Unstable Regime Research Articles

A Dynamic Model of Authoritarian Social Control

Abstract Authoritarian regimes often use targeted social control - unequal application of the law to limit expressive freedom and enforce social conformity. At the same time, their methods appear less draconian than in the past. In this model, an authority structures punishments and rewards to compel adherence to its preferred norm. The authority’s commitment is time-limited and depends on imperfectly informative signals of a citizen’ s behavior. Given two citizens with the same observed behavior, the authority imposes harsher punishments on the poorer and/or ex ante dissident individual. Lighter punishments are imposed on the wealthier citizen to prevent “overcompliance.” Wealth inequality increases over time. Some citizens become prosperous “lackeys” while others become destitute from confiscation. In stable regimes with high state capacity, the authority reduces punishments and/or increases rewards to allow citizens to accumulate wealth, leading to social conformity and balanced growth in the long run. In unstable regimes with low capacity, the citizenry splits into groups of wealthy lackeys and destitute proles.

On the Effect of Current Stabilizer on Dynamics of a Small Hybrid Wind Power Generator

The use of small wind power generators remains quite relevant. In particular, they can be efficient for charging batteries in remote locations where there is no centralized power supply (including in the Arctic, Far East, etc.). They can also be used as part of missions to planets with atmospheres. One of the promising design solutions for a small wind power generator with a vertical axis of rotation is a hybrid device. It consists of two wind turbines that have a common axis of rotation: external (Darrieus wind turbine) and internal (Savonius rotor). This scheme represents a compromise between the relatively high power coefficient of the Darrieus turbine and the good startup characteristics the Savonius rotor. It is known that one of the typical battery charging modes is constant current charging. Here we consider a hybrid installation, the generator of which is connected to a current stabilizer. The load is simulated with an active resistance. It is assumed that the generator is a DC generator. A closed mathematical model of the studied system is constructed. The aerodynamic load is described using the quasi-steady approach. It is assumed that the characteristic time of electrical processes is much smaller than the characteristic time of mechanical processes. The influence of load resistance on the behavior of the system is investigated. It is shown that, under certain conditions, several steady modes (up to five) exist in the system. In this case, at least two of them are attracting. Therefore, the hysteresis of the angular speed of the steady mode is possible when the load resistance changes. It should be noted that in a number of situations, an unstable steady mode (which corresponds to a lower angular speed of the turbine than a stable one) may be preferable (for example, to reduce the load on bearings). In this regard, a resistance control strategy has been proposed to ensure stabilization of the unstable stationary regime.

Stable-to-unstable transition in quantum friction

We investigate the frictional force arising from quantum fluctuations when two dissipative metallic plates are set in a shear motion. While early studies showed that the electromagnetic fields in the quantum friction setup reach nonequilibrium steady states, yielding a time-independent force, other works have demonstrated the failure to attain steady states, leading to instability and time-varying friction under sufficiently low-loss conditions. Here, we develop a fully quantum-mechanical theory without perturbative approximations, and we unveil the transition from stable to unstable regimes of the quantum friction setup. Due to the relative motion of the plates, their electromagnetic response may be active in some conditions, resulting in optical gain. We prove that the standard fluctuation-dissipation leads to inconsistent results when applied to our system, and, in particular, it predicts a vanishing frictional force. Using a modified fluctuation-dissipation relation tailored for gain media, we calculate the frictional force in terms of the system Green's function, thereby recovering early works on quantum friction. Remarkably, we also find that the frictional force diverges to infinity as the relative velocity of the plates approaches a threshold. This threshold is determined by the damping strength and the distance between the metal surfaces. Beyond this critical velocity, the system exhibits instability, akin to the behavior of a laser cavity, where no steady state exists. In such a scenario, the frictional force escalates exponentially. Our findings pave the way for experimental exploration of the frictional force in proximity to this critical regime. Published by the American Physical Society 2024

Three-dimensional dynamics of unstable lean premixed hydrogen-air flames: Intrinsic instabilities and morphological characteristics

