the turbulent parallel vorticity are consistent with the E × B background vorticity in the SOL in this regime, while in L-mode, the inferred turbulent vorticity is always above the background one. The sparse filamentary transport in the far SOL during H-mode is further confirmed from the measurements of a poloidally symmetric array of electrostatic sensors on the wall. Lastly, the radial velocity of filaments in both regimes was discussed in the framework of analytical scalings. Filaments in L-mode exhibit a reasonable agreement with the sheath-limited regime in the cold ion approximation, with a non-negligible associated parallel current density measured with a set of 3-axial pick-up coils installed in the probe head. In H-mode, the collisionality increases near the separatrix while filaments seem to follow the inertial regime before become trapped.

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

Abstract

Diagnostic values of shear wave elastography and strain elastography for breast lesions

Strain elastography (SE) and shear wave elastography (SWE) have high diagnostic yield for breast lesions, but the optimal parameters remain elusive. To evaluate the diagnostic yield of SWE and SE for breast lesions by multivariate logistic regression analysis. A total of 132 patients with 164 breast tumors were enrolled. Breast lesions were classified with the breast imaging reporting and data system (BI-RADS). Maximum (Emax), mean (Emean) and standard deviation (Esd) of elastic modulus, lesion/fat elasticity ratio and elastographic classification were obtained by SWE. Strain ratio (SR) and elastographic score were obtained by SE. A multivariate logistic regression analysis was performed. The diagnostic efficiencies of BI-RADS classification, SWE, SE and their combination were compared plotting ROC curves. There were 110 benign and 54 malignant lesions which had significantly different SWE and SE parameters. The parameters included in the logistic regression were Esd and elastographic classification obtained by SWE and the elastographic score obtained by SE. When combining SWE with SE, Esd, SR and SWE classification were included in the equation. The areas under ROC curves for BI-RADS classification, SWE, SE and their combination were 0.75, 0.88, 0.79 and 0.89, respectively. The diagnostic value of SWE in combination with SE for breast lesions exceeded that of SE or SWE alone. Esd showed a good diagnostic yield when SWE was used alone or combined with SE.

Internal Gravity Waves in a Stratified Medium with Model Shear Flow Distributions

The problem of the field of internal gravity waves in a stratified medium of finite depth is considered for model distributions of background shear flows. The constant distribution of the buoyancy frequency and various linear dependences of background shear flow on the depth are used to solve the problem analytically. The dispersion relations expressed in terms of the modified Bessel function of imaginary index are obtained. In satisfying the Miles–Howard stability condition in the case of large Richardson numbers, the Debye asymptotics of the modified Bessel function of imaginary index are used to construct the analytical solutions. The properties of the dispersion relation are studied and the basic analytical characteristics of the dispersion curves are investigated as functions of the parameters of background shear flows. The phase patterns of the excited fields are calculated numerically for various wave generation models.

Role of Fluid Injection on Earthquake Size in Dynamic Rupture Simulations on Rough Faults

AbstractAn outstanding question for induced seismicity is whether the volume of injected fluid and/or the spatial extent of the resulting pore pressure and stress perturbations limit rupture size. We simulate ruptures with and without injection‐induced pore pressure perturbations, using 2‐D dynamic rupture simulations on rough faults. Ruptures are not necessarily limited by pressure perturbations when (1) background shear stress is above a critical value, or (2) pore pressure is high. Both conditions depend on fault roughness. Stress heterogeneity from fault roughness primarily determines where ruptures stop; pore pressure has a secondary effect. Ruptures may be limited by fluid volume or pressure perturbation extent when background stress and fault roughness are low, and the maximum pore pressure perturbation is less than 10% of the background effective normal stress. Future work should combine our methodology with simulation of the loading, injection, and nucleation phases to improve understanding of injection‐induced ruptures.

A Nonlinear Multiscale Theory of Atmospheric Blocking: Dynamical and Thermodynamic Effects of Meridional Potential Vorticity Gradient

AbstractIn this paper, an extended nonlinear multiscale interaction model is proposed to examine nonlinear behavior of eddy-driven blocking as a Rossby wave packet in a three-dimensional background flow by dividing the background meridional potential vorticity gradient (PVy) into dynamical PVy related to the horizontal (mainly meridional) shear of background westerly wind (BWW) and thermodynamic PVy associated with the meridional temperature gradient (MTG). It is found that eddy-driven baroclinic blocking with large amplitude in the midtroposphere tends to have a longer lifetime (~20 days) in a baroclinic atmosphere with stratification than eddy-driven barotropic blocking without vertical variation (less than 15 days). It is shown that barotropic blocking shows a northwest–southeast orientation and has long lifetime, large retrogression, and slow decay only for weaker barotropic BWW and in higher latitudes. In a baroclinic atmosphere with stratification, baroclinic blocking shows long lifetime, strong eastward movement, slow decay, weak strength, and less local persistence for large barotropic BWW and under , but becomes less slow decay, weak retrogression, and large local persistence for small barotropic BWW and . Such a blocking with a north–south antisymmetric dipole, large amplitude, and long local persistence, characterized by a persistent large meander of westerly jet streams, is easily seen when baroclinic BWW and are small in the lower to midtroposphere. Comparatively, the magnitude of plays a larger role in the blocking change than that of , whereas the vertical variation of MTG is more important for the blocking change than the MTG itself for some cases.

