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In this paper, we are interested to explore stable configurations of $d$-dimensional gravastars constructed from the interior $d$-dimensional de Sitter and exterior $d$-dimensional Schwarzschild/Reissner-Nordstr\"om (de Sitter) black holes through cut and paste approach. We consider the linearized radial perturbation preserving the original symmetries to explore their stability by using three different types of matter distributions. The resulting frameworks represent unstable structures for barotropic, Chaplygin, and phantomlike models for every considered choice of exterior geometries. However, matter contents with variable equations of state have a remarkable role to maintain the stability of gravastars. We conclude that stable structures of gravastars are obtained only for generalized variable models with exterior $d$-dimensional Schwarzschild/Reissner-Nordstr\"om-de Sitter black holes., Comment: 21 pages, 12 figures, to appear in Chinese J. Physics

In this paper, we explore analytic solutions of self-gravitating celestial objects known as gravastars in energy–momentum squared gravity. A gravastar is referred as an alternative model to a black hole which is exhibited by three different regions, i.e., the intermediate shell, interior, and exterior regions. We examine these regions for a particular model of this gravity with conformal motion. The field equations are developed with perfect fluid for a spherically symmetric spacetime. The mathematical formulation for these domains is expressed by using a barotropic equation of state. We use Israel matching conditions for the smooth joining of outer and inner spacetimes. We analyze various physical features of gravastars along with the thickness of the shell, i.e., equation of state parameter, proper length, entropy and energy. These characteristics represent physically consistent non-singular solutions.

Galaxy rotation curves are considered to be convincing evidence for dark matter or some dynamically equivalent alternative mechanism. Starting only from the rotation curve data, we present a model independent approach of testing a general hypothesis that dark matter has the properties of a barotropic fluid. It is shown how the speed of sound squared can be expressed in terms of rotation curve data and their radial derivatives and how model independent constraints can be obtained from the requirements that it is confined between 0 and $c^2$. Using the Milky Way rotation curve data available in the literature, we obtain the constraints on the barotropic fluid speed of sound and illustrate the potential of this approach. Technical challenges, limitations and possible future extensions and improvements of the proposed approach are discussed., Comment: v1: 17 pages, 7 figures; v2: minor corrections, references added; v3: minor corrections and clarifications; v4: discussions extended, one figure added, v4 to appear in The European Physical Journal C

Using observations and numerical simulations, this study examines the intraseasonal variability of the surface zonal current (u ISV) over the equatorial Indian Ocean, highlighting the seasonal and spatial differences, and the causes of the differences. Large-amplitude u ISV occurs in the eastern basin at around 80°–90°E and near the western boundary at 45°–55°E. In the eastern basin, the u ISV is mainly caused by the atmospheric intraseasonal oscillations (ISOs), which explains 91% of the standard deviation of the total u ISV. Further analysis suggests that it takes less than ten days for the intraseasonal zonal wind stress to generate the u ISV through the directly forced Kelvin and Rossby waves. Driven by the stronger zonal wind stress associated with the Indian summer monsoon ISO (MISO), the eastern u ISV in boreal summer (May to October) is about 1.5 times larger than that in boreal winter (November to April). In the western basin, both the atmospheric ISOs and the oceanic internal instabilities contribute substantially to the u ISV, and induce stronger u ISV in boreal summer. Energy budget analysis suggests that the mean flow converts energy to the intraseasonal current mainly through barotropic instabilities.

Diabatic heating by convection in the eyewall often produces an annular region of high potential vorticity (PV) around the relatively low PV eye in a strong tropical cyclone (TC). Such a PV ring is barotropically unstable and can encourage exponentially growing PV waves. In this study, such instability and the subsequent nonlinear evolutions of three TC-like vortices with different degrees of hollowness PV ring on an f-plane are first examined using an unforced, inviscid shallow-water-equation model. Results show that the simulated eyewalls evolve similarly to those in the nondivergent barotropic model. It is also found that the polygonal eyewall structure can be decomposed into vortex Rossby waves (VRWs) of different wavenumbers with different amplitudes, allowing for wave-wave interaction to produce complicated behaviors of mesovortices in the TC eyewall. The same set of PV rings has been examined on a beta-plane. Although the beta effect has been rendered unimportant to the eyewall evolution due to the relatively small-scale of inner-core circulation, it is shown in this study that the beta effect may erode the coherent structure of mesovortices in the eyewall of an initially hollow PV-ring vortex. Mesovortices modeled on the beta-plane with greater beta parameter tends to experience an earlier breakdown along with the enhanced radial gradients of the basic-state (azimuthal mean) angular velocity, followed by wave-wave and wave-flow interactions, leading to earlier merger and axisymmetrization processes. This implies that the beta effect could be one of the forcings that shorten the lifetime of quasi-steady mesovortices in the eyewall of real TCs.

Based on the daily Japanese 55-yr Reanalysis dataset, this study analyzes the maintenance mechanism of 53 boreal winter blocking highs around the Ural Mountains (UBHs) during the period from 1958 to 2018 via the energy budget equations. After decomposing the circulation into background flow, low-frequency anomalies and high-frequency eddies, it was found that the interference between the background flow and low-frequency anomalies is conducive to the maintenance of the UBHs. Due to the southwestward gradient of the climatological mean air temperature over the Eurasian continent, it is easy for the air temperature anomalies as well as the wind velocity anomalies in the middle and lower troposphere induced by the UBHs to facilitate the positive conversion of baroclinic energy associated with the background flow into the UBHs. Likewise, the conversion of barotropic energy associated with the background flow is also evident in the upper troposphere in which the climatological mean westerlies have evident southward gradient to the northwest of Lake Baikal and southwestward gradient over Barents sea. Note that the conversion of baroclinic energy associated with the background flow is dominant throughout the lifecycle of UBHs, acting as the major contributor to the maintenance of the UBHs. Although transient eddies facilitate the maintenance of UBHs via the positive conversion of barotropic energy in the middle and upper troposphere, they hinder the maintenance of UBHs via the negative conversion of baroclinic energy in the lower troposphere. The diabatic heating anomalies tend to counteract the local air temperature anomalies in the middle and lower troposphere, which damps the available potential energy of UBHs and acts as a negative contributor to the UBHs.

