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The quality of wave measurements is of primary importance for the validation of wave forecasting models, satellite wave calibration and validation, wave physics, offshore operations and design and climate monitoring. Validation of global wave forecasts revealed significant regional differences, which were linked to the different wave buoy systems used by different countries. To fully understand the differences between the wave measurement systems, it is necessary to go beyond investigations of the integral wave parameters height, period and direction, into the frequency spectra and the four directional Fourier parameters that are used to estimate the directional distribution. We here analyse wave data measured from three different sensors (non-directional Datawell Waverider buoy, WaveRadar Rex, Optech laser) operating at the Ekofisk oil production platform located in the central North Sea over a period of several months, with significant wave height ranging from 1 to 10 m. In general, all three sensors provide similar measurements of the integral wave properties and frequency spectra, although there are some significant differences which could impact design and operations, forecast verification and climate monitoring. For example, the radar underestimates energy in frequency bands higher than 8 s by 3–5%, swell (12.5–16 s) by 5–13%, while the laser has 1–2% more energy than the Waverider in the most energetic bands. Lee effects of structures are also estimated. Lower energy at the frequency tail with the radar has an effect on wave periods (they are higher); wave steepness is seen to be reduced by 10% in the wind seas. Goda peakedness and the unidirectional Benjamin-Feir index are also examined for the three sensors.

The North River estuary (Massachusetts, USA) is a tidal marsh creek network where tidal dispersion processes dominate the salt balance. A field study using moorings, shipboard measurements, and drone surveys was conducted to characterize and quantify tidal trapping due to tributary creeks. During flood tide, saltwater propagates up the main channel and gets “trapped” in the creeks. The creeks inherit an axial salinity gradient from the time-varying salinity at their boundary with the main channel, but it is stronger than the salinity gradient of the main channel because of relatively weaker currents. The stronger salinity gradient drives a baroclinic circulation that stratifies the creeks, while the main channel remains well-mixed. Because of the creeks’ shorter geometries, tidal currents in the creeks lead those in the main channel; therefore, the creeks never fill with the saltiest water which passes the main channel junction. This velocity phase difference is enhanced by the exchange flow in the creeks, which fast-tracks the fresher surface layer in the creeks back to the main channel. Through ebb tide, the relatively fresh creek outflows introduce a negative salinity anomaly into the main channel, where it is advected downstream by the tide. Using high-resolution measurements, we empirically determine the salinity anomaly in the main channel resulting from its exchange with the creeks to calculate a dispersion rate due to trapping. Our dispersion rate is larger than theoretical estimates that neglect the exchange flow in the creeks. Trapping contributes more than half the landward salt flux in this region.

The structure of locally soluble periodic groups in which every abelian subgroup is locally cyclic was described over 20 years ago. We complete the aforementioned characterization by dealing with the non-periodic case. We also describe the structure of locally finite groups in which all abelian subgroups are locally cyclic.

It is well-known that the notion of limit in the sharp topology of sequences of Colombeau generalized numbers$$\widetilde{\mathbb {R}}$$R~does not generalize classical results. E.g. the sequence$$\frac{1}{n}\not \rightarrow 0$$1n↛0and a sequence$$(x_{n})_{n\in \mathbb {N}}$$(xn)n∈Nconvergesifand only if$$x_{n+1}-x_{n}\rightarrow 0$$xn+1-xn→0. This has several deep consequences, e.g. in the study of series, analytic generalized functions, or sigma-additivity and classical limit theorems in integration of generalized functions. The lacking of these results is also connected to the fact that$$\widetilde{\mathbb {R}}$$R~is necessarily not a complete ordered set, e.g. the set of all the infinitesimals has neither supremum nor infimum. We present a solution of these problems with the introduction of the notions of hypernatural number, hypersequence, close supremum and infimum. In this way, we can generalize all the classical theorems for the hyperlimit of a hypersequence. The paper explores ideas that can be applied to other non-Archimedean settings.

In the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

In August 2018, a remarkable polynya was observed off the north coast of Greenland, a perennial ice zone where thick sea ice cover persists. In order to investigate the formation process of this polynya, satellite observations, a coupled ice-ocean model, ocean profiling data, and atmosphere reanalysis data were applied. We found that the thinnest sea ice cover in August since 1978 (mean value of 1.1 m, compared to the average value of 2.8 m during 1978−2017) and the modest southerly wind caused by a positive North Atlantic Oscillation (mean value of 0.82, compared to the climatological value of −0.02) were responsible for the formation and maintenance of this polynya. The opening mechanism of this polynya differs from the one formed in February 2018 in the same area caused by persistent anomalously high wind. Sea ice drift patterns have become more responsive to the atmospheric forcing due to thinning of sea ice cover in this region.

We consider the generalised Hahn sequence space $$h_{d}$$ , where d is an unbounded monotone increasing sequence of positive real numbers, and characterise several classes of bounded linear operators or matrix transformations from $$h_{d}$$ into the spaces of all bounded, convergent and null sequences, and into the space of all abolutely convergent series and $$h_{d}$$ , and also from spaces of all absolutely convergent series, all null, convergent and bounded sequences into $$h_{d}$$ . Furthermore, we establish identities or estimates for the norms of the corresponding bounded linear operators. We also derive identities for the Hausdorff measure of noncompactness for the operators in the above classes with the exception of the final space being the space of all bounded sequences and charcaterise the classes of all corresponding compact operators. Finally, we apply our results to present a Fredholm operator from $$h_{d}$$ into itself given by a tridiagonal matrix.