Mixing in forced stratified turbulence and its dependence on large-scale forcing

We study direct numerical simulations of turbulence arising from the interaction of an initial background shear, a linear background stratification and an external body force. In each simulation the turbulence produced is spatially intermittent, with dissipation rates varying over orders of magnitude in the vertical. We focus analysis on the statistically quasi-steady states achieved by applying large-scale body forcing to the domain, and compare flows forced by internal gravity waves with those forced by vertically uniform vortical modes. By considering the turbulent energy budgets for each simulation, we find that the injection of potential energy from the wave forcing permits a reversal in the sign of the mean buoyancy flux. This change in the sign of the buoyancy flux is associated with large, convective density overturnings, which in turn lead to more efficient mixing in the wave-forced simulations. The inhomogeneous dissipation in each simulation allows us to investigate localised correlations between the kinetic and potential energy dissipation rates. These correlations lead us to the conclusion that an appropriate definition of an instantaneous mixing efficiency, (where and are the volume-averaged turbulent viscous dissipation rate and fluctuation density variance destruction rate respectively) in the wave-forced cases is independent of an appropriately defined local turbulent Froude number, consistent with scalings proposed for low Froude number stratified turbulence.

Formation of Recirculating Cores in Convectively Breaking Internal Solitary Waves of Depression Shoaling over Gentle Slopes in the South China Sea

AbstractThe formation of a recirculating subsurface core in an internal solitary wave (ISW) of depression, shoaling over realistic bathymetry, is explored through fully nonlinear and nonhydrostatic two-dimensional simulations. The computational approach is based on a high-resolution/accuracy deformed spectral multidomain penalty-method flow solver, which employs the recorded bathymetry, background current, and stratification profile in the South China Sea. The flow solver is initialized using a solution of the fully nonlinear Dubreil–Jacotin–Long equation. During shoaling, convective breaking precedes core formation as the rear steepens and the trough decelerates, allowing heavier fluid to plunge forward, forming a trapped core. This core-formation mechanism is attributed to a stretching of a near-surface background vorticity layer. Since the sign of the vorticity is opposite to that generated by the propagating wave, only subsurface recirculating cores can form. The onset of convective breaking is visualized, and the sensitivity of the core properties to changes in the initial wave, near-surface background shear, and bottom slope is quantified. The magnitude of the near-surface vorticity determines the size of the convective-breaking region, and the rapid increase of local bathymetric slope accelerates core formation. If the amplitude of the initial wave is increased, the subsequent convective-breaking region increases in size. The simulations are guided by field data and capture the development of the recirculating subsurface core. The analyzed parameter space constitutes a baseline for future three-dimensional simulations focused on characterizing the turbulent flow engulfed within the convectively unstable ISW.

Run-up of long waves on background shear currents

Long waves in shallow water propagating over a background shear current towards a sloping beach are investigated, and exact solutions are found using a hodograph transform and separation of variables. Inspired by the work of Carrier and Greenspan on steady waves over a uniform beach profile in the irrotational setting, we study waves which propagate over a background shear current. The shallow-water equations are obtained from the nonlinear Benney equations, and exact solutions are found with help of the hodograph transformation in conjunction with several further changes of variables. The hodograph transformation is effected by finding the Riemann invariants after the equations are written in the standard form of barotropic gas dynamics. In the current work, the background flow features zero mass flux, as would be required by a real flow at a beach. Moreover, in contrast with previous work, the present approach allows separate study of the influence of the strength of the shear current and the slope of the bottom profile. This enables us to provide an estimate of the run-up as a function of the shear flow while keeping the bottom slope constant.

Solitary zonal structures in subcritical drift waves: a minimum model

Solitary zonal structures have recently been identified in gyrokinetic simulations of subcritical drift-wave (DW) turbulence with background shear flows. However, the nature of these structures has not been fully understood yet. Here, we show that similar structures can be obtained within a reduced model, which complements the modified Hasegawa–Mima equation with a generic primary instability and a background shear flow. We also find that these structures can be qualitatively reproduced in the modified Hasegawa–Wakatani equation, which subsumes the reduced model as a limit. In particular, we illustrate that in both cases, the solitary zonal structures approximately satisfy the same ‘equation of state’, which is a local relation connecting the DW envelope with the zonal-flow velocity. Due to this generality, our reduced model can be considered as a minimum model for solitary zonal structures in subcritical DWs.