The 3D swinging laser sheet technique was employed to study the development and morphological characteristics of premixed hydrogen-air unstable flames in a spherical explosion vessel. Pressure dependencies for laminar flame propagation were sought to exploit the role of the Darrieus-Landau (DL) and Thermal-diffusive (TD) instabilities in the unstable self-accelerating flame regime. A sufficiently low Markstein number, as a consequence of the increased pressure, leads to more cracking and smaller cells over the flame surface. The degree of wrinkling on the flame surface is proportional to the increase in flame burning velocity, a relationship that holds true for low pressures but is not applicable under high pressures. External turbulence can significantly alter the extent of flame surface wrinkling even at low root mean square velocities, producing a more wrinkled flame surface compared to intrinsic cellularity, and distinctly affecting flame dynamics. The increased wrinkling and flame speed due to external turbulence can be attributed to the synergistic effects between thermo-diffusive instabilities and turbulence, resulting in higher fuel consumption rates per flame surface area and the formation of finger-like structures that enhance flame displacement speed in curved segments. The parameters, ϵ, deviation of the Lewis number from a critical value, and ω2, obtained through classical linear stability analysis, display a clear linear relationship with the ratio of the wrinkled surface area observed in planar flames. This study enhances the understanding of hydrogen flame instabilities, which is crucial for preventing explosions in hydrogen storage and utilization, and provides valuable insights into flame dynamics, supporting the design of safer and more efficient hydrogen-fueled engines and turbines.

Wrinkling of differentially growing bilayers with similar film and substrate moduli

Growth-induced surface wrinkling in constrained bilayers comprising a thin film attached to a thick substrate is a canonical model for understanding pattern formation in many biological systems. While the bilayer model has received much prior attention, the nonlinear behaviour for arrangements with similar film and substrate properties, or substrate growth that outpaces film growth, remains poorly understood. This paper therefore focuses on these cases in which the substrate’s elasticity dominates surface wrinkling. By combining analytical modelling and finite element simulations incorporating advanced path-following techniques, we characterise critical wrinkling states and explore the initial and advanced post-buckling behaviour for a wide range of film-to-substrate modulus and growth rate ratios. It is shown that the classical leading-order asymptotic expression for the critical strain is not of sufficient accuracy for film-to-substrate modulus ratios below 50, and higher order correction terms are presented. Leveraging a weakly nonlinear analytical model, we introduce a phase diagram categorising stable and unstable post-buckling regimes. Advanced path-following simulations are employed to unveil the evolution of wrinkling patterns, from initial sinusoidal instabilities to complex formations involving period doubling, quadrupling, and eventual surface creasing. These comprehensive phase diagrams, parameterised by film-to-substrate modulus and growth rate ratios, provide new insights into the rich dynamics of surface wrinkling. Finally, we demonstrate the existence of multi-stability in the advanced post-buckling regimes for bilayers experiencing substrate-dominated growth. This work contributes to the understanding of the mechanics underlying pattern formation in growing bilayers over the entire parameter regime, with potential implications for explaining biological morphogenesis and informing the development of novel diagnostic tools and artificial flexible electronic skins.

Performances of the ITER Pressure Suppression System during unstable steam condensation regimes

Abstract The paper deals with the qualification of the main safety system of the nuclear fusion reactor ITER: the Vacuum Vessel Pressure Suppression System (VVPSS). This safety system manages the Loss of Coolant Accident (LOCA), that could occur in the Vacuum Vessel (VV), avoiding a significant increase of the internal pressure that could breach the primary confinement barrier. Steam condensation occurs at sub-atmospheric pressure. This condition is original respect the usual applications of steam direct condensation in nuclear fission reactors. An extensive experimental research program, funded by ITER Organization, on reduced scale experimental rigs (scale 1/22 and 1/10) have been carried out at the University of Pisa. Unstable condensation regimes occurred during some tests at about 500 g/s of steam mass flow rate (10 % of the maximum steam mass flow rate foreseen for the relevant accidental scenarios). In these conditions, high intensity vibrations of the whole experimental rig occurred. These events can be classified as ‘Chugging’ or Condensation Induced Water Hammer (CIWH). 
The performed tests have been analysed elaborating the images of the video-cameras located in the pool and comparing the steam jet shape with the acceleration values recorded by an accelerometer mounted on the sparger structure.
These elaborations permitted to evaluate the dynamic of bubble collapse, the volume of the developed external bubbles, the collapse frequency as function of thermal-hydraulic parameters. 
Moreover, the paper emphasizes the beneficial effects of non-condensable gases on the unstable condensation regimes. In fact, the non-condensable gas inhibits the occurrences of Water Hammer inside the sparger and eliminates the thermal stratification inside the water pool increasing the turbulence.

