Divergence and Curl of COVID19 Spreading in the Lower Peninsula of Michigan

This paper explores the COVID19 transmission pattern and circulation dynamics in the Euclidean space at the lower peninsula of Michigan by using the divergence and curl concept in vector field. The COVID19 transmission volume flux can be calculated for each county by using vector divergence. The results shows Wayne county had the highest divergence (162660), the Kent county had the second highest divergence (152540), and the Saginaw county had the third highest divergence (103240), the divergence is positive which means the COVID19 virus was transmitted from these counties to other places. The results also shows Monroe county had the lowest divergence (-187843), the Allegan county had the second lowest number in divergence (-90824), the divergence is negative which means the COVID19 virus was transmitted from other places to these counties. The circulation of the virus is also calculated by using vector curl. The positive curl means that the virus has circulated in a counter-clockwise direction, and the negative curl means the virus has circulated in a clockwise direction. The divergence is an operator of the COVID19 transmission vector field, which produces a scalar field giving the quantity of the transmission vector field’s source at each location. The COVID19 spreading volume density of the outward flux of transmission field is represented by divergence around a given location. The curl is an operator of the COVID19 transmission field, which describes the circulation of a transmission vector field. The curl at a location in COVID19 transmission field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a transmission field is formally defined as the circulation density at each location of COVID19 transmission field.

A Wind–Wave-Dependent Sea Spray Volume Flux Model Based on Field Experiments

Sea spray can contribute significantly to the exchanges of heat and momentum across the air–sea interface. However, while critical, sea spray physics are typically not included in operational atmospheric and oceanic models due to large uncertainties in their parameterizations. In large part, this is because of the scarcity of in-situ sea spray observations which prevent rigorous validation of existing sea spray models. Moreover, while sea spray is critically produced through the fundamental interactions between wind and waves, traditionally, sea spray models are parameterized in terms of wind properties only. In this study, we present novel in-situ observations of sea spray derived from a laser altimeter through the adoption of the Beer–Lambert law. Observations of sea spray cover a broad range of wind and wave properties and are used to develop a wind–wave-dependent sea spray volume flux model. Improved performance of the model is observed when wave properties are included, in contrast to a parameterization based on wind properties alone. The novel in-situ sea spray observations and the predictive model derived here are consistent with the classic spray model in both trend and magnitude. Our model and novel observations provide opportunities to improve the prediction of air–sea fluxes in operational weather forecasting models.

A tension assessment model for digital twins of continuous rolling processes

The paper deals with the calculation of interstand tensions in continuous rolling mills for flat and long products. A fast calculation method for the interstand tensions from measurable process quantities is a mcritical point to enable the construction of digital twins for the rolling process, which must be adjusted to the real-world tension behaviour of the production system. It is straightforward to calculate the effects of the tensions on roll forces, torques and the strip or bar velocity. However, the inverse problem of calculating the acting interstand tensions including their effects from the process parameters is of much greater interest but also of a higher complexity, because the interactions between all of the stands in the continuous rolling mill must be taken into account. The paper presents a mathematical model to solve the inverse problem by subsequent linearization of the tensions influences in the rolling mill.Extra nonlinearities are taken into account by modeling the tension-dependent spread by an empirical model. The overall model is solved by an iteration method to yield a fully compatible solution for the constant volume flux as well as the force and torque equilibria in the roll gaps. Results are shown for the tension distributions in strip and rod mills. The results indicate that the present friction conditionsand the spreading behaviour of the rolled material have a high impact on the tension distributions.

Divergence and Curl of COVID19 Spreading in Lower Peninsula of Michigan

Divergence and Curl concept in vector field is applied to the COVID19 spreading data for Lower Peninsula of Michigan State, U.S.A. The Divergence is an operator of COVID19 transmission vector field, which produces a scalar field giving the quantity of transmission vector field’s source at each location. The COVID19 spreading volume density of the outward flux of transmission field is represented by divergence around a given location. The Curl is an operator of COVID19 transmission field, which describes the circulation of a transmission vector field. The Curl at a location in COVID19 transmission field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a transmission field is formally defined as the circulation density at each location of COVID19 transmission field. From data analysis of divergence of curl of Lower Michigan Peninsula, the COVID19 transmission volume flux and circulation can be identified for each County. Summary: This paper is to use vector Divergence and Curl concept to apply to COVID19 confirmed cases in Lower Peninsula of Michigan, U.S.A.