If we consider a real hypersurface M in a complex projective space we have the covariant derivatives associated to both the Levi-Civita connection and, for any nonnull real number k, to the k-th generalized Tanaka-Webster connection. We also have the Lie derivative and a derivative of Lie type associated to the k-th generalized Tanaka-Webster connection. If we consider the structure Lie operator $$L_{\xi }$$ on M, we can define two tensor fields of type (1,2) on M from $$L_{\xi }$$ associated to the derivatives mentioned above, $$L_{{\xi }_F}^{(k)}$$ and $$L_{{\xi }_T}^{(k)}$$ . Kaimakamis, Panagiotidou and Perez obtained the classifications of real hypersurfaces for which either $$L_{{\xi }_F}^{(k)}$$ or $$L_{{\xi }_T}^{(k)}$$ identically vanish. We generalize such results classifying real hypersurfaces in complex projective space such that $$L_{{\xi }_F}^{(k)}$$ (respectively, $$L_{{\xi }_T}^{(k)}$$ ) is either symmetric or skew symmetric.

Elucidating the mechanisms of fluctuations in fish populations are key to sustainable fisheries management. However, limited data combined with climate variability and fishing further constrain our understanding of fish population dynamics. Fortunately, marine sedimentary archives of fish abundance and environmental changes in the past, may provide new insights into long-term fish population fluctuations. Here, we used 150-year sediment records of the abundance of Japanese anchovy (Engraulis japonicus) scales, phytoplankton, and zooplankton biomarkers, and δ15N data previously reported from the central Yellow Sea (YS). We discussed the linkages of the anchovy abundance to ecosystem structure and sea surface temperatures (SSTs). Principal component analysis (PCA) identified negative effects of strong stratification (higher δ15N) and high abundance of haptophytes (higher alkenone content) on the anchovy stock through our analytical period (~1860–2005 AD). In addition, we found positive relationships between the anchovy abundance and plankton productivity in proxies before the period of intense fishing (1860–1980 AD), indicating bottom-up processes affecting the anchovy stock. However, the bottom-up processes became unclear under excessive fishing. This was possibly due to overfishing becoming a major driver after 1980, thereby altering the cascading of the marine ecosystem towards a different structure. Climate variability seems to indirectly influence the anchovy stock through bottom-up control via a cascading effect from the changes in the North Pacific Gyre Oscillation (NPGO) or the Pacific North American pattern (PNAP). The impacts of these changes on the hydrodynamic features of YS in turn influence the productivity of plankton prey for the anchovy. Collectively, our findings suggest that synergistic effects of climate and fishing on the anchovy need to be paid greater attention. Our results also contribute to an improved understanding of fish population fluctuations in other seas.

In this study, we investigated the mechanism of eutrophication and hypoxia in the upper Gulf of Thailand from August 2014 to June 2015 based on field observation data, box model analysis, and the unscaled trophic status index (UNTRIX). Fresh water residence time derived from a simple box model was long (38.61 days) during the transition period between the southwest to northeast monsoon in September 2014. In contrast, fresh water residence time was short (2.63 days) during the late northeast monsoon in February 2015. Long residence time was related to the development of widespread strong hypoxia in near-bottom waters in over half of the gulf during the transition between the southwest and the northeast monsoon, when river discharge was also very large. UNTRIX is used to assess water trophic levels, and is based on water qualities including concentrations of chlorophyll-a (Chl-a), dissolved oxygen (DO), dissolved inorganic nitrogen (DIN), and dissolved inorganic phosphorus (DIP). Hypertrophic and eutrophic conditions were observed at river mouths; their seasonal eutrophication was related to river discharge and circulation. Nutrients were mainly increased by river discharge. Water column stratification and long residence time were required for the development of severe hypoxia in the study area.

Since August 2017, the Kuroshio has taken a large-meander (LM) path, which has forced the Kuroshio extension (KE) to be in its stable state against its wind-forced decadal variability. How such current conditions have impacted the formation and advection of North Pacific subtropical mode water (STMW) over its distribution region was examined using Argo float data during 2005–2020. Out of the whole STMW defined as a low-potential vorticity layer of 16–19.5 ºC, a relatively cold variety of 16–18 ºC, which was formed south of the KE and advected westward and southward, occupied more than 80% of the total volume. The formation rate of the 16–18 ºC variety was low during 2006–2009 in an unstable-KE period and high during 2010–2015 in a stable-KE period, and then dropped drastically in 2016 despite the KE still being in the stable state. After a short unstable-KE period in 2016–2017, the LM-forced, stable-KE period began, but the formation rate of the 16–18 ºC variety has not restored, possibly due to stronger background stratification propagated from the central North Pacific. In addition, the 16–18 ºC variety has had to make a southern detour around the LM, and its westward advection from the formation region south of the KE to the region south of Japan has been significantly decreased, possibly because it is dissipated more strongly over a southern part of the Izu–Ogasawara Ridge. Due to such decline in the formation and advection, the volume of the 16–18 ºC variety and hence that of the whole STMW have gradually decreased since 2016.

Five high-resolution hydrographic sections were conducted at the periphery of an anticyclonic mesoscale eddy north of the Kuroshio Extension (KE) to explore the evolution of submesoscale structure in the subsurface layer associated with mesoscale eddies. The five sections continuously captured patches of low temperature and salinity water originated from the subarctic region with a horizontal scale of 10–20 km and a vertical scale of 100 m in the strain field at the periphery and in the interior of the eddy detected mainly by the surface Okubo-Weiss parameter. Each patch on the same isopycnal constituted a submesoscale filament. A cold and fresh filament in the intermediate layer in and around the eddy was recently ventilated compared with ambient water, suggesting that submesoscale filaments contribute to a rapid water mass transport from the outside to the inside of the eddy, as well as from the subarctic to the KE region. Filaments at the periphery of the eddy were forced by the convergence in the cross-frontal direction. The horizontal tracer gradient of the filaments evolved in the downstream direction, and 10–50% of the evolution was explained by geostrophic forcing. Moreover, the analysis implied that the evolution of the vertical tracer gradient might have been caused by the vertical shear of the horizontal velocity. The resulting patches were expected to contribute to an effective mixing, suggesting the influence of submesoscale filaments on not only the water mass transport but also the transformation in and around mesoscale eddies in the KE region.