Nonlinear Dynamics Induced by Coil Heat in the PMDC Motor and Control

In this paper, the interesting dynamics of chaos induced by the effect of the variation of internal average heat during operation in the DC motor control by the full bridge drive are analyzed. By using simple powerful tools of analyzing nonlinear dynamical systems like phase portraits, time traces and frequency spectrum in the MATLAB-SIMULINK environment, we showed that under certain conditions, the PMDC motor develops different behaviors so as periodic limited, and chaotic attractors, when the motor drive different form of external load torque and the windings resistance variation. This paper presents the first studies on the variation of the average heat of the motor and the amplitude of the triangular load torque to produce the strange phenomena like chaos as far as our knowledge go. A chaos control of the unstable regime is proposed to stabilize the PM DC motor in a desire regime. This contribution is very important in industry because some unexplained dynamical behaviors of the DC motor driven by a full bridge now can be avoided.

Физиологическое состояние стерляди в условиях садковых и бассейновых хозяйств

The growing conditions of sturgeon fish affect the growth and physiological state, their morphological characteristics. The study of changes in physiological processes under the influence of a complex of factors in the conditions of cage complexes and closed water supply systems will allow for timely adjustment of technology and reduce risks when growing commercial products. The repair and breeding herds of fish breeding enterprises contain sterlet individuals of different ages, which annually, upon reaching puberty, enter the fish breeding process as producers. In this regard, we have studied the main morphophysiological indicators of two-year-olds kept in cages and in closed water supply installations (CWSI). The influence of environmental factors was noted not only on growth indicators, but also on the size of the internal organs of fish and their condition. The unstable temperature regime in the cages, dependence on unpredictable changes in the hydrochemical parameters of the aquatic environment contributes to deep physiological transformations of an adaptive nature, which slows down the growth rate and accumulation of reserve substances. Changes in morphometric parameters were also evident. In sturgeon, there is an increase in the relative weight of the heart, spleen and gonads, a decrease in the weight of the kidneys and liver. The influence of optimal temperature and trophic conditions on the index of the gastrointestinal tract was noted, which was slightly lower in fish from the CWSI than in individuals exposed to negative factors in cages. Sterlet blood counts, regardless of the conditions of detention, corresponded to physiologically healthy individuals. The creation of optimal hydrological and trophic conditions in CWSI contribute to the accumulation of phospholipids and linolenic fatty acids in tissues, which play an important role in the adaptation of the body to negative environmental factors.

Monitoring the risk of a tailings dam collapse through spectral analysis of satellite InSAR time-series data

Slope failures possess destructive power that can cause significant damage to both life and infrastructure. Monitoring slopes prone to instabilities is therefore critical in mitigating the risk posed by their failure. The purpose of slope monitoring is to detect precursory signs of stability issues, such as changes in the rate of displacement with which a slope is deforming. This information can then be used to predict the timing or probability of an imminent failure in order to provide an early warning. Most approaches to predicting slope failures, such as the inverse velocity method, focus on predicting the timing of a potential failure. However, such approaches are deterministic and require some subjective analysis of displacement monitoring data to generate reliable timing predictions. In this study, a more objective, probabilistic-learning algorithm is proposed to detect and characterise the risk of a slope failure, based on spectral analysis of serially correlated displacement time-series data. The algorithm is applied to satellite-based interferometric synthetic radar (InSAR) displacement time-series data to retrospectively analyse the risk of the 2019 Brumadinho tailings dam collapse in Brazil. Two potential risk milestones are identified and signs of a definitive but emergent risk (27 February 2018-26 August 2018) and imminent risk of collapse of the tailings dam (27 June 2018-24 December 2018) are detected by the algorithm as the empirical points of inflection and maximum on a risk trajectory, respectively. Importantly, this precursory indication of risk of failure is detected as early as at least five months prior to the dam collapse on 25 January 2019. The results of this study demonstrate that the combination of spectral methods and second order statistical properties of InSAR displacement time-series data can reveal signs of a transition into an unstable deformation regime, and that this algorithm can provide sufficient early-warning that could help mitigate catastrophic slope failures.