The Regional Ocean Modeling System (ROMS), including an ice shelf component, has been applied on a circum-Antarctic domain to derive estimates of ice shelf basal melting. Significant improvements made compared to previous models of this scale are the inclusion of tides and a horizontal spatial resolution of 2 km, which is sufficient to resolve on-shelf heat transport by bathymetric troughs and eddy-scale circulation. We run the model with ocean–atmosphere–sea ice conditions from the year 2007 to represent nominal present-day climate. We force the ocean surface with buoyancy fluxes derived from sea ice concentration observations and wind stress from ERA-Interim atmospheric reanalysis. Boundary conditions are derived from the ECCO2 ocean state estimate; tides are incorporated as sea surface height and barotropic currents at the open boundary. We evaluate model results using satellite-derived estimates of ice shelf melting and established compilations of ocean hydrography. The Whole Antarctic Ocean Model (WAOM v1.0) qualitatively captures the broad scale difference between warm and cold regimes as well as many of the known characteristics of regional ice–ocean interaction. We identify a cold bias for some warm-water ice shelves and a lack of high-salinity shelf water (HSSW) formation. We conclude that further calibration and development of our approach are justified. At its current state, the model is ideal for addressing specific, process-oriented questions, e.g. related to tide-driven ice shelf melting at large scales.

The midwinter suppression (MWS) of the North Pacific Storm Track (NPST) has been an active research topic for decades. Based on the daily-mean NCEP/NCAR reanalysis from 1948 to 2018, this study investigates the MWS-related atmospheric circulation characteristics in the Northern Hemisphere by regression analysis with respect to a new MWS index, which may shed more light on this difficult issue. The occurrence frequency of the MWS of the upper-tropospheric NPST is more than 0.8 after the mid-1980s. The MWS is accompanied by significantly positive sea-level pressure anomalies in Eurasia and negative anomalies over the North Pacific, which correspond to a strengthened East Asian winter monsoon. The intensified East Asian trough and atmospheric blocking in the North Pacific as well as the significantly negative low-level air temperature anomalies, lying upstream of the MNPST, are expected to be distinctly associated with the MWS. However, the relationship between the MWS and low-level atmospheric baroclinicity is somewhat puzzling. From the diagnostics of the eddy energy budget, it is identified that the inefficiency of the barotropic energy conversion related to the barotropic governor mechanism does not favor the occurrence of the MWS. In contrast, weakened baroclinic energy conversion, buoyancy conversion, and generation of eddy available potential energy by diabatic heating are conducive to the occurrence of the MWS. In addition, Ural blocking in the upstream region of the MNPST may be another candidate mechanism associated with the MWS.

We are concerned about the barotropic compressible Navier-Stokes equations with density-dependent viscosities which may degenerate in vacuum. We show that any classical solution to barotropic compressible Navier-Stokes equations in bounded domains will blow up, when the initial density admits an isolated mass group and the viscosity coefficients satisfy some conditions. A new condition on viscosities is first put forward in this paper.

Secondary eyewall formation and the ensuing eyewall replacement cycles may take place in mature tropical cyclones (TCs) during part of their lifetime. A better understanding of the underlying dynamics is beneficial to improving the prediction of TC intensity and structure. Previous studies suggested that the barotropic instability (BI) across the moat (aka type-2 BI) can make a substantial contribution to the inner-eyewall decay through the associated eddy radial transport of absolute angular momentum (AAM). Simultaneously, the type-2 BI can also increase the AAM of the outer eyewall. While the previous studies focused on the early stage of the type-2 BI, this paper explores the long-term effect of the type-2 BI and the underlying processes in forced and unforced shallow-water experiments. Under the long-term effect, it will be shown that the inner eyewalls repeatedly weaken and strengthen (while the order is reversed for the outer eyewalls). Sensitivity tests are conducted to examine the sensitivity of the long-term effect of the type-2 BI to different vortex parameters and the strength of the parameterized diabatic heating. Implication of the long-term effect for the intensity changes of the inner and outer eyewalls of real TCs are also discussed.

We investigate the dynamical evolution of a homogeneous and isotropic flat universe filled with a barotropic fluid satisfying the linear equation of state in Rastall gravity. Using the dynamical system approach, we determined the fixed points of the system and studied their stability. We further explore the thermodynamic aspects at the apparent horizon by investigating the validity of the generalised second law of thermodynamics with an equilibrium description.

Numerical simulations of steady and unsteady viscous flows are presented by adopting two different numerical methodologies: the Smoothed Particle Hydrodynamics formulation implemented in the open-source code DualSPHysics and an in-house lattice Boltzmann code based on a concise central-moments scheme. Both methods employ a weakly compressible assumption to simulate incompressible flow, which means the fluid is assumed barotropic and the density and pressure are related through an equation of state. The accuracy of the two approaches is evaluated against well-defined and consolidated benchmark tests. Advantages and disadvantages of the two methodologies are discussed and substantiated by quantitative comparisons that focus on accuracy and efficacy of the two methodologies against other well-established computational methods. Overall, both formulations proposed herein are able to capture the relevant flow physics with a good level of accuracy when compared to other more affirmed techniques. Remarkably, this is observed in spite of the proposed two methods lacking key strategies commonly used in grid-based methods, such as adaptive mesh refinement.

The large ensembles of the IPSL-CM6A-LR model output for the historical forcing experiment were employed to investigate the role of internal variability in the formation of the recent “warm Arctic–cold Eurasia” trend pattern in winter surface air temperature (SAT). In the simulations, the winter SAT trends during 1991–2014 display remarkable inter-member diversity over the Barents–Kara Seas region and central Eurasia, suggesting an important role played by internal variability. It is indicated that internally generated SAT trends over the Barents–Kara Seas are induced mainly by the change in local sea surface temperature (SST) trends. Furthermore, we find that the warming trend over the Barents–Kara Seas can induce an anomalous anticyclone over northern Eurasia, which in turn can contribute positively to the warming anomalies over the Barens–Kara Seas, but cannot account for the cooling trend over central Eurasia. The cooling trend over central Eurasia can be attributed to the negative Arctic Oscillation (AO)-like atmospheric circulation pattern, which is independent of the climate change over the Arctic. Therefore, the observed opposite winter SAT trends over the Barents–Kara Seas and central Eurasia arise partly from the linear combination of high SST trends over the Barents–Kara Seas and decline in the winter AO index.