Assume that $${{\mathfrak {H}}}$$ and $${{\mathfrak {K}}}$$ are two real or complex Hilbert spaces, A a linear relation from $${{\mathfrak {H}}}$$ to $${{\mathfrak {K}}}$$ and B a linear relation from $${{\mathfrak {K}}}$$ to $${{\mathfrak {H}}}$$ , respectively. Necessary and sufficient conditions for B to be equal to the adjoint of A are provided. New characterizations for closed, skew–adjoint and selfadjoint linear relations are obtained.

Grazing significantly affects the distribution, growth, and productivity of shrubs. In this study, we evaluated the effects of grazing disturbance on the spatial distribution patterns and interspecific relationships of two desert shrubs, Ammopiptanthus mongolicus and Sarcozygium xanthoxylon. Three types of grazing conditions were considered, including enclosed area (EA), seasonal rotational grazing area (SRGA), and grazing area (GA) (100 m × 100 m), in the West Ordos Nature Reserve of Inner Mongolia, China. The results showed that A. mongolicus and S. xanthoxylon populations were uniformly distributed at a small scale, and the distribution in EA and SRGA became gradually random. In GA, A. mongolicus population showed aggregated distribution but S. xanthoxylon population showed random distribution at a small scale. Moreover, both A. mongolicus and S. xanthoxylon populations at the 5–7 m scale showed random distribution. At the small and intermediate scales, the two species showed positive interspecific relationships of GA. However, no interspecific relationship was noted between the two species in EA and SRGA. A significant positive relationship (P P P P

A classical construction associates to a transient random walk on a discrete group $$\Gamma $$ a compact $$\Gamma $$ -space $$\partial _M \Gamma $$ known as the Martin boundary. The resulting crossed product $$C^*$$ -algebra $$C(\partial _M \Gamma ) \rtimes _r \Gamma $$ comes equipped with a one-parameter group of automorphisms given by the Martin kernels that define the Martin boundary. In this paper we study the KMS states for this flow and obtain a complete description when the Poisson boundary of the random walk is trivial and when $$\Gamma $$ is a torsion free non-elementary hyperbolic group. We also construct examples to show that the structure of the KMS states can be more complicated beyond these cases.

We show that, with the exception of the symmetric derivative, each limit of the form $$\begin{aligned} \lim _{h\rightarrow 0}\frac{Af(x+ah)+Bf(x+bh)}{h},\qquad (A+B=0,Aa+Bb=1), \end{aligned}$$ is equivalent to the ordinary derivative, for all continuous functions at x. And, up to a non-zero scalar multiple, these are the only criteria for differentiating all continuous functions at x, by taking limits of first order difference quotients with two function evaluations.

In this paper, we study three-dimensional equatorial flows with constant vorticity beneath a wave train and above a flat bed in the modified $$\beta $$ -plane approximation. It is proved that the equatorial flow is necessarily irrotational and the free surface is necessarily flat if it exhibits a constant vorticity, due to the incorporation of a gravitational-correction term in the tangent plane approximation.

Third-generation models employ a host of parameterization schemes to consider the input wind forcing and the wave energy dissipation under different physical settings and environmental conditions. To evaluate the performance of such models in large-scale enclosed water bodies, WAVEWATCH-III model has been employed for the Caspian Sea which is a land-locked water body, located in the north of Iran. The Caspian Sea consists of three interconnected regions, called the northern, middle, and southern Caspian Sea. The division is based on the bathymetry and morphologic features, and the rapid variability in depth provides a unique modeling challenge. Recently implemented “ST6” physics in the WAVEWATCH-III model is calibrated and evaluated for the Caspian Sea. Moreover, both bottom friction methods, viz., JONSWAP and SHOWEX, in combination with calibrated ST6 were employed to fine-tune the model for this fetch-limited basin. Model performance was assessed using recent coastal measurements along the southern Caspian Sea as well as altimeter data via statistical parameters. Using ST6 calibration, the HH index for model performance against altimeter data was decreased by 7.7%. For the ADCP data, this improvement was ~17% at Noshahr station, and ~7% at Roudsar station, both along the southern boundary of the sea. The bias was decreased by 19.3% by calibrating the ST6 source term, specifically in the deeper areas. It should be noted that the bias against altimeter data has been improved by 19.5%. Due to the steep slope of the surf zone, the model was not so sensitive to the bottom friction formulation; however, the 1D propagation tests confirmed a slightly better performance of the SHOWEX formulation than that of the JONSWAP formulation.

The South China Sea (SCS) experienced a significant reduction in warming rate (− 0.01 °C decade−1, $$p>0.10$$ p > 0.10 ) during 1999–2010 following an accelerated and unprecedented warming (+ 0.15 °C decade−1, $$p p < 0.01 ) in the last three decades (1970–1998). However, most global climate models of the CMIP5 RCP4.5 scenario failed to capture this SCS warming slowdown. In this study, we identify two drivers through numerical simulations by using a regional high-resolution, ocean–atmosphere coupled climate model: the major variance (75%) in the sea surface warming slowdown could be explained by the strengthened winter monsoon over the SCS, and the minor variance (12%) could be explained by the changes in the upper ocean circulations. The winter monsoon over the SCS is likely linked to the La Niña-like SST pattern in the eastern tropical Pacific, which strengthens the Walker circulation and results in anticyclonic circulation over the northwestern Pacific. This enhanced winter monsoon is the atmospheric driver that slows down the SCS basin-scale warming, while the largest reduction of the warming rate occurs in the northern SCS that can be attributed to the oceanic throughflow via the Luzon Strait. These findings could have important implications for future climate projections over the SCS and adjacent oceans.

