Geophysical Flows Research Articles

Multiparticle Lagrangian statistics in homogeneous rotating turbulence

Geophysical flows are often turbulent and subject to rotation. This rotation modifies the structure of turbulence and is thereby expected to sensibly affect its Lagrangian properties. Here, we investigate the relative dispersion and geometry of pairs, triads and tetrads in homogeneous rotating turbulence, by using direct numerical simulations at different rotation rates. Pair dispersion is shown to be faster in the vertical direction (along the rotation axis) than in the horizontal one. At long times, in Taylor's regime, this is due to the slower decorrelation of the vertical velocity component as compared to the horizontal one. At short times, in the ballistic regime, this result can be interpreted by considering pairs of different orientations at the release time, and is a signature of the anisotropy of Eulerian second-order functions. Rotation also enhances the distortion of triads and tetrads also present in homogeneous and isotropic turbulence. In particular, at long times, the flattening of tetrads increases with the rotation rate. The maximal dimension of triads and tetrads is shown to be preferentially aligned with the rotation axis, in agreement with our observations for pairs.

Rigorous derivation of the full primitive equations by the scaled Boussinesq equations with rotation

The primitive equations of large-scale oceanic dynamics form a fundamental model in geophysical flows. It is well-known that the primitive equations can be formally derived by the hydrostatic approximation. In this paper, we rigorously derive the full primitive equations from the mathematical point of view. More precisely, we prove that the scaled Boussinesq equations with rotation converge to the full primitive equations in a strong sense, globally in time, with the convergence rate $$O(\varepsilon )$$ , as the aspect ratio $$\varepsilon $$ goes to zero.

Multiphase Turbulence Modeling Using Sparse Regression and Gene Expression Programming

Turbulence in two-phase flows drives many important natural and engineering processes, from geophysical flows to nuclear power generation. Strong interphase coupling between the carrier fluid and disperse phase precludes the use of classical turbulence models developed for single-phase flows. In recent years, there has been an explosion of machine learning techniques for turbulence closure modeling, though many rely on augmenting existing models. In this work, we propose an approach that blends sparse regression and gene expression programming (GEP) to generate closed-form algebraic models from simulation data. Sparse regression is used to determine a minimum set of functional groups required to capture the physics, and GEP is used to automate the formulation of the coefficients and dependencies on operating conditions. The framework is demonstrated on homogeneous turbulent gas-particle flows in which two-way coupling generates and sustains carrier-phase turbulence.

Thermal analysis in an electrically conducting fluid with multiple slips and radiation along a plate: A case study of Stokes' second problem

Stoke's problems significantly impact several domains, including industrial manufacturing, geophysical flows, chemical engineering, and heat conduction. Stoke's second problem deals with the movement of a semi-infinite viscous incompressible fluid caused by an oscillating flat plate. Thus, this work examines Stoke's second problem for an unsteady hydromagnetic surface-driven flow along an infinite flat plate in the presence of thermal radiation and heat dissipation. The governing momentum and energy equations form an emerging nonlinear system of partial differential equations through dimensionless proxies. MAPLE 2022 is employed to solve the resulting system of nonlinear partial differential equations that control the flow both analytically and numerically in specific situations. The analytical solutions are displayed graphically, along with variations of skin friction and Nusselt number at the plate. It has been observed that momentum and thermal slips significantly diminished the flow characteristics to cause damping flow rate and temperature distributions. Rising the values of Magnetic and velocity slip parameters, an oscillatory motion is observed in skin friction. This is due to the periodic and wavy nature of the boundary wall. Furthermore, a rise in the Prandtl number and radiation value correspondingly boosted the wall heat gradient profiles. Finally, this study will assist industry and engineering in understanding the sensitivity of their working fluids to parameter variations and for the exact prediction of their base fluids.

Assessing the Departures from the Energy- and Flux-Budget (EFB) Model in Heterogeneous and Urbanized Environment for Stable Atmospheric Stratification

Turbulence closure schemes, besides their intrinsic theoretical importance, represent a fundamental component in the atmospheric numerical models. Among his numerous and diverse scientific contributions, Prof. Sergej S. Zilitinkevich, with his coauthors, elaborated a turbulence closure model for stably-stratified geophysical flows, the Energy and Flux Budget (EFB) model. This closure has been verified and applied on many different experimental datasets and case studies, for steady state and homogeneous conditions. Having available observational datasets for urban and suburban sites in different cities in Italy, we investigate the deviation of the observations of turbulent kinetic energy and momentum flux from the EFB turbulence closure model in heterogeneous conditions. This allows addressing and interpreting the features that induce such deviation between the model and the observations. The EFB model is then revisited including residual terms that can account for the non-stationarity and heterogeneity of the considered cases. The correction with the residual terms leads to improve the agreement between the theoretical formulations and the observed behaviour for the turbulent kinetic energy shares and for the vertical momentum flux.

