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In this study, the effect of throughflow and variable gravity field on the stability of double diffusive convection in a fluid layer for the system when heating and salting both are done from below, are investigated. The linear and energy techniques are regulated to check the stability characteristics of the system. The numerical results of linear and non-linear techniques are compared to check the subcritical region. The Chebyshev pseudo-spectral technique is applied to find the influences of distinct physical parameters on the stability of the system. [ABSTRACT FROM AUTHOR]

This study provides a theoretical analysis of how time-dependent injection strategies affect the development of viscous fingering in a miscible finite slice. We are specifically examining a sinusoidal injection, which is characterized by its amplitude (Γ ) and periodicity (T). This study presents two case studies: injection-extraction ( Γ > 0 ) and extraction-injection ( Γ < 0 ), which have been examined for different values of T. The extraction-injection process demonstrates that diffusion plays a prominent role, leading to a notable delay in the interaction between stable and unstable interfaces. In the injection-extraction case, the onset of fingers does not change with an increase in T, whereas the onset gets delayed in the case of extraction-injection in a nearly linear fashion as the time period increases. Additionally, by quantifying the impact of convective forces on the time-dependent injection strategy, we can gain a deeper understanding of the underlying physical mechanism responsible for the observed delay in onset at higher T values. The delayed onset of instability will have a positive impact on the separation of chemicals in chromatographic applications. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the linear and the nonlinear Rayleigh–Taylor instability for the gravity-driven incompressible Navier–Stokes equations with Navier-slip boundary conditions around a smooth increasing density profile ρ 0 (x 2) in a slab domain 2 π L T × (- 1 , 1) ( L > 0 , T is the usual 1D torus). The linear instability study of the viscous Rayleigh–Taylor model amounts to the study of the following ordinary differential equation on the finite interval (- 1 , 1) , 0.1 - λ 2 [ ρ 0 k 2 ϕ - (ρ 0 ϕ ′) ′ ] = λ μ (ϕ (4) - 2 k 2 ϕ ′ ′ + k 4 ϕ) - g k 2 ρ 0 ′ ϕ , with the boundary conditions 0.2 ϕ (- 1) = ϕ (1) = 0 , μ ϕ ′ ′ (1) = ξ + ϕ ′ (1) , μ ϕ ′ ′ (- 1) = - ξ - ϕ ′ (- 1) , where λ > 0 is the growth rate in time, g > 0 is the gravity constant, k is the wave number and two Navier-slip coefficients ξ ± are nonnegative constants. For each k ∈ L - 1 Z \ { 0 } , we define a k-supercritical regime of viscosity coefficient, i.e. μ > μ c (k , Ξ) with Ξ = (ξ + , ξ -) to describe a spectral analysis by adapting an operator method of Lafitte and Nguyễn (Water Waves 4:259–305, 2022) and to prove that there are infinite nontrivial solutions (λ n , ϕ n) n ≥ 1 of (0.1)–(0.2) with λ n → 0 as n → ∞ and ϕ n ∈ H 4 ((- 1 , 1)) . Hence, we prove the linear Rayleigh–Taylor instability for any viscosity coefficient μ > 0 . As a by-product, based on the existence of infinitely many normal modes of the linearized problem, we construct a wide class of initial data to the nonlinear equations, being inspired by the previous framework of Guo–Strauss (Commun Pure Appl Math 48:861–894, 1995) and of Grenier (Commun Pure Appl Math 53:1067–1091, 2000) with a refinement, to prove the nonlinear Rayleigh–Taylor instability in a high regime of viscosity coefficient, namely μ > 3 sup k ∈ L - 1 Z \ { 0 } μ c (k , Ξ) . [ABSTRACT FROM AUTHOR]

A model is developed to describe thermal convection in a mixture of fluids in a porous medium, where the layer is heated from below while simultaneously the fluid density at the base of the porous layer is greater than that higher up. In addition to buoyancy forces which are essentially due to gravity the fluid mixture is subject to Korteweg stresses which arise because of density gradients in the mixture. A complete stability analysis is provided and the critical Rayleigh number for convective motion is derived for both stationary and oscillatory convection and this is complemented with a global energy stability analysis. The analogous problem in a bidisperse porous medium is also briefly discussed. [ABSTRACT FROM AUTHOR]