Coastal communities around the Caribbean Sea are vulnerable to global warming impacts, partly because of constraints on their adaptive capacity. We use three climate models provided by the Coupled Model Intercomparison Project Phase 5 (CMIP5) under two representative concentration pathways scenario (RCP4.5 and RCP8.5) to assess the trends and spatial behavior of six atmospheric and ocean variables in the Caribbean Basin during the twenty-first century. Atmospheric results are reported from the model ensemble; however oceanic results are reported from ACCESS1.0 model, as its resolution captures mesoscale processes which are important for regional sea level projections. Surface atmospheric pressure and wind do not show significant trends. On the contrary, air and sea surface temperature, surface salinity, and mean sterodynamic sea level have coherent positive trends in the Caribbean Basin, which increase with a greater RCP scenario. Air temperature will probably increase by 2 °C over the preindustrial period during the century. Moreover, sea surface temperature is expected to rise between 1.92° and 3.01 °C in the 1976–2005 to 2071–2100 period. The Caribbean Sea warming will have the potential to extend the hurricane season, increase the frequency of tropical storms, and intensify coral bleaching events. In the same period, mean sterodynamic sea level is expected to rise in the basin between 32.53 and 43.25 cm, depending on the RCP scenario used. The strongest trend expected in 2005-2100 is 50.84 ± 1.48 cm cy−1 under RCP8.5 scenario. Furthermore, the trends appear to accelerate since the last century in the basin. Besides, sterodynamic sea level rise would account for slightly over half of the total sea level rise in the Caribbean, after land-ice melting among other contributions not accounted by CMIP5 models are included. These trends have the potential to exacerbate flooding and erosion, putting at risk coastal areas, including low-elevation islands such as some in the San Andres and Providencia Archipelago.

Holonomy algebras of Lorentzian Weyl spin manifolds with weighted parallel spinors are found. For Lorentzian Weyl manifolds admitting recurrent null vector fields are introduced special local coordinates similar to Kundt and Walker ones. Using that, the local form of all Lorentzian Weyl spin manifolds with weighted parallel spinors is given. The Einstein-Weyl equation for the obtained Weyl structures is analyzed and examples of Einstein-Weyl spaces with weighted parallel spinors are given., The final version to appear in Monatshefte f\"ur Mathematik

Archaeobotanical analyses together with historical records can provide unique information about the cargoes and histories of sunken ships, which are found as wrecks at the bottom of the seas all over the world. An interdisciplinary research project was undertaken on the Vrouw Maria (Lady Mary), a Dutch wooden two-masted merchant ship that sank on October 9th in 1771 in the Finnish Baltic Sea. She rested at a depth of 41 m and was in good condition when discovered. Based on written sources and archaeological research, the ship was carrying a valuable cargo including, for example, sugar, dyes, cloth, porcelain, wood and goods that the Russian nobility had ordered. Among them were paintings that the Russian Empress Catherine the Great (1729–1796) had bought at an auction in Amsterdam. Samples from four wooden barrels and from one wooden packing crate among the ship’s cargo were investigated. Botanical analysis revealed products such as stimulants, dyes and fruits originating from the Mediterranean, India, Africa and South America. One of the most intriguing finds from the cargo was Indigofera tinctoria L. (true indigo), a valuable dye plant. Our paper presents the botanical data analysed from the barrels and summarizes the plants mentioned in the historical records on the cargo of the Vrouw Maria.

This paper is devoted to the study of a non-isothermal incompressible Navier–Stokes–Allen–Cahn system which can be considered as a model describing the motion of the mixture of two viscous incompressible fluids. This kind of models is physically relevant for the analysis of non-isothermal fluids. The governing system of nonlinear partial differential equations consists of the Navier–Stokes equations coupled with a phase-field equation, which is the convective Allen–Cahn equation type, and an energy transport equation for the temperature. We investigate the well-posedness of the nonlinear system. More precisely, existence and uniqueness of local strong solutions in two and three dimensions for any initial data are proved. Moreover, existence of global weak solutions and existence and uniqueness of global strong solution in dimension two, when the initial temperature is suitably small, are established.

We improve a normality result of Liu–Li–Pang [4] concerning shared values between two families. Let $$\mathcal F$$ and $$\mathcal G$$ be two families of meromorphic functions on D whose zeros are multiple. Suppose that $$\mathcal G$$ is normal on D, and no sequence contained in $$\mathcal G$$ $$\chi $$ -converges locally uniformly to $$\infty $$ or a function g satisfying $$g'\equiv 1$$ . If for every $$f\in \mathcal F$$ , there exists a function $$g\in \mathcal G$$ such that f and g share 0 and $$\infty $$ while $$f'$$ and $$g'$$ share 1, then $$\mathcal F$$ is also normal on D.

Interest in wave energy converters to provide autonomous power to various ocean-bound systems, such as autonomous underwater vehicles, sensor systems, and even aquaculture farms, has grown in recent years. The Monterey Bay Aquarium Research Institute has developed and deployed a small two-body point absorber wave energy device suitable to such needs. This paper provides a description of the system to support future open-source access to the device and further the general development of similar wave energy systems. Additionally, to support future control design and system modification efforts, a set of hydrodynamic models are presented and cross-compared. To test the viability of using a linear frequency-domain admittance model for controller tuning, the linear model is compared against four WEC-Sim models of increasing complexity. The linear frequency-domain model is found to be generally adequate for capturing system dynamics, as the model agreement is good and the degree of nonlinearity introduced in the WEC-Sim models is generally less than 2.5%.