Thermoacoustic parametric instability of premixed ammonia flames propagating downwards in an open-closed tube

This work investigates the self-excited thermoacoustic parametric instability of downward propagating laminar premixed ammonia flames in an open-closed combustion tube. NH3/O2/N2 flames were propagated at different laminar burning velocities at equivalence ratios of ɸ = 0.8 and ɸ = 1.2. Different unstable flame regimes were observed through pressure fluctuation measurements and synchronized high-speed imaging capturing the lateral and longitudinal perspectives of flame propagation. The observed propagation speed of quasi-planar flames showed a strong correlation with the calculated laminar burning velocities of NH3/O2/N2 mixtures. For the first time, the cellular structures of laminar premixed ammonia flames at the onset of parametric instability were clearly observed from the present experimental approach. The experimental cellular flame wavenumbers and acoustic velocity fluctuation amplitudes at the onset of parametric instability are in qualitative agreement with the theory of stability of laminar flames under acoustic excitation. Experiments have shown that NH3/O2/N2 flames are more unstable than CH4/O2/N2 flames at the same laminar burning velocity independent of Lewis number within the range of tested conditions. The influence of activation energy on parametric instability is investigated through a comparative thermoacoustic analysis between two different fuels at varied equivalence ratios. Ammonia flames are characterized by large overall activation energy and Zeldovich numbers compared to hydrocarbon flames. This work elucidates how this unique property characterizes the acoustic instability of downward propagating premixed ammonia flames in a tube based on classical theories on acoustic instability of laminar premixed flames.

Air bubbles crossing a stratified water-diesel fuel interface

This study examines the behavior of a single air bubble moving through a stratified interface between two liquid phases: purified water as the denser liquid and diesel fuel as the lighter counterpart. The study investigates the impact of the upper liquid's height on bubble behavior, particularly under low gas flow rates, using high-speed video imaging. The experimental findings unveil two distinct scenarios: stable and unstable regimes. In stable conditions, the bubble follows a linear trajectory, simultaneously transferring some of the denser liquid into the lighter phase. Conversely, under unstable conditions, the bubble undergoes oscillations, navigating a zigzag or spiral path. The study also explores the correlation between the upper liquid height and the deformation and division of the dragged volume. This comprehensive investigation sheds light on the intricate interplay between liquid heights and bubble dynamics at liquid-liquid interfaces.

Wind farm power curve characterization under different atmospheric stability regimes

Wind farm power curves are particularly relevant in different applications. A better understanding of wind farm power curves under different atmospheric regimes is sought. In the present work, the atmospheric stability regime was identified by the vertical gradient of the potential temperature. Vertical profile of the wind velocity presented a clearly different pattern during the stable and unstable regimes. Analysis was performed considering 5 years of data from three wind farms, each corresponding to different mesoscale wind. Power curves are presented as a function of atmospheric stability. For each wind farm, we utilized wind velocity and temperature data measurements of a correspondent near the tower location. Clearly different patterns of wind farm power curves were observed as a function of the stability regime, with clear differences in the dependence of mesoscale wind regimes. For the same mean velocity, wind power production is greater for higher values of turbulence intensity TI.

Flux‐gradient relations and their dependence on turbulence anisotropy

AbstractMonin–Obukhov similarity theory (MOST) is used in virtually all Earth System Models to parametrize the near‐surface turbulent exchanges and mean variable profiles. Despite its widespread use, there is high uncertainty in the literature about the appropriate parametrizations to use. In addition, MOST has limitations in very stable and unstable regimes, over heterogeneous terrain and complex orography, and has been found to represent the surface fluxes incorrectly. A new approach including turbulence anisotropy as a non‐dimensional scaling parameter has recently been developed and has been shown to overcome these limitations and generalize the flux‐variance relations to complex terrain. In this article, we analyze the flux‐gradient relations for five well‐known datasets, ranging from flat and homogeneous to slightly complex terrain. The scaling relations show substantial scatter and highlight the uncertainty in the choice of parametrization even over canonical conditions. We show that, by including information on turbulence anisotropy as an additional scaling parameter, the original scatter becomes well bounded and new formulations can be developed that drastically improve the accuracy of the flux‐gradient relations for wind shear () in unstable conditions and for temperature gradient () in both unstable and stable regimes. This analysis shows that both and are strongly dependent on turbulence anisotropy and allows us finally to settle the extensively discussed free convection regime for , which clearly exhibits a power law when anisotropy is accounted for. Furthermore, we show that the eddy diffusivities for momentum and heat and the turbulent Prandtl number are strongly dependent on anisotropy and that the latter goes to zero in the free convection limit. These results highlight the necessity to include anisotropy in the study of near‐surface atmospheric turbulence and lead the way for theoretically more robust simulations of the boundary layer over complex terrain.