Cosmological analogies for geophysical flows, Lagrangians, and new analogue gravity systems

Formal analogies between the ordinary differential equations describing geophysical flows and Friedmann cosmology are developed. As a result, one obtains Lagrangian and Hamiltonian formulations of these equations, while laboratory experiments aimed at testing geophysical flows are shown to constitute analogue gravity systems for cosmology.

Efficient lattice Boltzmann simulation of free-surface granular flows with μ(I)-rheology

This paper presents a lattice Boltzmann framework for accurate and efficient simulation of free-surface granular flows. The granular assembly is treated as a viscoplastic fluid, whose apparent viscosity varies locally with the shear rate and pressure according to a regularized μ(I)-rheology. A single-phase free-surface model is employed to track the evolution of the particle-air interface. The lattice Boltzmann implementation is first validated by simulating a steady-state granular flow on a rough inclined plane and a good agreement with the analytical solution is achieved. The validated model is then applied to simulate a transient granular column collapse problem. Compared to a companion discrete element simulation, the lattice Boltzmann model with the μ(I)-rheology is able to capture the overall dynamic behaviors of granular column collapse. However, a different behavior is observed when a similar Bingham viscoplastic model with a fixed yield stress is applied, highlighting the pressure dependent nature of granular flows. The proposed lattice Boltzmann formulation is highly efficient compared to the conventional computational fluid dynamics, and has the potential to conduct three-dimensional continuum simulation of large-scale geophysical flows with microscopic granular physics.

Bathymetry and friction estimation from transient velocity data for one-dimensional shallow water flows in open channels with varying width

The shallow water equations (SWE) model a variety of geophysical flows. Flows in channels with rectangular cross sections may be modeled with a simplified one-dimensional SWE with varying width. Among other model parameters, information about the bathymetry and friction coefficient is needed for the correct and precise prediction of the flow. Although synthetic values of the model parameters may suffice for testing numerical schemes, approximations of the bathymetry and other parameters may be required for specific applications. Estimations may be obtained by experimental methods, but some of those techniques may be expensive, time consuming, and not always available. In this work, we propose to solve the inverse problem to estimate the bathymetry and the Manning's friction coefficient from transient velocity data. This is done with the aid of a cost functional, which includes the SWE through Lagrange multipliers. We prove that the velocity data determine uniquely the derivative of the bathymetry in a linearized shallow water system. That is, the inverse problem is identifiable. The solution is obtained by solving the constrained optimization problem by a continuous descent method. The direct and the adjoint problems are both solved numerically using a second-order accurate Roe-type upwind scheme. Numerical tests are included to show the merits of the algorithm.

Virtual laboratory experiments on the interaction of a vortex with small-scale topography

This study presents numerical analogs of laboratory experiments designed to explore the interaction of broad geophysical flows with irregular small-scale bathymetry. The previously reported “sandpaper” theory offered a succinct description of the cumulative effect of small-scale topographic features on large-scale flow patterns. However, initial investigations have been conducted using numerical models with simplified quasi-geostrophic equations that may inadequately represent the dynamics realized in the world’s oceans. This investigation advances previous efforts by using a fully nonlinear Navier–Stokes model configured for rotating tank experiments to (i) validate the theory and (ii) offer guidance for future physical experiments that will confirm theoretical ideas.

Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper: part 1.

In 1923, the Philosophical Transactions published G. I. Taylor's seminal paper on the stability of what we now call Taylor-Couette flow. In the century since the paper was published, Taylor's ground-breaking linear stability analysis of fluid flow between two rotating cylinders has had an enormous impact on the field of fluid mechanics. The paper's influence has extended to general rotating flows, geophysical flows and astrophysical flows, not to mention its significance in firmly establishing several foundational concepts in fluid mechanics that are now broadly accepted. This two-part issue includes review articles and research articles spanning a broad range of contemporary research areas, all rooted in Taylor's landmark paper. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