Cut-off Lows (COLs) in the Southern Hemisphere (SH) and the mechanisms involved in their development are investigated in detail using the eddy kinetic energy (EKE) budget applied to data from the ERA-Interim reanalysis. This approach considers the most important processes that are typical for the evolution of midlatitude disturbances such as the baroclinic (BRC) and barotropic (BRT) conversions, and the ageostrophic flux convergence (AFC), known as downstream development. Composites of the volume-integrated EKE and its components are evaluated based on the 200 most intense SH COLs (> 98th percentile) observed in a 36-yr period. Results show that the AFC together with the BRC conversion are the most important contributor to the EKE growth for the COLs, characterizing the downstream baroclinic development. The AFC plays an important role in genesis and intensification phases of the COLs, while the BRC conversion is important for the system maintenance. The dissipation of the COLs occurs due to dispersive fluxes (ageostrophic flux divergence) together with other processes not directly computed in the EKE equation, such as friction and latent heat release which are problematic in reanalysis datasets. The BRT conversion contributes negatively to the COL development by transferring EKE to the zonal flow kinetic energy, though this is not enough to dampen the intensification. Regional differences were found in the energetics, indicating that COLs originating upstream of the continents are clearly dominated by ageostrophic fluxes, while the systems over the Australian region are mostly driven by baroclinic processes.

This paper is devoted to constructing the geometry of thin-shell gravastars from the joining of inner de Sitter and outer Ayon-Beato Garcia (de Sitter) black hole. We use cut and paste technique to match these spacetimes at thin-shell. The presence of thin layer of matter at thin-shell plays a vital role to explain dynamics and stability of gravastars. It is evaluated that the physical features such as proper length, entropy and shell’s energy contents are proportional to the thickness of shell’s region. The stability of gravastars is explored by using linearized radial perturbation and barotropic equation of state. It is found that stable regions of Ayon-Beato and Garcia–de Sitter black hole are greater than Ayon-Beato and Garcia as well as Schwarzschild black holes. We conclude that thin-shell gravastar becomes more stable if the shell radius is less than the expected event horizon for the barotropic equation of state.

Shipboard velocity profiles collected in July 2018 are used to study coastal current in the south of Sri Lanka during the summer monsoon. The observations reveal that there is a narrow (~ 50 km wide) westward coastal current against the summer monsoon, separated the eastward southwest monsoon current (SMC) from the island of Sri Lanka. However, the climatological south Sri Lanka coastal current (SSLCC) is eastward following the direction of the SMC. The deviations between the observations and climatology of the SSLCC suggest its significant interannual variability. The dynamics of the westward SSLCC and its impact factors are thus focused on in this study. The results indicate that two main processes are responsible. First, the boreal summer intraseasonal oscillation (BSISO) plays an important role in the presence of westward SSLCC. The BSISO signal intensifies the wind strength east and south of Sri Lanka, reinforces the east India coastal current (EICC), and bends the SMC favoring occurrence of the westward SSLCC. Second, the upwelling Rossby wave signal propagates to Sri Lanka but stops at 82°E, which favors the Sri Lanka Dome developing. As the western flank of the SLD, the strengthened EICC flows southward and turns to west resulting in the westward SSLCC. Accordingly, the energy conversions by baroclinic and barotropic instability between mean flow and eddy are analyzed for both the westward and eastward SSLCC.

This study is concerned with properties of freely propagating barotropic Rossby waves in a circular polar cap, a prototype model for the Arctic Ocean. The linearised shallow-water equations are use...

We show that the stochastic 3D primitive equations with the Neumann boundary condition on the top, the lateral Dirichlet boundary condition and either the Dirichlet or the Neumann boundary condition on the bottom driven by multiplicative gradient-dependent white noise have unique maximal strong solutions both in the stochastic and PDE senses under certain assumptions on the growth of the noise. For the case of the Neumann boundary condition on the bottom, global existence is established by using the decomposition of the vertical velocity to the barotropic and baroclinic modes and an iterated stopping time argument. An explicit example of non-trivial infinite dimensional noise depending on the vertical average of the horizontal gradient of horizontal velocity is presented.

A large fraction of tropical cyclones (TCs) are generated near the intertropical convergence zone (ITCZ), and barotropic instability of the related wind shear has been shown to be an important generation mechanism. The latitudinal position of the ITCZ shifts seasonally and may shift poleward in response to global warming. Aquaplanet GCM simulations have shown TC-generation frequency to vary with position of the ITCZ. These results, and that moisture plays an essential role in the dynamics, motivate the present study on the growth rates of barotropic instability in ITCZ-like zonal wind profiles. Base-state zonal wind profiles are generated by applying a prescribed forcing (representing zonally averaged latent heat release in the ITCZ) to a shallow-water model. Shifting the latitudinal position of the forcing alters these profiles, with a poleward shift leading to enhanced barotropic instability. Next, an examination of how latent release impacts the barotropic breakdown of these profiles is considered. To do this, moisture is explicitly represented using a tracer variable. Upon supersaturation, precipitation occurs and the related latent heat release is parameterized as a mass transfer out of the dynamically active layer. Whether moisture serves to enhance or reduce barotropic growth rates is found to depend on how saturation humidity is represented. In particular, taking it to be constant or a function of the layer thickness (related to temperature) leads to a reduction, whereas taking it to be a specified function of latitude leads to an enhancement. Simple arguments are given to support the idea that moisture effects should lead to a reduction in the moist shallow-water model and that a poleward shift of the ITCZ should lead to an enhancement of barotropic instability.