The circulation in the northern South China Sea (SCS) strongly responds to anticyclonic eddies that shed from the Kuroshio intruding across Luzon Strait. An eddy tracking algorithm was applied to 26 years of altimetry data to better quantify the surface characteristics of eddies in and near the Luzon Strait with an emphasis on eddies with significant westward propagation across the northern SCS. Spatial mean eddy characteristics revealed that the most robust anticyclonic eddies are in the region of 20–22° N and 118–120° E (where eddies have been observed to shed from the Kuroshio into the northern SCS) and in the North Pacific Gyre east of the Luzon Strait (18–22° N, 121–124° E). The composite structure of mesoscale eddies revealed stronger, more high-amplitude eddies east of the Kuroshio for both circulation types, which was true in all seasons but the starkest contrast was during the summer monsoon. We then isolated the ten farthest westward-propagating eddies that generated in the Luzon Strait region. The majority of these long-propagating eddies occurred during the boreal fall and winter when the cyclonic basin-scale circulation was conducive to eddy propagation along the Chinese shelf break. Using the Kuroshio South China Sea Index (KSI), we find that a highly viable condition for generation of North Pacific Gyre eddies that propagated westward across the Luzon Strait was found when the Kuroshio bifurcates with one branch into the northern SCS and the other northward along eastern Taiwan. In this state, an anticyclonic eddy can generate east of the Kuroshio and be advected into the SCS.

To clarify the Tsushima Warm Current (TWC) system around a downstream region of Noto Peninsula (NP) where Toyama Trough (TT) causes a discontinuity of the along shelf-current, numerical experiments were performed using two-layered ocean model with simplified bottom topography. When a current trapped by the continental slope representing an offshore branch of TWC (OB) encounters the NP and TT, the OB was trapped by the coast facing the TT. A clockwise lee-eddy developed between a current axis and a coastline over the TT, which results in a current path transition offshore (CPT). The OB finally adjusted to a current path which crosses TT by shifting from the discontinuity point of the continental slope. If a coastal current representing a coastal branch of the TWC (CB) developed under this situation, the CB also formed lee-eddy within the identical region of the OB’s eddy, resulting in CPT. Period for the CPT of the CB was shorter with increase of the OB volume transport. These results indicate that the OB acted to accelerate CPT of the CB within the TT. To support these results, observational data comprising mooring current, tidal, and CTD measurements obtained in and around the TT, along with the output from high-resolution data-assimilated ocean model DR_C were analyzed. Although the lee-eddy of the CBs was generated in every summer, the CPT events did not fully develop when the OB was absent over the continental slope because of the slow growth rate of the lee-eddy.

In this paper we investigate the $$\infty $$ -capacity and the Faber–Krahn inequality on the Grushin space $${\mathbb {G}}^n_\alpha $$ . On the one hand we show that the $$\infty $$ -capacity equals the limit of the p-th root of the p-capacity as $$p\rightarrow \infty $$ and give a simple geometric characterization in terms of the Carnot–Caratheodory distance, on the other hand we establish some basic properties for the $$\infty $$ -capacity, $$\infty $$ -eigenvalue and the Faber–Krahn inequality on the Grushin space $${\mathbb {G}}^n_\alpha $$ .

Let $$\mu $$ be a Borel probability measure on $${\mathbb {R}}^n$$ . We call $$\mu $$ a spectral measure if there exists a countable set $$\Lambda \subset {\mathbb {R}}^n$$ such that $$E_\Lambda :=\{e^{2\pi i }:\lambda \in \Lambda \}$$ forms an orthogonal basis for the Hilbert space $$L^2(\mu )$$ . Let the measure $$\mu _{\{M,{\mathcal {D}}_n\}}$$ be defined by the following expression $$\mu _{\{M,{\mathcal {D}}_n\}}=\delta _{M^{-1}{\mathcal {D}}_1}*\delta _{M^{-2}{\mathcal {D}}_2}*\cdots $$ , where $$M=\text {diag}(\rho ^{-1},\rho ^{-1})$$ with $$|\rho

Long-term arrays of satellite optical measurements of Landsat-5,7,8 and Sentinel-2 were used to describe the characteristics of submesoscale eddy (SE) dynamics in different parts of the Crimean coast: their geometric and kinematic characteristics, the main sites and mechanisms of formation, and impact on the redistribution of suspended matter. The dynamic characteristics of SE were computed on the base of the 4D variational assimilation method from the pair of consecutive Landsat-8/Sentinel-2 images. The orbital velocity of submesoscale cyclonic eddies (SCE) with a diameter of 1 km reaches 0.15 m/s, indicating the cyclostrophic balance with a high Rossby number (RO) exceeding 2. Submesoscale cyclones were detected much more frequently than the usually larger submesoscale anticyclones. High-resolution satellite imagery gives a possibility to observe complex submesoscale dynamic processes, such as the generation of chains of SCE, large cyclones behind the capes consisting of densely packed arrays of SCEs, topographic submesoscale anticyclones with a number of attached SCEs, mushroom-like current structures, and frontal SE. Despite the diversity of the processes considered, several basic mechanisms of formation of submesoscale eddies can be identified on the basis of satellite data: (1) Separation of the boundary current, often wind-driven, behind the capes; (2) barotropic instability due to the horizontal shear on the coastal periphery of mesoscale anticyclones or alongshore currents; (3) formation of the mushroom-like structure due to the interaction of offshore currents with deep waters near the capes or due to offshore winds; and (4) frontal instabilities on the coastal upwelling. The results of the analysis were used to create a scheme of the spatial variability of submesoscale processes near the Crimean coast and compare it to the results of the high-resolution modeling. The model was able to describe the main areas of SE formation, which was located near the major capes. It provides additional data about SE generation near the rocky capes of the South Crimea, where satellite data was limited by the absence of optical tracers.