Submarine groundwater discharge from coastal peatlands of northeast Germany

<p>Submarine groundwater discharge (SGD) is an important pathway for water and compounds within the land-ocean transition zone that can impact coastal environments and marine life. Although SGD research from sandy shorelines has rapidly advanced in recent years, there is very little understanding of coastal areas dominated by coastal peatlands, where the prevailing soils are characterized by a low hydraulic conductivity. Peatlands, the world’s most efficient carbon storage, could be a potential source of carbon, nutrients, and trace metals via the SGD pathway. The objective of this study was to determine the magnitude and location of SGD in a coastal peatland in northeast Germany. We wanted to understand the factors controlling terrestrial SGD from coastal peatlands through numerical modelling employing the HYDRUS-2D modeling package. Steady-state scenarios were simulated based on soil physical properties, hydraulic heads, and geological stratifications and structure. In the model set-up, emphasis was laid upon peat layers extending from land into the sea. Our results show that terrestrial SGD occurs at a net discharge volume flux of 0.0803 m<sup>3</sup> m<sup>-1</sup> d<sup>-1</sup> with seepage rates of 1.05 cm d<sup>-1 </sup>near the shore and 0.16 cm d<sup>-1 </sup>at a second discharge region above the submerged peat layer. Calculated seepage rates compare to observations from other SGD sites in the Baltic Sea region and other wetland environments. The upscaled SGD estimate for the 3-km coastal peatland is 240 m<sup>3</sup> d<sup>-1</sup>, which is in correspondence to earlier estimates from the same site. Analysis of the model output reveals that magnitude and location of terrestrial SGD are mainly driven by the magnitude of hydraulic gradient and the hydraulic conductivity of both peat and mineral soils. Additional influencing factors are peat anisotropy, thickness of aquifer sands and peat layers, and peat elevation. Submerged peat layers extending into the sea can restrict SGD flow in deeper discharge regions but may be less critical in terms of volume flux as most SGD occurs near the shoreline. We conclude that coastal peatlands could be an essential source of carbon, nutrients, and other compounds via SGD and may influence local geochemistry budgets and marine ecosystems.</p>

Future salt intrusion climate scenarios: the case of the Po river

<p>A 2-layer Estuary Box Model, named CMCC EBM (Verri et al., 2020), has been devised by the CMCC Foundation to offer a proper representation of the estuarine overturning circulation and mixing processes in a coupled modelling framework with hydrology models and ocean models. The regional to global ocean models reaching the mesoscale cannot solve the estuarine dynamics because they cannot represent the estuary geometry due to their low resolution. Thus, the idea of an estuary box model that gives reasonable values of water volume flux and salinity at the river mouth, which in turn affects the ocean dynamics.</p><p>A further development of the model equations (Verri et al. 2021, under revision) considers the estuary length, i.e.  the length of the salt wedge intrusion, as a model unknown which depends on the competition between the riverine freshwater and the salt ocean water.</p><p>The physical core of the model consists of two conservation equations for volume flux and salt flux both averaged over the diurnal tidal cycle. Moreover, two non-dimensional equations based on the Buckingham theorem have been conceived to provide the estuary length and the along-estuary eddy diffusivity (Verri et al., under revision) as time-variable parameters instead of assuming they are static as most box models do.</p><p>The input fields required by the CMCC EBM are the river runoff at the estuary head and the ocean inflow at the river mouth in terms of both barotropic tidal inflow through the water column and baroclinic inflow at the bottom. The estuary width and depth at the river mouth are the only tunable parameters of the CMCC EBM.</p><p>The model capability to estimate the length of the salt wedge intrusion has been tested and validated. The Po di Goro branch of the Po delta system has been selected as case study. It is representative of the river-dominated estuaries in a micro-tidal sea, the so called “salt wedge estuaries”, with a multiannual average of the salt wedge intrusion around 15 km according to the ArpaE monitoring campaigns.</p><p>Overall the high statistical performance, the short computation time and the minimal calibration encourage to use the CMCC EBM in coupled mode with mesoscale ocean models to produce more realistic operational forecasts and climate scenarios.</p><p>In the framework of the Operandum H2020 project (https://www.operandum-project.eu), the CMCC EBM has been used to provided historical simulations (1981-2010 time window) and mid-term scenarios (2021-2050 time window under RCP 8.5) of both the salt wedge length and the salinity at the Po di Goro mouth. The final aim is to design and develop a site-specific nature-based solution which may address the pressing issue of the salinization of the inland waters. The CMCC EBM results clearly showed a stronger intrusion of saltier ocean water in the middle term. The average, the minimum and the maximum values of salinity at the river mouth provided by the model projections are assumed as reference values to investigate the behaviour of two halophyte species which have been selected to reduce the saline intrusion problem because of their high salinity absorption capacity.</p>