Particle-size segregation in self-channelized granular flows

Geophysical mass flows such as debris flows, dense pyroclastic flows and snow avalanches can self-channelize on shallow slopes. The confinement afforded by formed levees helps to maintain the flow depth, and hence mobility, allowing self-channelized flows to run out significantly farther than unconfined, spreading flows. Levee formation and self-channelization are strongly associated with particle-size segregation, but can also occur in monodisperse flows. This paper uses the monodisperse depth-averaged theory of Rochaet al.(J. Fluid Mech., vol. 876, 2019, pp. 591–641), which incorporates a hysteretic friction law and second-order depth-averaged viscous terms. Both of these are vital for the formation of a travelling wave that progressively deposits a pair of levees just behind the front. The three-dimensional velocity field is reconstructed in a frame moving with the front assuming Bagnold flow. This enables a bidisperse particle-size segregation theory to be used to solve for the large and small particle concentrations and particle paths in three-dimensions, for the first time. The model shows that the large particles tend to segregate to the surface of the flow, forming a carapace that extends over the centre of the channel, as well as along the external sides and base of the levee walls. The small particles segregate downwards, and are concentrated in the main channel and in the inner levee walls. This supports the contention that a low-friction channel lining provides a secondary mechanism for run-out enhancement. It is also shown that the entire theory scales with particle diameter, so experiments with millimetre-sized particles provide important insights into geophysical-scale flows with boulders and smaller rock fragments. The model shows that self-channelization does not need particle-size segregation to occur, but supports the hypothesis that particle-size segregation and the associated frictional feedback can significantly enhance both the flow mobility and the levee strength.

A Consistent Stochastic Large-Scale Representation of the Navier–Stokes Equations

In this paper we analyze the theoretical properties of a stochastic representation of the incompressible Navier–Stokes equations defined in the framework of the modeling under location uncertainty (LU). This setup built from a stochastic version of the Reynolds transport theorem incorporates a so-called transport noise and involves several specific additional features such as a large scale diffusion term, akin to classical subgrid models, and a modified advection term arising from the spatial inhomogeneity of the small-scale velocity components. This formalism has been numerically evaluated in a series of studies with a particular interest on geophysical flows approximations and data assimilation. In this work we focus more specifically on its theoretical analysis. We demonstrate, through classical arguments, the existence of martingale solutions for the stochastic Navier–Stokes equations in LU form. We show they are pathwise and unique for 2D flows. We then prove that if the noise intensity goes to zero, these solutions converge, up to a subsequence in dimension 3, to a solution of the deterministic Navier–Stokes equation. similarly to the grid convergence property of well established large-eddies simulation strategies, this result allows us to give some guarantee on the interpretation of the LU Navier–Stokes equations as a consistent large-scale model of the deterministic Navier–Stokes equation.

Semi-analytical solutions of shallow water waves with idealised bottom topographies

Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions. This work employs the Adomian decomposition method (ADM) to develop semi-analytical formulations of these problems that preserve the direct correlation of the physical parameters while capturing the nonlinear phenomenon. Furthermore, we exploit these techniques as reverse engineering mechanisms to develop key connections between some prevalent ansatz formulations in the open literature as well as derive new families of exact solutions describing geostrophic inertial oscillations and anticyclonic vortices with finite escape times. Our semi-analytical evaluations show the promise of this approach in terms of providing robust approximations against several oceanic variations and bottom topographies while also preserving the direct correlation between the physical parameters such as the Froude number, the bottom topography, the Coriolis parameter, as well as the flow and free surface behaviours. Our numerical validations provide additional confirmations of this approach while also illustrating that ADM can also be used to provide insight and deduce novel solutions that have not been explored, which can be used to characterise various types of geophysical flows.

Mass exchange between geophysical flows and beds: Idealised computational modelling using a Herschel-Bulkley rheology

A key mechanism by which geophysical flows evolve is mass exchange with the underlying bed, either by entraining material from the bed, or by depositing material. Although it is known that some consequences of these mass exchange processes include changes in the volume, momentum and local rheology of the flow, the circumstances under which specific changes occur are not well-established. Given the enormous number of competing mechanisms present in geophysical flows, it is not surprising that the state of the art for modelling entrainment is essentially still empirical. In this study, we implement a Herschel-Bulkley (non-Newtonian) rheology into an existing open-source Smoothed Particle Hydrodynamics solver (DualSPHysics). This rheology can reasonably represent clay-rich flows, typical of those observed in the French Prealps. We hence undertake a highly-idealised, quantitative investigation of entrainment mechanisms for flows overriding non-fixed beds. For the beds, we vary the yield stress and the depth. Preliminary results reveal a rich variety of behaviours that can be obtained for different bed properties, including both acceleration and deceleration of the flow material. These mechanisms are reminiscent (but not identical) of observations from other studies where geo-materials were used.