Currents in the Baltic Sea are generally weak, but during strong winds they can grow high enough to affect the surface wave propagation and evolution. To evaluate the significance of wave-current interactions in the Baltic Sea, we conducted a study using the wave model WAM, comparing a run without surface currents to one with current forcing from a NEMO hydrodynamical model simulation. The overall changes to the wave field caused by currents were quite small. Changes of over 10 cm in significant wave height (SWH) or 1 s in the peak period (Tp) occurred only in some areas and typically less than 3% of the time. Current refraction changed the SWH annual mean by up to 2 cm, but changes up to 60 cm were seen in the maximum values. Tp had occasionally large changes due to shifts in the peak energy in two-peaked swell and wind-sea spectra. Including currents typically led to a stronger changes in swell energy compared to the changes in wind sea energy. A comparison with a wave buoy in the Gulf of Finland showed that this change in the swell energy improved the accuracy of the simulation in this narrow gulf. Current-induced refraction was most prominent near the coastal areas, where current speed occasionally exceeded 0.3 m/s. In general, SWH decreased in the coastal areas with strong currents and slightly increased in adjacent open sea areas. The current effects were most frequent in the Gulf of Finland, the Western Gotland Basin and the Åland Sea.

In Li et al. (J Aust Math Soc 97:383–390, 2014), the authors discussed two classes of mappings in Banach spaces, which are $$\varphi $$ -quasiisometric mappings in the distance ratio metric (briefly, $$\varphi $$ -DRQI mappings) and fully $$\varphi $$ -quasiisometric mappings in the distance ratio metric (briefly, $$\varphi $$ -FDRQI mappings), where $$\varphi :$$ $$[0,\infty )\rightarrow [0,\infty )$$ denotes a quasiisometric control function. In this paper, we continue this discussion by introducing a new class of mappings, that is, $$\varphi $$ -PDRQI mappings. The purpose of this paper is twofold. Let f be a homeomorphism between two proper domains in a Banach space. First, we prove that f being $$\varphi $$ -PDRQI is equivalent to f being $$\varphi $$ -FDRQI. Then, as an application of the obtained equivalent relation, we show that f being $$\varphi $$ -DRQI, f being $$\varphi $$ -PDRQI and f being $$\varphi $$ -FDRQI are equivalent to each other when the quasiisometric control functions have the form $$\varphi (t)=Mt$$ .

The South Atlantic subtropical underwater (STUW) is a high-salinity water mass formed by subduction within the subtropical gyre. It is a major component of the subtropical cell and affects stratification in the downstream direction due to its high salinity characteristics. Understanding the interannual variability in STUW subduction is essential for quantifying the impact of subtropical variability on the tropical Atlantic. Using the output from the ocean state estimate of the Consortium for Estimating the Circulation and Climate of the Ocean (ECCO), this study investigates the interannual variability in STUW subduction from 1992 to 2016. We find that heat fluxes, wind stress, and wind stress curl cause interannual variability in the subduction rate. Heat fluxes over the subduction area modulate the sea surface buoyancy and regulate the mixed layer depth (MLD) during its deepening and shoaling phases. Additionally, the wind stress curl and zonal wind stress can modulate the size of the subduction area by regulating the probability of particles entrained into the mixed layer within 1 year of tracing. This analysis evaluates the influence of subtropical wind patterns on the South Atlantic subsurface high-salinity water mass, highlighting the impact of heat and wind on the interannual changes in the oceanic component of the hydrological cycle.

The Eastern Kamchatka Current (EKC) is the western boundary current of the North Pacific subpolar gyre. Southeast of the Kamchatka Peninsula lies a large anticyclonic eddy, the Kamchatka Eddy (KE). This eddy is quasi-stationary. More generally, the oceanic region east of the EKC contains many eddies, several of them large and long lasting. Using surface currents derived from altimetry, particle tracking and a simple two-dimensional numerical model of fluid flow, we investigate the variability of this eddy field, the generation of eddies in the bays of Kamchatka by the EKC and fluxes of water to and from these bays. Firstly, we recover in our analysis of long-lasting eddies, the main eddies of the region. Among strong eddies, the parity bias favors anticyclones. Our numerical simulations give a possible explanation for the process of eddy creation in the bays of the peninsula and show that the northernmost bay produces most anticyclones. Then, we track forward the water particles from these bays and we determine their fate in the open ocean; southeastward and southwestward trajectories are the most frequent. We also track water particles backward from the KE site; they often drift near the Kamchatka coast, but others drift south of this site and remain there, a priori trapped in other eddies. This study confirms the complexity of mesoscale motions and water exchanges in this region.

In this paper, we provide partial solutions to a problem raised by Vaisala on local properties of free quasiconformal mappings. In particular, we show that a locally free quasiconformal mapping is a globally free quasiconformal mapping under the condition of locally relative quasisymmetry.