We investigate thoroughly a model for thermal convection of a class of viscoelastic fluids in a porous medium of Brinkman–Darcy type. The saturating fluids are of Kelvin–Voigt nature. The equations governing the temperature field arise from Maxwell–Cattaneo theory, although we include Guyer–Krumhansl terms, and we investigate the possibility of employing an objective derivative for the heat flux. The critical Rayleigh number for linear instability is calculated for both stationary and oscillatory convection. In addition a nonlinear stability analysis is carried out exactly. [ABSTRACT FROM AUTHOR]

Sinusoidal flows are important explicit stationary solutions of the incompressible Euler equation on a flat two-torus. In this paper, we prove that sinusoidal flows related to least eigenfunctions of the negative Laplacian are, up to phase translations, nonlinearly stable under L p norm of the vorticity for any 1 < p < + ∞ , which improves a classical stability result by Arnold. The key point of the proof is to distinguish least eigenstates with different amplitudes by using isovortical property of the Euler equation. [ABSTRACT FROM AUTHOR]

The generalized Lorenz model for non-linear stability of Rayleigh-Bénard magneto-convection is derived in the present paper. The Boussinesq-Stokes suspension fluid in the presence of variable viscosity (temperature-dependent viscosity) and internal heat source/sink is considered in this study. The influence of various parameters like suspended particles, applied vertical magnetic field, and the temperature-dependent heat source/sink has been analyzed. It is found that the basic state of the temperature gradient, viscosity variation, and the magnetic field can be conveniently expressed using the half-range Fourier cosine series. This facilitates to determine the analytical expression of the eigenvalue (thermal Rayleigh number) of the problem. From the analytical expression of the thermal Rayleigh number, it is evident that the Chandrasekhar number, internal Rayleigh number, Boussinesq-Stokes suspension parameters, and the thermorheological parameter influence the onset of convection. The non-linear theory involves the derivation of the generalized Lorenz model which is essentially a coupled autonomous system and is solved numerically using the classical Runge-Kutta method of the fourth order. The quantification of heat transfer is possible due to the numerical solution of the Lorenz system. It has been shown that the effect of heat source and temperature-dependent viscosity advance the onset of convection and thereby give rise to enhancing the heat transport. The Chandrasekhar number and the couple-stress parameter have stabilizing effects and reduce heat transfer. This problem has possible applications in the context of the magnetic field which influences the stability of the fluid. [ABSTRACT FROM AUTHOR]

The Rayleigh-Bénard convection for a couple-stress fluid with a thermorheological effect in the presence of an applied magnetic field is studied using both linear and non-linear stability analysis. This problem discusses the three important mechanisms that control the onset of convection; namely, suspended particles, an applied magnetic field, and variable viscosity. It is found that the thermorheological parameter, the couple-stress parameter, and the Chandrasekhar number influence the onset of convection. The effect of an increase in the thermorheological parameter leads to destabilization in the system, while the Chandrasekhar number and the couple-stress parameter have the opposite effect. The generalized Lorenz's model of the problem is essentially the classical Lorenz model but with coefficients involving the impact of three mechanisms as discussed earlier. The classical Lorenz model is a fifth-order autonomous system and found to be analytically intractable. Therefore, the Lorenz system is solved numerically using the Runge-Kutta method in order to quantify heat transfer. An effect of increasing the thermorheological parameter is found to enhance heat transfer, while the couple-stress parameter and the Chandrasekhar number diminishes the same. [ABSTRACT FROM AUTHOR]

This paper sheds light on the impact of vertical oscillations (or gravity modulation) on triple-diffusive convection in a viscoelastic fluid using the Oldroyd-B model, in the presence of cross effects. Cross effects can significantly impact three-component convective systems, despite having small magnitudes. When the cross terms, indicating coupled molecular cross-diffusion of the mixture components, are included in the equations governing heat and species transport, then a deviation from the usual three-component convection process is observed. An analytical solution has been found using linear and nonlinear analysis. The conditions for the onset of convection have been obtained using the linear analysis, which is based on the perturbation technique and the Venezian method. In nonlinear analysis, the expressions for Nusselt and Sherwood numbers, which quantify the rate of heat and mass transport respectively, are obtained by deriving the Lorenz model. It has been found that the onset of convection and heat and mass transport can be controlled by choosing the appropriate values of the parameters. [ABSTRACT FROM AUTHOR]