Atmospheric transient eddy dynamical forcing (TEDF)-driven midlatitude unstable air–sea interaction has recently been recognized as a crucial positive feedback for the maintenance of the extratropical decadal variabilities. Our recent theoretical work (Chen et al., Clim Dyn 10.1007/s00382-020-05405-0, 2020) has characterized such an interaction through building an analytical midlatitude barotropic atmospheric model coupled to a simplified upper oceanic model. This study extends the analytical model to including a two-layer quasi-geostrophic baroclinic atmospheric model and then identifies the roles of vertical distributions of atmospheric TEDF and diabatic heating in midlatitude unstable air–sea interaction. It is found that midlatitude air–sea coupling with more realistic vertical profiles of atmospheric TEDF and diabatic heating destabilizes oceanic Rossby wave modes over the entire range of zonal wavelengths, in which the most unstable coupled mode features an equivalent barotropic atmospheric low (high) pressure over a cold (warm) oceanic surface. Spatial structure and period of the most unstable mode are more consistent with the observation than those from in previous model. Although either TEDF or diabatic heating alone can lead to a destabilized coupled mode, the former makes a dominant contribution to the instability. The increase of low-layer TEDF stimulates the instability more effectively if the TEDF in upper layer is larger than in lower layer, while the TEDF in either high or low layers can individually cause the instability. The surface heating always destabilizes the air–sea interaction, while the mid-level heating always decays the coupled mode. The results of this study further confirm the TEDF-driven positive feedback mechanism in midlatitude air–sea interaction proposed by recent observational and numerical experiment studies.

The Southern Annular Mode (SAM) is the main mode of variability in the Southern Hemisphere extra-tropical circulation and it is so called because of its zonally symmetric ring-like shape. However, the SAM pattern actually contains noticeable deviations from zonal symmetry. Thus, the purpose of this study is to describe the zonally asymmetric and symmetric components of the SAM variability and their impacts. We regress monthly geopotential height fields at each level onto the asymmetric and symmetric component of the SAM to create two new indices: Asymmetric SAM (A-SAM) and Symmetric SAM (S-SAM). In the troposphere, the A-SAM is associated with a zonal wave 3 which is rotated a quarter wavelength with respect to the climatological zonal wave 3, is much stronger in the Pacific ocean, where it extends vertically to the stratosphere with an equivalent barotropic structure. On the other hand, the S-SAM is associated with negative geopotential height anomalies over Antarctica surrounded by a zonally symmetric ring of positive geopotential height anomalies. The observed relationship between the El Nino Southern Oscillation and the SAM is fully explained by the A-SAM index. The positive trend of the SAM is present only in its symmetric component. Despite this, the SAM is becoming more zonally asymmetric. The regional impacts of the SAM in temperature and precipitation are strongly affected by its asymmetric component. We show that the asymmetric component of the SAM has its own unique variability, trends and impacts, some of these signals are only evident when the two SAM components are separated.

In this study, the differences in spatial distribution and controlling parameters for the formation of near-equatorial tropical cyclones (NETCs) between the western North Pacific (WNP) and the North Atlantic (NA) are investigated. NETCs exhibit distinctive spatial variabilities in different basins. Over the past few decades, the majority of NETCs took place in WNP while none was observed in NA. The mechanism behind such a distinguishing spatial distribution difference is analyzed by using statistical methods. It is noted that the dynamical variables such as low-level relative vorticity and vertical wind shear (VWS) are likely the primary controlling parameters. Compared with NA, larger low-level vorticity and smaller VWS appear over WNP. The increase of vorticity attributes a lot to the turning of northeast trade wind. NETCs in WNP tend to occur in the areas with VWS less than 9 m s−1, while the VWS in NA generally exceeds 10 m s−1. On the other hand, the sea surface temperature in the near-equatorial region of both of the two oceans exceeds 26.5℃ and the difference of mid-level moisture is not significant; thus, thermal factors have little contribution to the distinction of NETC activities between WNP and NA. Intraseasonal oscillation (ISO) and synoptic-scale disturbances in WNP are also shown to be more favorable for NETC genesis. More NETCs were generated in ISO active phase. Synoptic-scale disturbances in WNP obtain more energy from the mean flows through the barotropic energy conversion process. The overall unfavorable thermal and dynamic conditions lead to the absence of NETCs in NA.

We consider the homogenization limit of the compressible barotropic Navier–Stokes equations in a three-dimensional domain perforated by periodically distributed identical particles. We study the regime of particle sizes and distances such that the volume fraction of particles tends to zero but their resistance density tends to infinity. Assuming that the Mach number is decreasing with a certain rate, the rescaled velocity and pressure of the microscopic system converges to the solution of an effective equation which is given by Darcy’s law. The range of sizes of particles we consider is exactly the same which leads to Darcy’s law in the homogenization limit of incompressible fluids. Unlike previous results for the Darcy regime we estimate the deficit related to the pressure approximation via the Bogovskiĭ operator. This allows for more flexible estimates of the pressure in Lebesgue and Sobolev spaces and allows to proof convergence results for all barotropic exponents [Formula: see text].

The possible existence of distinct regimes of barotropic circulation in closed annular channels at the same external parameters governing the flow dynamics is investigated both experimentally and numerically. Transitions between the regimes are realized by means of varying the value of the main parameter determining the velocity field energy (for example, the current controlling the Ampere force in the case of MHD generation of a velocity field) with subsequent reconstruction of the former parameter value. Depending on the channel rotation period or the configurations of magnet locations in the case of MHD generation or sources and sinks in numerical experiments the following results are possible. (1) The initial and final regimes differ quantitavely in the number of cyclonic or anticyclonic vortices generatted. (2) The number of vortex formations does not change but their localization in space, for example, the angular coordinates of their centers, varies. (3) After the change and reconstruction of the original value of the governing parameter the flow returns to the regime almost undistinguishable from the original regime. The flow patterns and the corresponding diagrams for laboratory experiments and numerical simulations based on shallow water equations are presented.