A recent linear stability analysis and a numerical simulation suggest that diffusive convection (DC), a regime of the double-diffusive convection, plays a potential role in onset of thermohaline–shear instability, implying that DC could contribute to turbulence production in the oceans. However, an existence of such a thermohaline–shear instability has not been examined in real oceans. We examine if this newly proposed instability mechanism exists in the subarctic North Pacific by analyzing our fine- and micro-scale turbulence measurement data. Vertical inversions were cautiously detected in seawater density profiles and used as a proxy for instability events for gradient Richardson number larger than the critical value of 1/4. We found that a portion of inversions were associated with active DC. Such DC-related inversions exhibited elevated levels of turbulent kinetic energy dissipation rate even for gradient Richardson number largely exceeding 1/4. Our estimate suggested that the thermohaline–shear instability contributes to roughly only 10% of the dissipation of turbulent kinetic energy in the diffusively convective layer in our observation site.

The response of a jet to sudden winds was examined using a simple numerical regional model and an analytical model to investigate the mechanism underlying the local wind dynamics of seasonal velocity variations in the upper layer of the Kuroshio. The numerical model was used to simulate the distinct seasonal features in summer and autumn in the East China Sea and successfully reproduced the seasonal features in the velocity field under different sudden wind conditions. The current speed increased and decreased under summer and autumn wind conditions, respectively; and the current axis shifted to the offshore and inshore sides under summer and autumn wind conditions, respectively. We focused on the current speed variation and hypothesized that the current speed variation is forced by the thermocline variation due to nonlinear Ekman pumping. This hypothesis was examined using a rigid-lid reduced-gravity analytical model with Ekman layer dynamics. The analytical model results showed that the asymmetry of the jet profile has a marked effect on the current speed variation. With a higher wavenumber on the west side of a northward jet, the current speed increased and decreased under summer and autumn wind conditions, respectively. These findings can be used to explain the seasonal velocity variations in the upper layer in the East China Sea and over the entire Kuroshio path.

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.

The coexistence of multiple wave systems generated locally and by remote storms is common in the ocean and its quantification is required in the design of marine facilities. This study identifies the multimodal sea states at six locations in the shelf seas of India based on partitioned wave output data from numerical model WAVEWATCH-III for 26 years (1990 to 2015). The different systems are identified by the propagation direction and frequencies with a relatively high probability of occurrence of spectral partitions. Four to seven types of distinct clusters of wave systems are present among the study locations. The occurrence of these systems and co-occurrence of this with other systems are examined. The southernmost location experiences the effect of seven wave systems. At all locations, two wave systems from the south with relatively low partial significant wave height (Hs) are present for more than 71% of the time and co-occurred with other systems during 2–67%. The most energetic systems are observed 23% (system 5 at station 3) to 60% (system 4 at station 4) of the time with maximum mean partial Hs values of 1 to 3 m during summer monsoon months. The southernmost location (3) experienced maximum opposing (18%) and crossing (78%) sea states.

We prove a two-parameter family of second order geometric Rellich type equalities on the half-space $$ \mathbb {R} _{+}^{n}$$ . We then use it to derive several refined geometric Rellich type inequalities. We also prove an improved version of the Rellich–Sobolev–Maz’ya type inequality.

We used historical CTD observations and Argo data to obtain the characteristics of the Kamchatka Current halocline and its eddies. Kamchatka Current eddies have a cold low salinity core in contrast with Aleutian eddies that contain warm and saline waters of Alaskan Stream origin. The Kamchatka Current eddies are smaller with diameter of ~ 100–120 km. Kamchatka Current eddies have a thick cold layer in a halocline. The temperature in their core increased by ~ 2.4 °C from the beginning of observations in 1990, while salinity decreased. We found that 2012 was the coldest year in the Kamchatka Current. Record-breaking warming occurred in the Kamchatka Current during 2015 to 2018. Temperature in the halocline rose by ~ 3 °C from 2012 to 2018 at 26.6σθ, while in the western Bering Sea temperature rose by 2.3 °C. It is plausible that the warming in the Kamchatka Current halocline during 2012 to 2018 is associated with the lowest recorded sea ice coverage in the Bering Sea. Similar warming occurred in the Oyashio Current. Salinity, temperature and specific density in the 2012 Simushir eddy were extremely low for the 30-year row of observations from 1990 to 2020. Extremely low salinity was also found in the 2012 Aleutian eddy off the Near Strait.

This study addresses the air–sea interaction processes and mixed layer variability, which cause the intraseasonal oscillations in the sea surface temperature (SST) during January 2013–December 2014 using the Regional Ocean Modeling System (ROMS). We have analyzed the SST variability at three locations—northern Bay of Bengal (BoB)/15°N, 90°E (R15), central BoB/12°N, 90°E (R12), and equatorial Indian Ocean (EIO)/0°N, 80.5°E (R0). During northeast monsoon (NEM) and southwest monsoon (SWM), intraseasonal SST variability is respectively controlled by the intense outgoing fluxes (sum of longwave radiation, latent heat flux, and sensible heat flux) and zonal wind stress. The intraseasonal SST variability in spring and fall is modulated by intense incoming shortwave radiation. There is a profound impact of mixed layer depth (MLD) variations on the intraseasonal SST oscillations in the BoB and EIO. At R15, and R12, deepened simulated MLD is associated with the lowered SST variability in the NEM and SWM. In spring and fall, the shallow MLD variability corresponds to higher intraseasonal SST variability at the buoy locations. In the northern BoB, ROMS cannot capture barrier layer (BL) and temperature inversion (TI) accurately in the winter and premonsoon season due to salinity bias, resulting in the difference between simulated and actual MLD. But the simulated MLD bias does not affect the intraseasonal SST structures in the NEM and pre-SWM. In the northern BoB, the proper representation of salinity structure may represent BL, TI, and MLD, accurately in the simulation during the winter and premonsoon season.

In this paper, we study a new model for a jet component of the Antarctic Circumpolar Current. In the case of vorticity with perturbation, we present the existence results for positive solutions to periodic boundary value problems for general nonlinear, weak nonlinearity and semilinear terms. A computational method is established and an approximate scheme of solution is also given.