We present numerical techniques for calculating instability thresholds in a model for thermal convection in a complex viscoelastic fluid of Kelvin–Voigt type. The theory presented is valid for various orders of an exponential fading memory term, and the strategy for obtaining the neutral curves and instability thresholds is discussed in the general case. Specific numerical results are presented for a fluid of order zero, also known as a Navier–Stokes–Voigt fluid, and fluids of order 1 and 2. For the latter cases it is shown that oscillatory convection may occur, and the nature of the stationary and oscillatory convection branches is investigated in detail, including where the transition from one to the other takes place. [ABSTRACT FROM AUTHOR]

In the present work we show some results on the effect of the Smagorinsky model on the stability of the associated perturbation equation. We show that in the presence of a spectral gap, such that the flow can be decomposed in a large scale with moderate gradient and a small amplitude fine scale with arbitratry gradient, the Smagorinsky model admits stability estimates for perturbations, with exponential growth depending only on the large scale gradient. We then show in the context of stabilized finite element methods that the same result carries over to the approximation and that in this context, for suitably chosen finite element spaces the Smagorinsky model acts as a stabilizer yielding close to optimal error estimates in the L 2 -norm for smooth flows in the pre-asymptotic high Reynolds number regime. [ABSTRACT FROM AUTHOR]

In this paper, we prove nonlinear stability of planar vortex patches concentrated near a non-degenerate minimum point of the Robin function in a general bounded domain. These vortex patches are stationary solutions of the two-dimensional incompressible Euler equations. The result is obtained by showing that these concentrated vortex patches are in fact isolated maximizers of the kinetic energy among isovortical patches. [ABSTRACT FROM AUTHOR]

In this paper, we study a more general diffusive spatially dependent vaccination model for infectious disease. In our diffusive vaccination model, we consider both therapeutic impact and nonlinear incidence rate. Also, in this model, the number of compartments of susceptible, vaccinated and infectious individuals are considered to be functions of both time and location, where the set of locations (equivalently, spatial habitats) is a subset of R n with a smooth boundary. Both local and global stability of the model are studied. Our study shows that if the threshold level R 0 ≤ 1 , the disease-free equilibrium E 0 is globally asymptotically stable. On the other hand, if R 0 > 1 then there exists a unique stable disease equilibrium E ∗ . The existence of solutions of the model and uniform persistence results are studied. Finally, using finite difference scheme, we present a number of numerical examples to verify our analytical results. Our results indicate that the global dynamics of the model are completely determined by the threshold value R 0 . [ABSTRACT FROM AUTHOR]

The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work, we implemented an elaborated deflated continuation method that relies on the spectral element method (SEM) and on the reduced basis (RB) one to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations. [ABSTRACT FROM AUTHOR]

The paper deals with the study of effect of gravity modulation on double-diffusive convection in a dielectric liquid for the cases of rigid-rigid and free-free boundaries. Using a modified Venezian approach, expressions for the Rayleigh number and its correction are determined. Fourier–Galerkin expansion is employed for a weakly nonlinear stability analysis and this results in a fifth-order Lorenz system that retains the structure of the classical one in the limiting case. A local nonlinear stability analysis using the method of multiscales leads to the time-periodic Ginzburg–Landau equation from the time-periodic generalized Lorenz system and the numerical solution of this simpler equation helps in quantifying unsteady heat and mass transports. Influence of various non-dimensional parameters (Lewis number, solutal Rayleigh number, electrical Rayleigh number and Prandtl number), amplitude and frequency of gravity modulation on onset of convection and heat and mass transports is discussed. The study reveals that the influence of gravity modulation is to stabilize the system and enhance heat and mass transports. The results from free-free boundaries are qualitatively similar to that of rigid-rigid boundaries. Further, it is shown that in the case of free-free boundaries the heat and mass transports are less compared to those of rigid-rigid boundaries. [ABSTRACT FROM AUTHOR]

We present a study devoted to a detailed description of modulated rotating waves (MRW) in the magnetised spherical Couette system. The set-up consists of a liquid metal confined between two differentially rotating spheres and subjected to an axially applied magnetic field. When the magnetic field strength is varied, several branches of MRW are obtained by means of three-dimensional direct numerical simulations. The MRW originate from parent branches of rotating waves and are classified according to Rand's (Arch Ration Mech Anal 79:1–37, 1982) and Coughling and Marcus (J Fluid Mech 234:1–18, 1992) theoretical description. We have found relatively large intervals of multistability of MRW at low magnetic field, corresponding to the radial jet instability known from previous studies. However, at larger magnetic field, corresponding to the return flow regime, the stability intervals of MRW are very narrow and thus they are unlikely to be found without detailed knowledge of their bifurcation point. A careful analysis of the spatio-temporal symmetries of the most energetic modes involved in the different classes of MRW will allow in the future a comparison with the HEDGEHOG experiment, a magnetised spherical Couette device hosted at the Helmholtz-Zentrum Dresden-Rossendorf. [ABSTRACT FROM AUTHOR]