The African easterly jet (AEJ) and African easterly waves (AEWs) can have both local and far-reaching impacts on weather. It is therefore crucial to understand how the AEJ and AEWs will respond to future climate change. In this study, we examine anthropogenic influences on the AEJ–AEW system using the Weather Research and Forecasting (WRF) model configured as a tropical channel model (TCM). Hindcast simulations for the years 2001–2010 were performed using the WRF TCM, and ten additional years of simulations were performed using the pseudo-global warming method with the initial and boundary conditions of the model modified as if it were the late twenty-first century. A comparison of the simulations from the two climate scenarios indicates robust changes to both the AEJ and AEWs. For the AEJ, the jet is weaker and shifted northwards and upwards in the future climate, in association with an increase in precipitation over the Sahel and a strengthening of the meridional temperature gradient. For the AEWs, there is an increase in the number and strength of the waves in the future climate, in association with an increase in the baroclinic and barotropic energy conversions. The barotropic energy conversion in particular has a larger contribution in the future climate, which manifests in the southern AEW track experiencing greater future strengthening than the northern track.

Stationary configuration of a rotating electrically charged ideal fluid with self-gravitation is considered within the framework of general relativity. Barotropic equation of state of the liquid is p = we (w = const). A combination of a longitudinal magnetic field and a vortex gravitational field is considered. The boundaries of the interval of the barotropic coefficient w in which the material system under study can exist are found. It has been shown that for w > 0, the formation of wormholes is possible. Corresponding solutions describing the space-time wormhole geometry are found.

The behavior of the second band of the Intertropical Convergence Zone (ITCZ) near the Peruvian coast during early 2017 is studied, using precipitation, surface winds, sea surface temperature (SST) and atmospheric variables in different isobaric levels. The proposal of a daily index (Ia) to identify opportunely the formation of this band and the Lorenz energy terms in the region is also considered. This band was present from late January to early April 2017, associated with an anomalous dipole of sea level pressure between the east and west eastern Equatorial Pacific that configured anomalously northerly surface winds and the release of southeasterly trade winds near Peru. In medium levels, a zonally oriented positive mixing ratio anomaly was observed in early March over the ITCZ second band, associated with heavy rain systems over the northern Peruvian coastal region. In the same period, positive anomalies of divergence in high tropospheric levels were observed. The daily Ia index allowed an effective detection of the ITCZ second band 11 days before the maximum coastal precipitation, and the Lorenz energy terms showed eddy kinetic energy (KE) peaks in January and February and a contribution of barotropic instability in equatorial regions.

Peridynamic governing equations of fluid mechanics for barotropic flow are developed. As a special case of such a flow, linearized acoustics is also considered. The peridynamic governing equation of acoustics is also developed and discussed in detail. In order to obtain these new peridynamic governing equations, integral operators called “peridynamic D operators” are developed systematically, which are obtained by directly requiring the peridynamic D operators to converge to corresponding classical differential operators as the generalized material horizon approaches 0. Even though peridynamic D operators are applied only to fluid mechanics, acoustics, and heat conduction in an anisotropic inhomogeneous material in the present paper, it is clear that these peridynamic D operators can be used in any other field of mathematical physics to obtain a peridynamic (nonlocal) version of the governing equations. As an application of the newly obtained peridynamic governing equations, a time-dependent 3D (three-dimensional) peridynamic acoustics equation with a sound source is analytically solved for two different initial pressure disturbance profiles, and the results are discussed. These are believed to be the first exact analytical solutions for peridynamic acoustics.

We have deduced that bulk viscous Bianchi type I barotropic fluid cosmological model with varying $\Lambda$ and functional relation on hubble parameter by solving the field equations bimetric theory of gravitation. It is observed that our model has exponentially accelerating expansion at late time starting with decelerating expansion which agreed the observation of Perlmutter (1998), Knop (2003), Tegmark (2004) and Spergel (2006). In the beginning, our model has more than three spatial-dimensions then it switched over to three-dimensional spatial geometry at late epoch of time and it is agreed with Borkar et al. (2013). Other geometrical and physical behavior of the model have been studied.

This paper is devoted to small motions problem of composite hydrodynamic systems containing a viscoelastic fluid. Hydrodynamic systems of two or more viscoelastic fluids are considered, as well as partially dissipative systems containing ideal fluids or a barotropic gas (in addition to a viscoelastic fluid). The listed initial-boundary-value problems are investigated using the operator approach developed by N. D. Kopachevsky. This approach makes it possible to pass from the initial-boundary-value problem to the Cauchy problem for an operator-differential equation in the sum of Hilbert spaces and to prove the correct solvability theorem.

Intense tropical cyclones (TCs) often experience secondary eyewall formations and the ensuing eyewall replacement cycles. Better understanding of the underlying dynamics is crucial to make improvements to the TC intensity and structure forecasting. Radar imagery of some double-eyewall TCs and a real-case simulation study indicated that the barotropic instability (BI) across the moat (aka type-2 BI) may play a role in inner eyewall decay. A three-dimensional numerical study accompanying this paper pointed out that type-2 BI is able to withdraw the inner eyewall absolute angular momentum (AAM) and increase the outer eyewall AAM through the eddy radial transport of eddy AAM. This paper explores the reason why the eddy radial transport of eddy AAM is intrinsically nonzero. Linear and nonlinear shallow water experiments are performed and they produce expected evolutions under type-2 BI. It will be shown that only nonlinear experiments have changes in AAM over the inner and outer eyewalls, and the changes solely originate from the eddy radial transport of eddy AAM. This result highlights the importance of nonlinearity of type-2 BI. Based on the distribution of vorticity perturbations and the balanced-waves arguments, it will be demonstrated that the nonzero eddy radial transport of eddy AAM is an essential outcome from the intrinsic interaction between the mutually growing vortex Rossby waves across the moat under type-2 BI. The analyses of the most unstable mode support the findings and will further attribute the inner eyewall decay and outer eyewall intensification to the divergence and convergence of the eddy angular momentum flux, respectively.