This study modeled Stokes drift in the marginal ice zone (MIZ) of the Arctic Ocean using WAVEWATCH III. Applying two viscoelastic and one empirical frequency-dependent wave–ice models, modeled wave parameters and spectra were compared with field observations from the Beaufort–Chukchi Sea. The three wave–ice parameterizations showed similar ability in reproducing the surface Stokes drift estimated using buoy measurements. Comparison with buoy drift showed the estimation of total surface drift was improved by considering Stokes drift during significant wave events. Based on 5-year (2015–2019) hindcasted directional spectra of the summer-autumn Arctic, we investigated monthly mean surface Stokes drift (1–10 cm/s), e-folding depth (1–14 m), and vertically integrated transport (< 0.23 m2/s) in the MIZ. The results showed that Stokes drift in the MIZ increased in strength from July to October. When bulk wave parameters were adopted to estimate Stokes drift fields, the surface Stokes drift was underestimated by about 34–50%, while the Stokes e-folding depth was overestimated by approximately 1.4–5.0 times, increasing from the interior to the edge of the ice cover. We compared the modeled surface Stokes drift with the Eulerian mean flow from reanalyzed data. It showed the mean surface Stokes drift is typically approximately 30% of the Eulerian current over large parts of the Arctic Ocean MIZ with mean ice concentration < 60%, and is the same order of magnitude as (or even larger than) some areas of the Chukchi, East Siberian, and Laptev Seas. It implies Stokes drift should be considered to improve modeling of the dynamic processes of sea ice, especially ice floe drift.

Wind dominates the ocean surface circulation in the subtropical coastal upwelling regions. Although the wind events in these regions are mostly favorable for upwelling, other types of wind events are occasionally dominant. The typical patterns and statistics of wind events over the waters off northern Baja California are described. The identification of wind events was carried out using a systematic technique based on both the admittance magnitude and phase. This technique proved useful and has some of the crucial characteristics expected from a classification standpoint. This technique is applied to 29 years (1990–2018) of cross-calibrated multiplatform (CCMP) 10-m wind data. Equatorward along the coast (upwelling-favorable), offshore (Santa Ana), onshore, poleward along the coast (downwelling-favorable), and relaxation events are identified. The wind stress and wind stress curl mean fields and the statistics of occurrence are described on a year-to-year and month-to-month basis for each wind type. The upwelling-favorable and relaxation events are the most frequent and occur throughout the year; the typical duration is 4 and 1.5 days, respectively. The offshore (Santa Ana), onshore, and poleward wind events are sporadic and occur only during autumn-winter. The year-to-year variation of the frequency of occurrence of the equatorward wind events shows no trend during the study period.

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.

Seasonal variability of the upper ocean on meso- and submesoscales is investigated in the framework of the quasi-normal scale elimination theory, or QNSE. The longitudinal and transverse velocity spectra in this theory have a bi-component structure comprised of the Coriolis and Kolmogorov-like branches that are identified with meso- and submesoscales, respectively. For the former, spectral amplitudes are determined by the Coriolis parameter, f, while for the latter, the amplitudes are quantified in terms of the energy flux, πe, proceeding from larger to smaller scales. This flux can be identified with the effective submesoscale dissipation. The Kolmogorov and Coriolis subranges are delineated at a length scale Lc that marks a crossover between the respective spectra. The theoretical spectra agree well with those obtained in many observational campaigns. In phase with the seasonal variations of the intensities of instabilities and turbulence, the magnitudes of πe and Lc increase in winter and decrease in summer. Mirroring these changes, the bi-component structure of the kinetic energy spectra changes with seasons and renders meaningless the characterization of their seasonal variability in terms of a single slope. The theoretical results are validated against the data collected in Oleander, LatMix and North-Western Pacific observations.

To describe the geometry of normed space, many geometric constants have been investigated. Among them, the von Neumann–Jordan constant has been treated by a lot of mathematicians. Here we also consider Birkhoff orthogonality and isosceles orthogonality. The usual orthogonality in inner product spaces and isosceles orthogonality in normed spaces are symmetric. However, Birkhoff orthogonality is not symmetric in general normed spaces. A two-dimensional normed space in which Birkhoff orthogonality is symmetric is called Radon plane. We consider the upper bound of a geometric constant in Radon planes. Then we estimate the von Neumann–Jordan constant in Radon planes.

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.

International audience; The input of mechanical power to the ocean due to the surface wind-stress, in regions which correspond to different regimes of ocean dynamics, is considered using data from satellites observations. Its dependence on the coarse-graining range of the atmospheric and oceanic velocity in space from 0.5 o to 10 o and time from 6h to 40 days is determined. In the area of the Gulf Stream and the Kuroshio extensions the dependence of the power-input on space-time coarse-graining varies over tenfold for the coarse-graining considered. It decreases over twofold for the Gulf Stream extension and threefold for the Kuroshio extension, when the coarse-graining length-scale passes from a few degrees to 0.5 o at a temporal coarse-graining scale of a few days. It increases over threefold in the Gulf Stream and the Kuroshio extensions when the coarse-graining passes from several days to 6h at a spatial coarse-graining of a few degrees. The power input is found to increase monotonically with shorter coarse-graining in time. Its variation with coarse-graining in space has no definite sign. Results show that including the dynamics at scales below a few degrees reduces considerably the power input by air-sea interaction in regions of strongly non-linear ocean currents. When the ocean velocities are not considered in the shear calculation the power-input is considerably (up to threefold) increased. The dependence of the power input on coarse-graining in space and time is close to being multiplicatively separable in all regions and for most of the coarse-graining domain considered.