Arbitrary-order sensitivities of the incompressible base flow and its eigenproblem

First-order sensitivities and adjoint analysis are used widely to control the linear stability of unstable flows. Second-order sensitivities have recently helped to increase accuracy. In this paper, a method is presented to calculate arbitrary high-order sensitivities based on Taylor expansions of the incompressible base flow and its eigenproblem around a scalar parameter. For the incompressible Navier–Stokes equations, general expressions for the sensitivities are derived, into which parameter-specific information can be inserted. The computational costs are low since, for all orders, a linear equation system has to be solved, of which the left-hand-side matrix stays constant and thus its preconditioning can be exploited. Two flow scenarios are examined. First, the cylinder flow equations are expanded around the inverse of the Reynolds number, enabling the prediction of the two-dimensional cylinder base flow and its leading eigenvalue as a function of the Reynolds number. This approach computes accurately the base flow and eigenvalue even in the unstable regime, providing, when executed subsequently, a mean to calculate unstable base flows. This case gives a clear introduction into the method and allows us to discuss its constraints regarding convergence behaviour. Second, a small control cylinder is introduced into the domain of the cylinder flow for stabilization. Higher-order sensitivity maps are calculated by modelling the small cylinder with a steady forcing. These maps help to identify stabilizing areas of the flow field for Reynolds numbers within the laminar vortex shedding regime, with the required number of orders increasing as the Reynolds number rises. The results obtained through the proposed method align well with numerically calculated eigenvalues that incorporate the cylinder directly into the grid.

Modelling supercritical CO2 flow in a co-rotating twin screw extruder using the level-set method

Supercritical CO2 has been used in recent years to replace conventional blowing agents in extrusion processes. So far, computational fluid dynamics analyses of such extrusion processes are relatively scarce. In this work, a multiphase model of a co-rotating twin screw extruder is presented that uses the level-set method to describe the interface between supercritical CO2 and polypropylene - which is modelled as an inelastic, non-Newtonian fluid - under various operating conditions. The results show that the level-set method is a promising technique to describe multiphase flow and can predict both stable and unstable processing regimes as described by experimentalists in literature.

On the Unstable Convergence Regime of Gradient Descent

Traditional gradient descent (GD) has been fully investigated for convex or L-smoothness functions, and it is widely utilized in current neural network optimization. The classical descent lemma ensures that for a function with L-smoothness, the GD trajectory converges stably towards the minimum when the learning rate is below 2 / L. This convergence is marked by a consistent reduction in the loss function throughout the iterations. However, recent experimental studies have demonstrated that even when the L-smoothness condition is not met, or if the learning rate is increased leading to oscillations in the loss function during iterations, the GD trajectory still exhibits convergence over the long run. This phenomenon is referred to as the unstable convergence regime of GD. In this paper, we present a theoretical perspective to offer a qualitative analysis of this phenomenon. The unstable convergence is in fact an inherent property of GD for general twice differentiable functions. Specifically, the forwardinvariance of GD is established, i.e., it ensures that any point within a local region will always remain within this region under GD iteration. Then, based on the forward-invariance, for the initialization outside an open set containing the local minimum, the loss function will oscillate at the first several iterations and then become monotonely decreasing after the GD trajectory jumped into the open set. This work theoretically clarifies the unstable convergence phenomenon of GD discussed in previous experimental works. The unstable convergence of GD mainly depends on the selection of the initialization, and it is actually inevitable due to the complex nature of loss function.

Real-time measurements of breathing dissipative soliton pairs in mode-locked fiber lasers