An internal energy function of the mass density, the volumetric entropy and their gradients at n-order generates the representation of multi-gradient fluids. Thanks to Hamilton's principle, we obtain a thermodynamical form of the equation of motion which generalizes the case of perfect compressible fluids. First integrals of flows are extended cases of perfect compressible fluids. The equation of motion and the equation of energy are written for dissipative cases, and are compatible with the second law of thermodynamics. [ABSTRACT FROM AUTHOR]

We reduce the mathematical model for a chemical reaction in a moving medium to the general nonlinear parabolic equation (GNPE) for the complex amplitude of envelope wave to analyse weakly nonlinear interactions in supercritical regions. We use the method of many scales, wave packages, modification of Mandelshtam method and take into account the group velocity of envelope wave that is typical for nonlinear dispersive medium. GNPE describes the long-term system behaviour after stability loss and its coefficients are explicitly expressed through parameters of the initial nonlinear partial differential equations. It is taking into account the location of wave packet centre out of harmonics with maximum increment. [ABSTRACT FROM AUTHOR]

Statistical bounds controlling the total fluctuations in mean and variance about a basic steady-state solution are developed for the truncated barotropic flow over topography. Statistical ensemble prediction is an important topic in weather and climate research. Here, the evolution of an ensemble of trajectories is considered using statistical instability analysis and is compared and contrasted with the classical deterministic instability for the growth of perturbations in one pointwise trajectory. The maximum growth of the total statistics in fluctuations is derived relying on the statistical conservation principle of the pseudo-energy. The saturation bound of the statistical mean fluctuation and variance in the unstable regimes with non-positive-definite pseudo-energy is achieved by linking with a class of stable reference states and minimizing the stable statistical energy. Two cases with dependence on initial statistical uncertainty and on external forcing and dissipation are compared and unified under a consistent statistical stability framework. The flow structures and statistical stability bounds are illustrated and verified by numerical simulations among a wide range of dynamical regimes, where subtle transient statistical instability exists in general with positive short-time exponential growth in the covariance even when the pseudo-energy is positive-definite. Among the various scenarios in this paper, there exist strong forward and backward energy exchanges between different scales which are estimated by the rigorous statistical bounds. [ABSTRACT FROM AUTHOR]

We present an explicit exact solution of the nonlinear governing equations with Coriolis and centripetal terms in the f-plane approximation for internal geophysical trapped waves with a uniform current near the equator. This solution describes in the Lagrangian framework azimuthal equatorial internal waves propagating westward in a stratified rotational fluid. [ABSTRACT FROM AUTHOR]

In the paper we introduce a new approximation scheme for modelling a spherical cloud of cavitation bubbles based upon a model developed in (Wang and Brennen in J. Fluids Eng. 121(4):872-880, 1999) which consists of fully nonlinear continuum mixture equations coupled with the Rayleigh-Plesset equation for dynamics of the bubbles. We prove existence of a unique, local-in-time solution to the equations using the Banach fixed-point theorem which also provides us with the convergent scheme for a numerical simulation of the solution. We further demonstrate acquired numerical results. [ABSTRACT FROM AUTHOR]

One of the most important sections of nonlinear wave theory is related to the collisions of single pulses. These often exhibit corpuscular properties. For example, it is well known that solitons described by the Korteweg-de Vries equation and a few other conservative model equations exhibit properties of elastic particles, while shock waves described by dissipative models like Burgers' equation stick together as absolutely inelastic particles when colliding. The interactions of single pulses in media with modular nonlinearity considered here reveal new physical features that are still poorly understood. There is an analogy between the single pulses collision and the interaction of clots of chemical reactants, such as fuel and oxidant, where the smaller component disappears and the larger one decreases after a reaction. At equal 'masses' both clots can be annihilated. In this work various interactions of two and three pulses are considered. The conditions for which a complete annihilation of the pulses occurs are indicated. [ABSTRACT FROM AUTHOR]