An internal gravity wave model was employed to simulate the generation of internal solitary waves (ISWs) over a sill by tidal flows. A westward shoaling pycnocline parameterization scheme derived from a three-parameter model was adopted, and then 14 numerical experiments were designed to investigate the influence of the pycnocline thickness, density difference across the pycnocline, westward shoaling isopycnal slope angle and pycnocline depth on the ISWs. When the pycnocline thickness on both sides of the sill increases, the total barotropic kinetic energy, total baroclinic energy and ratio of baroclinic kinetic energy (KE) to available potential energy (APE) decrease, whilst the depth of isopycnal undergoing maximum displacement and ratio of baroclinic energy to barotropic energy increase. When the density difference on both sides of the sill decreases synchronously, the total barotropic kinetic energy, ratio of baroclinic energy to barotropic energy and total baroclinic energy decrease, whilst the depth of isopycnal undergoing maximum displacement increases. When the westward shoaling isopycnal slope angle increases, the total baroclinic energy increases whilst the depth of turning point almost remains unchanged. When the depth of westward shoaling pycnocline on both sides of the sill reduces, the ratio of baroclinic energy to barotropic energy and total baroclinic energy decrease, whilst the total barotropic kinetic energy and ratio of KE to APE increase. When one of the above four different influencing factors was increased by 10% while the other factors keep unchanged, the amplitude of the leading soliton in ISW Packet A was decreased by 2.80%, 7.47%, 3.21% and 6.42% respectively. The density difference across the pycnocline and the pycnocline depth are the two most important factors in affecting the characteristics and energetics of ISWs.

The Kuroshio extension (KE) exhibits interdecadal variability, oscillating from a stable state to an unstable state. In this paper, ERA-Interim reanalysis data are used to discuss the possible reasons for the asymmetric response of the atmosphere to symmetric sea surface temperature anomaly (SSTA) during periods of differential KE states. The analysis has the following results: the SSTA presents a nearly symmetrical distribution with opposite signs during the KE stable and unstable periods. During the KE stable period, the storm track is located north of 40°N and is significantly enhanced in the northeast Pacific Ocean. The atmospheric response is similar to the West Pacific/North Pacific Oscillation teleconnection (WP/NPO like pattern) and presents a barotropic structure. The inversion results of the potential vorticity equation show that the feedback of transient eddy vorticity manifests a WP/NPO like pattern and presents a barotropic structure, which is the main reason for bringing about the response of the WP/NPO like pattern. The magnitude of the feedbacks of both diabatic heating and transient eddy heating is small, which can offset one another. During the KE unstable period, the main body of the storm track is located to the south of 40°N, and there is no significant response signal in the atmosphere, except near the west coast of North America. Compared with the KE stable period, the asymmetry of response of the transient eddy vorticity is the main reason for the asymmetric response of the atmosphere.

Why does the 1909 typhoon, Lekima, become so destructive after making landfall in China? Using a newly developed mathematical apparatus, the multiscale window transform (MWT), and the MWT-based localized mutliscale energetics analysis and theory of canonical transfer, this study is intended to give a partial answer from a dynamical point of view. The ECMWF reanalysis fields are first reconstructed onto the background window, the TC-scale window, and the convection-scale window. A localized energetics analysis is then performed, which reveals to us distinctly different scenarios before and after August 8–9, 2019, when an eyewall replacement cycle takes place. Before that, the energy supply in the upper layer is mainly via a strong upper layer-limited baroclinic instability; the available potential energy thus-gained is then converted into the TC-scale kinetic energy, with a portion to fuel Lekima’s upper part, another portion carried downward via pressure work flux to maintain the cyclone’s lower part. After the eyewall replacement cycle, a drastic change in dynamics occurs. First, the pressure work is greatly increased in magnitude. A positive baroclinic transfer almost spreads throughout the troposphere, and so does barotropic transfer; in other words, the whole air column is now both barotropically and baroclinically unstable. These newly occurred instabilities help compensate the increasing consumption of the TC-scale kinetic energy, and hence help counteract the dissipation of Lekima after making landfalls.

Herein, seasonal velocity variations from the sea surface to a depth of 1000 m over the entire Kuroshio path are investigated using satellite altimetry and reanalysis datasets. The data analysis results show that velocities in the upper layer (from 0 to approximately 500 m) reach a maximum in July and a minimum in autumn (October to November) or winter (December to February) with different tendencies in each region. However, those in the lower layer (> 500 m depth) show a reversed seasonal variation—reaching a maximum in winter—especially in the continental slope area from the east of Luzon Island to the east of the Ryukyu Islands chain, which is regarded as a route of the deeper Kuroshio flow. Using a realistic general circulation model, we performed numerical experiments to clarify the role of the local wind stress as the driving force in seasonal Kuroshio velocity variations in the upper layer. These experiments revealed that seasonal Kuroshio velocity variations in the upper layer are mainly caused by the local response to wind stress upon the current itself. These numerical results cannot be explained by conventional mechanisms, such as flow–topography interactions or coastal upwelling/downwelling. On the other hand, seasonal Kuroshio velocity variations in the lower layer can be explained by the Sverdrup theory, in which barotropic responses to the wind stress curl over the area west of the Izu–Ogasawara Ridge are responsible.

In this paper, we prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth (strong) solutions for the three dimensional (3D) compressible non-isentropic magnetohydrodynamic (MHD) equations with zero heat-conductivity. Therefore, if the maximum norm of the deformation tensor of velocity gradients remains bounded, it is not possible for other kinds of singularities. Our results are same as Beale-Kato-Majda type criterion for compressible viscous barotropic flows (Huang et al., 2011 [17] ), and do not depend on further sophistication of the non-isentropic MHD model, it is independent of the pressure and magnetic field. Furthermore, this extends the corresponding Zhong's results (Zhong, 2019 [46] ), and removes the viscous coefficients restriction condition 3 μ > λ and the boundedness of pressure. As a byproduct, the same results also hold for compressible non-isentropic Navier-Stokes equations without heat-conductivity.