The emergence of breathing solitons, as well as the breathing soliton molecules undergoing periodic evolution in peak power and spectral width has attracted growing research attentions in dissipative systems. Beyond the intense pulse interactions within tightly-bound states with picoseconds interval, the long-range interplay between pulses separated by nanosecond-scale starts to be investigated in recent years, thus filling the long-standing academic gap between the bound solitons and independent multiple pulses. In this work, we report on the real-time observations of breathing dissipative soliton pairs with nanoseconds’ separations in a fiber laser operating under the threshold of stationary mode locking. Compared with conventional soliton counterpart, here the breathing soliton pair exhibit even more fascinating inter-pulse nonlinear dynamics due to the intriguing self-excited periodic evolutions. The shot-to-shot measurements of pulse intensity profiles, associated with dispersive Fourier transform clearly uncover not only the different breathing phase synchronization and pulse separations among different pulses but also the hysteresis behaviors of the breathing ratio by continuously varying the laser parameters. Moreover, we observed various transient stages in this unstable lasing regime, including the transition between stable single soliton and breathing soliton pair, as well as their long-range breather interaction. These results reveal the breathing multi-pulse state and the instantaneous non-equilibrium dynamics involving the breather pairs, enriching the framework of breathing solitons and opening a novel possibility to explore the internal motions of breathing soliton complex in nonlinear systems.

Kinetic instability of whistlers in electron beam-plasma systems

The whistlers in space plasmas and in magnetic fusion experiments are destabilized by beams of fast electrons. While the linear regime of instability is analytically tractable, in most practical cases, the instability operates at the saturated level during the stages of observation and measurement. The saturated states, however, involve nonlinear whistlers, which remain best accessible for analysis by kinetic simulations. Results of electromagnetic Vlasov simulations are presented, analyzing an anisotropic electron beam driven whistler instability. The simulations cover the initially unstable regime followed by a saturated or marginally stable regime. Both regimes are separated by an intermediate nonlinear regime during which the electron distribution undergoes a kinetically self-consistent modification. A linearly obtained generalized marginal stability condition is applied to the stabilized state. The condition obtained in its dispersive version shows the β|| at threshold and, in turn, the residual anisotropy, to be a function of the whistler mode number k.

Structure of Zoocenoses in the Ephemeral Pond Lilov Vir, Western Bulgaria

This study aimed to observe the development of zoocenoses in an ephemeral karst water body providing a dynamically changing habitat and unstable hydrological regime with an emphasis on assessing the main factors influencing the structure of the macrozoobenthos and zooplankton communities. The study was conducted in Pond Lilov Vir near Karlukovo Vil., Western Bulgaria. The main physicochemical parameters and the concentrations of nutrients were recorded. The macrozoobenthos (MZB) and zooplankton samples were taxonomically determined and statistical analyses of the obtained results were performed. The results have shown that the pond supports a variety of species and species typical to temporary waters. The variation in hydroperiod (HP) duration over the years leads to the formation of different communities. Longer HPs suggest greater biodiversity. In drying pools, especially those with a short HP, the leading factor for structuring communities is the abiotic environmental factors-HP and water volume (WVOL). Biotic factors, such as competition and predation, are not leading, due to the lack of fish and insufficient time for the development of invertebrate predators.

Buoyancy-Driven Dissolution Instability in a Horizontal Hele-Shaw Cell.

The dissolution of minerals within rock fractures is fundamental to many geological processes. Previous research on fracture dissolution has highlighted the significant role of buoyancy-driven convection leading to dissolution instability. Yet, the pore-scale mechanisms underlying this instability are poorly understood primarily due to the challenges in experimentally determining flow velocity and concentration fields. Here, we integrate pore-scale simulations with theoretical analysis to delve into the dissolution instability prompted by buoyancy-driven convection in a radial horizontal geometry. Initially, we develop a pore-scale modeling approach incorporating gravitational effects, subsequently validating it through experiments. We then employ pore-scale numerical simulations to elucidate the 3D intricacies of flow-dissolution dynamics. Our findings reveal that a simple criterion can delineate the condition for the onset of buoyancy-driven dissolution instability. If the characteristic length falls below a critical threshold, dissolution remains stable. Conversely, exceeding this threshold leads to two distinct regimes: the unstable regime of the confined domain affected by the initial aperture and the unstable regime of the semi-infinite domain independent of the initial aperture where the instability is no longer influenced by the lower boundary. We demonstrate that the pore-scale mechanism for this instability is due to the concentration boundary layer attaining a gravitationally unstable critical thickness. Through theoretical analysis of this layer and the time scales of diffusion and advection, we establish a theoretical model to predict where the dissolution instability occurs. This model aligns closely with our numerical simulations and experimental data across diverse conditions. Our work improves the understanding of buoyancy-driven dissolution instability in radial horizontal geometry. It is also of practical significance in understanding cavity formation in karst hydrology and preventing leaks in geological CO2 storage.