Numerical investigation of particle dynamic behaviours in geophysical flows considering solid-fluid interaction

Solid-fluid interaction vitally influences the flow dynamics of particles in a geophysical flow. A coupled computational fluid dynamics and discrete element method (CFD-DEM) is used in this study to model multiphase geophysical flow as a mixture of fluid and solid phases. The two non-Newtonian fluids (i.e., Bingham and Hershcel-Bulkley fluids) and water mixed with particles are considered in the simulation, while dry granular flow with the same volume is simulated as a control test. Results revealed that the solid-fluid interaction heavily governs the particle dynamic behaviours. Specifically, compared to dry case, particles in three multiphase cases are characterized by larger flow mobility and greater shear rate while smaller basal normal force. In addition, a power-law distribution with a crossover to a generalized Pareto Distribution is recommended to fit the distribution of normalized interparticle contact force.

Deciphering controls for the impact of geophysical flows on a flexible barrier: Insights from coupled CFD-DEM modeling

Geophysical flows impacting a flexible barrier can create complex flows and solid-fluid-structure interactions, which are challenging to quantify and characterize towards a unified description. Here, we examine the common physical laws of multiphase, multiway interactions during debris flows, debris avalanches and rock avalanches against a flexible barrier system using a coupled computational fluid dynamics and discrete element (CFD-DEM) method. This model captures essential physics observed in experiments and fields. The bi-linear, positive correlations are found between peak impact load and Fr or maximum barrier deflection, with inflection points due to the transitions from trapezoid- to triangle-shaped dead zones. Our findings quantitatively elucidate how flow materials (wet versus dry) and impact dynamics (slow versus fast) control the patterns of the identified bi-linear correlations. This work offers a physics-based reference and insights for improving widely-used impact solutions for geophysical flows against flexible barriers.

Static and dynamic impact forces on a rigid barrier due to dry debris flow simulated by a DEM-based granular column collapse

Geophysical flows like debris flows require protective barriers so as to scale down their disastrous effects. The impact force exerted on these barriers depends upon several factors like the velocity and height of flowing debris, the density and other associated characteristics of flowing mass, and the height of the sediment deposited behind the barrier. These factors are found to vary with time during the debris flow process, thereby causing significant temporal variations in the magnitude of impact force. Assessing the impact force on a barrier is a prerequisite for its design. In this work, the impact of dry debris flow, emanating from a granular column collapse, on a rigid barrier has been investigated using 3-D Discrete Element Method (DEM). It has been found that the impact force is predominantly influenced by dynamic thrust at the initial stages, which, with elapse time, subsequently transits to the sole contribution of static pressure. The applicability of the existing hydraulic models comprising hydrostatic and hydrodynamic formulae has also been analysed in this exercise. Furthermore, the empirical coefficients associated with these formulae have been evaluated for the dry debris flow impacting the rigid barrier.

Analysis of Stationary Points and Bifurcations of a Dynamically Consistent Model of a Two-Dimensional Meandering Jet

A dynamically consistent model of a meandering jet stream with two Rossby waves obtained using the law of conservation of potential vorticity is investigated. Stationary points are found in the phase space of advection equations and the type of their stability is determined analytically. All topologically different flow regimes and their bifurcations are found for the stationary model (taking into account only the first Rossby wave). The results can be used in the study of Lagrangian transport, mixing, and chaotic advection in problems of cross-frontal transport in geophysical flows with meandering jets.

Применение физически-обоснованной нейронной сети на примере моделирования гидродинамических процессов, допускающих аналитическое решение

We consider an actual approach to develop a physically based neural network for solving model problems for the Kovazhny flow, for the geophysical Beltrami flow, and for the flow in a section of the river by the shallow water theory. Physics-informed neural networks (PINN) allow to significantly reduce the computation time compared to conventional computations. There is a different analytical solution for each model flow. The architecture of the DeepXDE software library, its composition by modules, and fragments of program code in the Python programming language are discussed. The PINN model is tested on a test sample. The prediction is evaluated using the MSE metric. The fully connected neural network can contain 4, 7, 10 hidden layers with the number of neurons 50, 50, 100 respectively. The influence of hyperparameters of the neural network on the magnitude of the prediction error is discussed. The calculations performed on a server with Nvidia GeForce RTX 3070 card can significantly reduce the training time for PINN.

Granular column collapse: The role of particle size polydispersity on the velocity and runout

Geophysical mass flows involve particles of different sizes, a property termed polydispersity. The granular column collapse is a simplified experiment for studying transitional granular flows. Our research focuses on the role that polydispersity has on the velocity and runout distance of dry and immersed granular columns, undergoing a numerical and experimental study. Our results highlight that polydispersity does not have a strong effect on the collapse of dry columns. On the contrary, the collapse sequence of immerse granular columns strongly depend on the polydispersity level.