The estimation of sea spray at wind speeds ranging from light to extreme

<p>As one of typical elements in the air-sea boundary layer, sea spray is expected to mediate energy flux exchange in the air and ocean boundary layers, and therefore it is of crucial importance to the meteorology, oceanology, and regional climatology. In addition, the spray is also considered as one of the missing physical mechanisms in atmospheric and oceanic numerical models. Hence, it is necessary to accurately predict how much sea spray is produced at the air-sea boundary layer. Though spray has been studied for a number of decades, large uncertainties still linger. For instance, uncertainties in qualifying how much spray is produced on the sea surface reach 10<sup>6</sup> times. This is because of the rarity of spray observations in the field, especially under strong wind condition.</p><p>To give a reliable spray production model, scientists tried to employ laser-based facilities in the field to observe sea spray by interpreting infrared laser-beam intensity into sea spray volume flux over the water surface. Hence, in the current study, we collected datasets in the field measured by laser-based facilities on the North-West Shelf of the coast of Western Australia, thereafter, further analyzed, and calibrated them through a series of academic, statistical, and physical analysis to ensure the data quality. After that, assuming the existence of spray drops in the air-sea layer would attenuate the infrared laser-beam intensity, the weakening extends of laser-beam intensity is used to estimate the volume flux of sea spray above the ocean surface at winds speed ranging from light to extreme during the passage of Tropical Cyclone Olwyn (2015). It should be noted that our observations of sea spray volume flux are within the ranges of existing models and are consistent with the model proposed by Andreas (1992) in both trend and magnitude.</p><p>Using the field observations of the sea spray volume flux, a sea spray volume flux model can be constructed. Given that sea spray droplets are generated at the ocean surface through breaking waves and wind shear, the sea spray volume flux is expected to be dominated by the properties of the local wind and wave field. For physical consistency across the wide range of scales observed in the field and laboratory, non-dimensional parameters (i.e., non-dimensional wind speed and the mean wave steepness) were adopted to construct the model. Consequently, a power-law non-dimensional spray volumetric flux model is suggested based on the estimation of the spray volume flux. It should be noted that one sensitive test was conducted to substantiate the inclusion of wave breaking process, here simply included with the mean wave steepness, improves spray volume flux parameterization.</p>

Cohesive Channel Response to Watershed Urbanization: Insights from the Sand River, Aiken SC

Stream channel degradation is among the most widely documented symptoms of urban stream syndrome arising from watershed urbanization. Nevertheless, our present understanding of space and time scales associated with channel response to urbanization is poorly constrained and largely limited to assessments of non-cohesive systems. The purpose of this study is to assess the evolution of a cohesive, ephemeral river channel in response to watershed urbanization. The assessment of historical images document the stable, pre-urbanized channel conditions from 1870 to 1930. Historical assessments revealed a 131% increase in urbanized watershed area from 1930 to 1992, and a minimal increase in urbanized extent from 1992 to 2012. A 2012 lidar dataset was used to generate the modern long-channel profile, to reconstruct cross-channel profiles observed in 2002, and to estimate the volume flux of sediment removed from the channel from 1930 to 1992, and from 1992 to 2012. The long-channel profile reveals incision of up to 35 m in response to urbanization from 1930 to 1992. Cross-channel profiles reveal incision and widening of 2.5 and 3 m, respectively, from 2002 to 2012. Volume flux estimates indicate erosion rates of 9000 m3/yr during the first 62 years of the study period, and a flux of 4000 m3/yr after installation of stormwater control measures in 1992. Collectively, our findings highlight a cohesive channel that has undergone substantial incision and widening at a rate of ~0.20 m/yr since 1930, and the channel continues to adjust. Hence, we contend that the channel has not yet attained a new equilibrium “shape” at 82 years after peak land use change within the watershed, and that the channel will continue to adjust its shape until this new balance is achieved.

Scrutiny of entropy optimized tangent hyperbolic fluid (non-Newtonian) through perturbation and numerical methods between heated plates

Objective: Many methods have been used to maximize the capacity of heat transport. A constant pressure gradient or the motion of the wall can be used to increase the heat transfer rate and minimize entropy. The main goal of our investigation is to develop a mathematical model of a non-Newtonian fluid bounded within a parallel geometry. Minimization of entropy generation within the system also forms part of our objective. Method: Perturbation theory is applied to the nonlinear complex system of equations to obtain a series solution. The regular perturbation method is used to obtain analytical solutions to the resulting dimensionless nonlinear ordinary differential equations. A numerical scheme (the shooting method) is also used to validate the series solution obtained. Results: The flow and temperature of the fluid are accelerated as functions of the non-Newtonian parameter (via the power-law index). The pressure gradient parameter escalates the heat and volume flux fields. The energy loss due to entropy increases via the viscous heating parameter. A diminishing characteristic is predicted for the wall shear stress that occurs at the bottom plate versus the time-constant parameter. The Reynolds number suppresses the volume flux field.