The mechanisms of the propagation and maintenance of the South Asian jet wave train are investigated in this study by examining the eddy kinetic energy (EKE) balance along the wave train. The intensity and evolution of the disturbances along the wave train can be well represented by the variation of EKE centers. The east-to-west discrepancy in the intensity of EKE centers indicates the wave train is not only maintained by the waveguide effect of the jet stream, but also fueled and damped by other physical processes along the wave train. It is found that both baroclinic and barotropic conversions are key energy sources during the lifespan of the wave train, characterized by regional differences. They evolve with the eddies and are offset mainly by energy exported by the ageostrophic geopotential fluxes after the peak of the eddies. They are strong upstream of the wave train, as extremely strong cooling/warming advection appears behind/ahead of the trough over the eastern Mediterranean Sea-Middle East where abnormal descent/ascent occurs, and potential energy is transformed into kinetic energy. As this trough tilts southwestward, kinetic energy can be converted from the mean flow to eddies on the north flank of the South Asian jet. Strong dissipation occurs over the Middle East, which might be responsible for the relatively weaker EKE centers downstream. Over China, the eddy is fueled by strong barotropic conversion again, as a result of the northward shift of the jet axis.

The nonlinear effect of the summer southeast wind and density on the 3D structures of the full Lagrangian residual velocity (LRV) was quantified for a generally nonlinear system, using Jiaozhou Bay (JZB), China as the test site. In the tidally energetic JZB, the basic patterns of the wind- and density-driven full LRVs were found to be consistent with semi-analytical solutions but highly dependent on initial times. The wind-driven full LRVs at different tidal phases flowed similarly downwind over shoals and upwind in the deep region; however, the main branches could migrate across nearly half of the bay. A density-driven, clockwise flow was dominant in the western inner bay at low tide, but it almost disappeared at high tide. The effect of density generally enhanced the outward flow in the surface layer and inward flow in the bottom layer. Along-trajectory integrated momentum balances indicated that viscosity was the main factor responsible for the time dependence of the wind-driven full LRVs, while viscosity, barotropic and baroclinic pressure gradients were the main drivers of the intra-tidal variations in the density-driven full LRVs. Generally, the summer wind and density had opposing effects, although their influence was weaker than that of the tide and could not change the patterns of the tide-driven full LRVs. When analysing the effects of wind and density on the coastal circulation in JZB, both the 3D structures and the possibility of a high initial tidal phase dependency should be considered.

In this article, we consider a fluid-structure interaction system where the fluid is viscous and compressible and where the structure is a part of the boundary of the fluid domain and is deformable. The fluid is governed by the barotropic compressible Navier-Stokes system whereas the structure displacement is described by a wave equation. We show that the corresponding coupled system admits a unique strong solution for an initial fluid density and an initial fluid velocity in $H^3$ and for an initial deformation and an initial deformation velocity in $H^4$ and $H^3$ respectively. The reference configuration for the fluid domain is a rectangular cuboid with the elastic structure being the top face. We use a modified Lagrangian change of variables to transform the moving fluid domain into the rectangular cuboid and then analyze the corresponding linear system coupling a transport equation (for the density), a heat-type equation, and a wave equation. The corresponding results for this linear system and estimations of the coefficients coming from the change of variables allow us to perform a fixed point argument and to prove the existence and uniqueness of strong solutions for the nonlinear system, locally in time.

Seasonal modulation of subthermocline eddy kinetic energy (EKE) east of the Philippines and its associated dynamics are studied, using mooring measurements and outputs from an eddy-resolving ocean general circulation model for the period from 2000 to 2017. Significantly high EKE appears below the thermocline in the latitude band between 5° and 14°N east of the Philippines. Separated by 10°N, the EKE in the northern and southern parts of the region shows nearly opposite seasonal cycles, with its magnitude reaching a maximum in early spring and minimum in summer in the northern part and reaching a maximum in summer and minimum in winter in the southern part of the region. Further investigation indicates that both baroclinic and barotropic instabilities are essential in generating the subthermocline eddies, but the seasonal variation of subthermocline EKE is mainly caused by the seasonal modulation of barotropic instability. The seasonal modulation of barotropic instability in the northern and southern part of the region is associated with the seasonal evolution of North Equatorial Undercurrent and Halmahera Eddy, respectively.

Stratifified geostrophic turbulence theory predicts an inverse energy cascade for the barotropic (BT) mode. Satellite altimetry has revealed a net inverse cascade in the baroclinic (BC) mode. Here the spatial variabilities of BT and BC kinetic energy flfluxes in the Antarctic Circumpolar Current (ACC) were investigated using ECCO2 data, which synthesize satellite data and in situ measurements with an eddy-permitting general circulation model containing realistic bathymetry and wind forcing. The BT and BC inverse kinetic energy cascades both reveal complex spatial variations that could not be explained fully by classical arguments. For example, the BC injection scales match better with most unstable scales than with the fifirst-mode deformation scales, but the opposite is true for the BT mode. In addition, the BT and BC arrest scales do not follow the Rhines scale well in terms of spatial variation, but show better consistency with their own energy-containing scales. The reverse cascade of the BT and BC modes was found related to their EKE, and better correlation was found between the BT inverse cascade and barotropization. Speculations of the fifindings were proposed; however, further observations and modeling experiments are needed to test these in terpretations. Spectral flflux anisotropy exhibits a feature associated with oceanic jets that is consistent with classical expectations. Specififically, the spectral flflux along the along-stream direction remains negative at scales up to that of the studied domain ( ; 2000 km), while that in the perpendicular direction becomes positive close to the scale of the width of a typical jet.

The aim of this paper is to investigate the regime of high Mach number flows for compressible barotropic fluids of Korteweg type with density dependent viscosity. In particular we consider the models for isothermal capillary and quantum compressible fluids. For the capillary case we prove the existence of weak solutions and related properties for the system without pressure, and the convergence of the solution in the high Mach number limit. This latter is proved also in the quantum case for which a weak-strong uniqueness analysis is also discussed in the framework of the so-called “augmented” version of the system. Moreover, as byproduct of our results, in the case of a capillary fluid with a special choice of the initial velocity datum, we obtain an interesting property concerning the propagation of vacuum zones.