Finite-time circulation changes from topological rearrangement of distinguished curves and non-advective fluxes

A vorticity budget diagnoses the growth or decay of a vortex from advective transport, or non-advective fluxes such as those due to friction or vortex tilting. However, when a budget calculation is performed with respect to a fixed coordinate, errors may result from time-dependence of the flow, leading to disagreement between the vorticity tendency and the observed vorticity field. An adaptive Lagrangian coordinate resolves this problem, provided that the resulting Lagrangian structure does not become too complicated.In this study, a numerical simulation of Hurricane Nate (2011), the vorticity tendency is evaluated along distinguished material curves. There can be no net advective flux along a closed material curve, therefore, the total circulation tendency for a material region includes only the non-advective uxes acting along its boundary. A distinguished set of material curves (DMCs) associated with a distinguished hyperbolic trajectory (DHT) form a Lagrangian topology similar to that of a cat’s eye flow or “pouch” at each Eulerian snapshot. The time-dependence of velocities allows additional regions called lobes, which are formed by the intersections of DMCs, to exchange fluid across the vortex boundary by redefining the boundary.Because the vortex boundary changes, we refer to this redefinition of material boundary as “topological rearrangement”. The method is useful for unsteady cat’s-eye flows and more complex interactions of multiple waves, vortices and background shear. All advective changes of the vortex circulation are identified by exchanges of the lobes, and all non-advective uxes act between the vortex and either the lobes or environmental flow. The Lagrangian topology and combination of advective and non-advective uxes relative to the topology is used to describe the evolution of the circulation of Nate during its time of formation.

The Potential Vorticity Structure and Dynamics of African Easterly Waves

Abstract The dynamics of African easterly waves (AEWs) are investigated from the perspective of potential vorticity (PV) using data from global reanalysis projects. To a leading order, AEW evolution is governed by four processes: advection of the wave-scale PV by background flow, advection of background PV by the AEW, diabatic forcing due to wave-scale moist convection, and coupling between the wave and background diabatic forcing. Moist convection contributes significantly to the growth of AEWs in the midtroposphere, and to both growth and propagation of AEWs near the surface. The former is associated with stratiform clouds while the latter with deep convection. Moist convection helps maintain a more upright AEW PV column against the background shear, which makes the wave structure conducive for tropical cyclogenesis. It is also argued that—contrary to the hypothesis in some prior studies—the canonical diabatic Rossby wave model is likely not applicable to AEWs.

Influence of fault roughness on surface displacement: from numerical simulations to coseismic slip distributions

SUMMARYField studies have characterized natural faults as rough, non-planar surfaces at all scales. Fault roughness induces local stress perturbations during slip, which dramatically affect rupture behaviour, resulting in slip heterogeneity. However, the relation between fault roughness and slip heterogeneity remains a key knowledge gap between current numerical and field studies. In this study, we analyse numerical simulations of earthquake rupture to determine how roughness influences final slip. Using a rupture catalogue containing thousands of dynamic rupture simulations on band-limited self-similar fractal fault profiles with varying roughness and background shear stress levels, we quantify how fault roughness affects the spectral characteristics of the resulting slip distribution. We find that slip distributions become increasingly more self-affine, that is, containing more short wavelength fluctuations as compared to the self-similar fault profiles, as roughness increases. We also find that, at very short wavelengths (<1 km), the fractal dimension of the slip distributions dramatically changes with increasing roughness, background shear stress, and rupture speed (sub-Rayleigh versus supershear). The existence of a critical wavelength around 1 km, under which more short wavelengths are either preserved or created, suggests the role of rupture process and dynamic effects, together with fault geometry, in controlling the final slip distributions. The same spectral analysis is performed on high-resolution coseismic surface slip distributions from a catalogue of real strike-slip earthquakes. Compared to numerical simulations, all earthquakes feature slip distributions that are much more self-affine than the slip distributions from numerical simulations. A different critical wavelength, here around 5–6 km, appears, potentially informing about a critical asperity length. While we show here that the relation between fault roughness and slip is much more complex than expected, this study is a first attempt at using statistical analyses of numerical simulations on rough faults to investigate observed coseismic slip distributions.

Internal waves in a shear background current: Transition from solitary-wave regime to dispersive-wave regime

For a given stratification, the presence of a shear background current may significantly alter the wave form of internal waves. Depending on the direction and strength of background shear, it could prevent the formation of solitary waves but enable the formation of a dispersive wave train.

Rigorous Justification of Taylor Dispersion via Center Manifolds and Hypocoercivity

Taylor diffusion (or dispersion) refers to a phenomenon discovered experimentally by Taylor in the 1950s where a solute dropped into a pipe with a background shear flow experiences diffusion at a rate proportional to $1/\nu$, which is much faster than what would be produced by the static fluid if its viscosity is $0 < \nu \ll 1$. This phenomenon is analyzed rigorously using the linear PDE governing the evolution of the solute. It is shown that the solution can be split into two pieces, an approximate solution and a remainder term. The approximate solution is governed by an infinite-dimensional system of ODEs that possesses a finite-dimensional center manifold, on which the dynamics correspond to diffusion at a rate proportional to $1/\nu$. The remainder term is shown to decay at a rate that is much faster than the leading order behavior of the approximate solution. This is proven using a spectral decomposition in Fourier space and a hypocoercive estimate to control the intermediate Fourier modes.