The fourth-gradient model for fluids-associated with an extended molecular mean-field theory of capillarity-is considered. By producing fluctuations of density near the critical point like in computational molecular dynamics, the model is more realistic and richer than van der Waals' one and other models associated with a second order expansion. The aim of the paper is to prove-with a fourth-gradient internal energy already obtained by the mean field theory-that the quasi-linear system of conservation laws can be written in an Hermitian symmetric form implying the stability of constant solutions. The result extends the symmetric hyperbolicity property of governing-equations' systems when an equation of energy associated with high order deformation of a continuum medium is taken into account. [ABSTRACT FROM AUTHOR]

The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two-dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This alongshelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclones and near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean. [ABSTRACT FROM AUTHOR]

Nonlinear interactions of the two-dimensional (2D) second mode with oblique modes are studied numerically in a Mach 6.0 flat-plate boundary layer, focusing on its selective enhancement effect on amplification of different oblique waves. Evolution of oblique modes with various frequencies and spanwise wavenumbers in the presence of 2D second mode is simulated successively, using a modified parabolized stability equation (PSE) method, which is able to simulate interaction of two modes with different frequencies efficiently. Numerical results show that oblique modes in a broad band of frequencies and spanwise wavenumbers can be enhanced by the finite amplitude 2D second mode instability wave. The enhancement effect is accomplished by interaction of the 2D second mode, the oblique mode, and a forced mode with difference frequency. Two types of oblique modes are found to be more amplified, i.e., oblique modes with frequency close to that of the 2D second mode and low-frequency first mode oblique waves. Each of them may correspond to one type of transition routes found in transition experiments. The spanwise wavenumber of the oblique wave preferred by the nonlinear interaction is also determined by numerical simulations. [ABSTRACT FROM AUTHOR]

Brand-new equations which can be regarded as modifications of Khokhlov-Zabolotskaya-Kuznetsov or Ostrovsky-Vakhnenko equations are suggested. These equations are quite general in that they describe the nonlinear wave dynamics in media with modular nonlinearity. Such media exist among composites, meta-materials, inhomogeneous and multiphase systems. These new models are interesting because of two reasons: (1) the equations admit exact analytic solutions and (2) the solutions describe real physical phenomena. The equations model nonlinear focusing of wave beams. It is shown that inside the focal zone a stationary waveform exists. Steady-state profiles are constructed by the matching of functions describing the positive and negative branches of exact solutions of an equation of Klein-Gordon type. Such profiles have been observed many times during experiments and numerical studies. The non-stationary waves can contain singularities of two types: discontinuity of the wave and of its derivative. These singularities are eliminated by introducing dissipative terms into the equations-thereby increasing their order. [ABSTRACT FROM AUTHOR]

We present an explicit exact solution of the nonlinear governing equations for internal geophysical water waves propagating westward above the thermocline in the f-plane approximation near the equator. Moreover, the mass transport velocity induced by this internal equatorial wave is eastward and a westward current occurs in the transition zone between the great depth where the water is still and the thermocline. [ABSTRACT FROM AUTHOR]

A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows. [ABSTRACT FROM AUTHOR]

Convective instability in miscible slices is important in understanding the contaminant spreading in groundwater and sample dispersion in a chromatographic column. In the present study, the temporal evolution of the Rayleigh-Taylor instability of a miscible high-density slice in a porous medium is analyzed theoretically using nonlinear numerical simulations. Nonlinear governing equations are derived and solved with the Fourier spectral method. To connect the previous linear stability analysis and the present nonlinear simulation, the most unstable disturbance which was identified in the linear analysis is employed as an initial condition for the nonlinear study. In contrast to the fingering between two semi-infinite regions, the nonlinear fingering of a finite slice is influenced by the depth of the high-density region. The present nonlinear analysis shows that there exists a critical depth below which the system is linearly unstable, but nonlinear phenomena cannot be expected. The nonlinear simulation results show that nonlinear competition yields a series of cells of slightly different widths and amplitudes. Also, it is found that the upper stable region hinders the development of instability motions and stabilizes the system. [ABSTRACT FROM AUTHOR]

A modified equation of Burgers type with a quadratically cubic (QC) nonlinear term was recently pointed out as a new exactly solvable model of mathematical physics. However, its derivation, analytical solution, computer modeling, as well as its physical applications and analysis of corresponding nonlinear wave phenomena have not been published up to now. The physical meaning and generality of this QC nonlinearity are illustrated here by several examples and experimental results. The QC equation can be linearized and it describes the experimentally observed phenomena. Some of its exact solutions are given. It is shown that in a QC medium not only shocks of compression can be stable, but shocks of rarefaction as well. The formation of stationary waves with finite width of shock front resulting from the competition between nonlinearity and dissipation is traced. Single-pulse propagation is studied by computer modeling. The nonlinear evolutions of N- and S-waves in a dissipative QC medium are described, and the transformation of a harmonic wave to a sawtooth-shaped wave with periodically recurring trapezoidal teeth is analyzed. [ABSTRACT FROM AUTHOR]