The North Shandong Coastal Current (NSCC) is an important transporting route for sediment, drifting algae, and spilled oil from the Bohai Sea to the Yellow Sea. This study investigated the features and formation mechanism of the NSCC using observational data of current velocity and a numerical coastal ocean model. Our results confirmed the existence of the NSCC in the sense of climatological current in winter when northerly wind prevails in the Bohai Sea and Yellow Sea. The magnitude of the NSCC in the monthly time scale ranged 0.07–0.12 m/s and the current direction was parallel to the coastline. The detided residual current on the pathway of the NSCC was unstable, but variable with the local wind speed. The residual current was well correlated with northerly wind speed and tended to be parallel to coastline with the increase of wind speed. Strong wind plays key roles in the formation of eastward mean flow on the pathway of the NSCC in winter. We found that strong wind can generate a stronger eastward current in the southern side of the northern Yellow Sea, but a smaller westward return flow during the strong wind relaxation period. The asymmetry of wind-related residual current during and after strong wind events accounts for the formation of the eastward NSCC. A momentum analysis was performed using the numerical model results during strong wind events. We found that the barotropic pressure gradient was the dominant driving force of the residual current both during and after a strong wind event.

Tropical climate model derived by Frierson et al. (Commun Math Sci 2:591–626, 2004) and its modified versions have been investigated in a number of papers [see, e.g., Li and Titi (Discrete Contin Dyn Syst Series A 36(8):4495–4516, 2016), Wan (J Math Phys 57(2):021507, 2016), Ye (J Math Anal Appl 446:307–321, 2017) and more recently Dong et al. (Discrete Contin Dyn Syst Ser B 24(1):211–229, 2019)]. Here, we deal with the 2D tropical climate model with fractional dissipative terms in the equation of the barotropic mode u and in the equation of the first baroclinic mode v of the velocity, but without diffusion in the temperature equation, and we establish a regularity criterion for this system.

Using observational temperature profiles, this study reveals that eddy-induced oceanic vertical temperature anomalies are geographically varying in the South China Sea (SCS). The maximum anomalies are more intensified in the central and south SCS. Due to ocean stratification, the eddy available potential energy (EAPE) can more comprehensively reflect the eddy effect on the ocean vertical structure. The EAPE within a composite eddy is the highest in the northern region and lowest in the southeastern region. The geographical variation of vertical anomalies induced by eddies is because of the combination effect of the ocean stratification, the background energy (available potential energy and barotropic kinetic energy), and the energy conversion rate. The anomalies induced by cyclonic and anticyclonic eddies might be asymmetrical in the same region. For example, in the regions to the west of Luzon Island and in the central west SCS, the temperature anomalies and EAPE within a composite cyclonic eddy are significantly larger than those within an anticyclonic eddy. This variation is owing to the different oceanic stratification along the tracks of cyclonic and anticyclonic eddies.

We study the impact of horizontal resolution in setting the North Atlantic gyre circulation and representing the ocean–atmosphere interactions that modulate the low-frequency variability in the region. Simulations from five state-of-the-art climate models performed at standard and high-resolution as part of the High-Resolution Model Inter-comparison Project (HighResMIP) were analysed. In some models, the resolution is enhanced in the atmospheric and oceanic components whereas, in some other models, the resolution is increased only in the atmosphere. Enhancing the horizontal resolution from non-eddy to eddy-permitting ocean produces stronger barotropic mass transports inside the subpolar and subtropical gyres. The first mode of inter-annual variability is associated with the North Atlantic Oscillation (NAO) in all the cases. The rapid ocean response to it consists of a shift in the position of the inter-gyre zone and it is better captured by the non-eddy models. The delayed ocean response consists of an intensification of the subpolar gyre (SPG) after around 3 years of a positive phase of NAO and it is better represented by the eddy-permitting oceans. A lagged relationship between the intensity of the SPG and the Atlantic Meridional Overturning Circulation (AMOC) is stronger in the cases of the non-eddy ocean. Then, the SPG is more tightly coupled to the AMOC in low-resolution models.

Linear and nonlinear barotropic vorticity model frameworks are constructed to understand the formation of the monsoon trough in boreal summer over the western North Pacific. The governing equation is written with respect to specified zonal background flows, and a wave perturbation is prescribed in the eastern boundary. Whereas a uniform background mean flow leads no scale contraction, a confluent background zonal flow causes the contraction of zonal wavelength. Under linear dynamics, the wave contraction leads to the development of smaller scale vorticity perturbations. As a result, there is no upscale cascade. Under nonlinear dynamics, cyclonic (anticyclonic) wave disturbances shift northward (southward) away from the central latitude due to the vorticity segregation process. The merging of small-scale cyclonic and anticyclonic perturbations finally leads to the generation of a pair of large-scale cyclonic and anti-cyclonic vorticity gyres, straddling across the central latitude. The large-scale cyclonic circulation due to nonlinear upscale cascade can be further strengthened through a positive convection-circulation feedback.

Radar imagery of some double-eyewall tropical cyclones shows that the inner eyewalls became elliptical prior to their dissipation during the eyewall replacement cycles, indicating that the barotropic instability (BI) across the moat (also known as type-2 BI) may play a role. To further examine the physics of inner eyewall decay and outer eyewall intensification under the influence of the type-2 instability, three-dimensional numerical experiments are performed. In the moist full-physics run, the simulated vortex exhibits the type-2 instability and the associated azimuthal wavenumber-2 radial flow pattern. The absolute angular momentum (AAM) budget calculation indicates, after the excitation of the type-2 instability, a significant intensification in the negative radial advection of AAM at the inner eyewall. It is further shown that the changes in radial AAM advection largely result from the eddy processes associated with the type-2 instability and contribute significantly to the inner eyewall decay. The budget calculation also suggests that the type-2 instability can accelerate the inner eyewall decay in concert with the boundary layer cutoff effect. Another dry no-physics idealized experiment is conducted and the result shows that the type-2 instability alone is able to weaken the inner eyewall and also strengthen the outer eyewall with nonnegligible effect.