A non-autonomous complex Ginzburg-Landau equation (CGLE) for the finite amplitude of convection is derived, and a method is presented here to determine the amplitude of this convection with a weakly nonlinear thermal instability for an oscillatory mode under throughflow and gravity modulation. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature, and solutal fields are treated by a perturbation expansion in powers of the amplitude of the applied gravity field. Throughflow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The Nusselt and Sherwood numbers are obtained numerically to present the results of heat and mass transfer. It is found that throughflow and gravity modulation can be used alternately to heat and mass transfer. Further, oscillatory flow, rather than stationary flow, enhances heat and mass transfer. [ABSTRACT FROM AUTHOR]

This paper presents the hydrodynamical stability of three-dimensional geophysical edge waves in the presence of an underlying longshore current. By implementing the short-wavelength perturbation approach, we show that the equatorial edge waves are linear unstable when the wave steepness exceeds a specific threshold. [ABSTRACT FROM PUBLISHER]

This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An L-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement. [ABSTRACT FROM AUTHOR]

This study presents an explicit exact solution for nonlinear geophysical equatorial waves in the $$f$$ -plane approximation near the Equator. The solution describes in the Lagrangian framework equatorial waves propagating westward in a homogenous inviscid fluid. [ABSTRACT FROM AUTHOR]

The effects of packing configurations on the phase transition of straight granular chute flow with two bottlenecks are studied. The granular flow shows a dilute-to-dense flow transition when the channel width is varied, accompanied with a peculiar bistable phenomenon. The bistable phenomenon is induced by the initial packing configuration of particles. When the packing is dense, the initial flux is small and will induce a dense flow. When the packing is loose, the initial flux is large and will induce a dilute flow. The fabric network of granular packing is analyzed from a complex network perspective. The degree distribution shows quantitatively different characteristics for the configurations. A two-dimensional (2D) packing clustering coefficient is defined to better quantify the fabric network. [ABSTRACT FROM AUTHOR]

We present an exact solution of the nonlinear governing equations for internal geophysical water waves propagating westward in the f-plane approximation near the equator. We show that the mass transport velocity induced by this internal equatorial wave is eastward. [ABSTRACT FROM AUTHOR]

This paper deals with two fundamental models for convection in a reacting porous medium with magnetic field effect. We demonstrate that the solution depends continuously on changes in the chemical reaction and the electrical conductivity coefficients. [ABSTRACT FROM AUTHOR]

Studying the evolution of 3D disturbances is of crucial theoretical importance for understanding the transition process. The present study concerns the nonlinear evolution of second mode unstable disturbances in a supersonic boundary layer by the numerical simulation, and discusses the selectivity of 3D disturbances and possibility to transition. The results indicate that a Klebanoff type nonlinear interaction between 2D and 3D disturbances with the same frequency may amplify a band of 3D disturbances centered at a finite spanwise wavenumber. That is, certain 3D disturbances can be selectively and rapidly amplified by the unstable 2D disturbances, and certain small-scale 3D structures will appear. [ABSTRACT FROM AUTHOR]

In this paper we construct a new noninvariant Riemannian metric on the semidirect product of the diffeomorphism group of a manifold and the space of positive functions on that manifold, which has the property that certain geodesics give the equations of barotropic fluid mechanics. We compute a formula for its curvature, analyze the sign of the curvature, and determine directly the growth of Jacobi fields in a few special cases. [ABSTRACT FROM AUTHOR]

The modulational stability of both the Korteweg-de Vries (KdV) and the Boussinesq wavetrains is investigated using Whitham's variational method. It is shown that both KdV and Boussinesq wavetrains are modulationally stable. This result seems to confirm why it is possible to transform the KdV equation into a nonlinear Schrödinger equation with a repulsive potential. Included is modulational instability of Stokes water waves based on the nonlinear Schrödinger equation in deep water. A brief discussion of Whitham's averaged variational method is included to make the paper self-contained to some extent with application to instability of deep water waves. [ABSTRACT FROM AUTHOR]