Self-similarity in incompressible Navier-Stokes equations.

The self-similarity conditions of the 3-dimensional (3D) incompressible Navier-Stokes equations are obtained by utilizing one-parameter Lie group of point scaling transformations. It is found that the scaling exponents of length dimensions in i = 1, 2, 3 coordinates in 3-dimensions are not arbitrary but equal for the self-similarity of 3D incompressible Navier-Stokes equations. It is also shown that the self-similarity in this particular flow process can be achieved in different time and space scales when the viscosity of the fluid is also scaled in addition to other flow variables. In other words, the self-similarity of Navier-Stokes equations is achievable under different fluid environments in the same or different gravity conditions. Self-similarity criteria due to initial and boundary conditions are also presented. Utilizing the proposed self-similarity conditions of the 3D hydrodynamic flow process, the value of a flow variable at a specified time and space can be scaled to a corresponding value in a self-similar domain at the corresponding time and space.

Scaling and self-similarity in two-dimensional hydrodynamics.

The conditions under which depth-averaged two-dimensional (2D) hydrodynamic equations system as an initial-boundary value problem (IBVP) becomes self-similar are investigated by utilizing one-parameter Lie group of point scaling transformations. Self-similarity conditions due to the 2D k-ε turbulence model are also investigated. The self-similarity conditions for the depth-averaged 2D hydrodynamics are found for the flow variables including the time, the longitudinal length, the transverse length, the water depth, the flow velocities in x- and y-directions, the bed shear stresses in x- and y-directions, the bed shear velocity, the Manning's roughness coefficient, the kinematic viscosity of the fluid, the eddy viscosity, the turbulent kinetic energy, the turbulent dissipation, and the production and the source terms in the k-ε model. By the numerical simulations, it is shown that the IBVP of depth-averaged 2D hydrodynamic flow process in a prototype domain can be self-similar with that of a scaled domain. In fact, by changing the scaling parameter and the scaling exponents of the length dimensions, one can obtain several different scaled domains. The proposed scaling relations obtained by the Lie group scaling approach may provide additional spatial, temporal, and economical flexibility in setting up physical hydraulic models in which two-dimensional flow components are important.

Generalizations of incompressible and compressible Navier-Stokes equations to fractional time and multi-fractional space.

This study develops the governing equations of unsteady multi-dimensional incompressible and compressible flow in fractional time and multi-fractional space. When their fractional powers in time and in multi-fractional space are specified to unit integer values, the developed fractional equations of continuity and momentum for incompressible and compressible fluid flow reduce to the classical Navier-Stokes equations. As such, these fractional governing equations for fluid flow may be interpreted as generalizations of the classical Navier-Stokes equations. The derived governing equations of fluid flow in fractional differentiation framework herein are nonlocal in time and space. Therefore, they can quantify the effects of initial and boundary conditions better than the classical Navier-Stokes equations. For the frictionless flow conditions, the corresponding fractional governing equations were also developed as a special case of the fractional governing equations of incompressible flow. When their derivative fractional powers are specified to unit integers, these equations are shown to reduce to the classical Euler equations. The numerical simulations are also performed to investigate the merits of the proposed fractional governing equations. It is shown that the developed equations are capable of simulating anomalous sub- and super-diffusion due to their nonlocal behavior in time and space.

Modeling impacts of future climate change on reservoir storages and irrigation water demands in a Mediterranean basin.

Water storage requirements in the Mediterranean region vary in time and are strongly affected by the local geography and climate conditions. The objective of this study is to assess the implications of climate change on the water balance of an agricultural reservoir in a Mediterranean-climate basin in Turkey throughout the 21st century. A monthly dynamic water balance model is developed to simulate the historical and future water availability in the reservoir. The model is driven by the fine-resolution dynamically downscaled climate data from four GCMs from the CMIP5 archive, namely CCSM4, GFDL-ESM2M, HadGEM2-ES, and MIROC5, under two different representative concentration pathway scenarios (RCP4.5 and RCP8.5), and the hydrologic data projected under the same scenarios. The reservoir outflows, including the reservoir evaporation and downstream irrigation water demands, are also modeled using the projected climate variables. The net irrigation water requirement of the crops in the irrigation system, seasonal evapotranspiration rates, and reservoir evaporation rates are estimated based on the Penman-Monteith Evapotranspiration method (FAO-56 Method). The study investigates whether the future water supply in the reservoir will be sufficient to meet the future irrigation water demands for the years from 2017 to 2100. The results show that under all eight modeled climate change projections, statistically significant increasing trends for the annual irrigation water demands are expected throughout the 21st century. Moreover, higher evapotranspiration rates are predicted under the ensemble average of the RCP8.5 projections, compared to those of the RCP4.5 projections. Ultimately, seven out of eight projections projected insufficient reservoir water levels during the 21st century, especially during the irrigation seasons when higher water demands are expected. These impacts indicate the importance of sustainable water resources management in the region to provide irrigation water from reservoirs, and to sustain agricultural productivity under projected water limitations due to climate change.

Coupling hydroclimate-hydraulic-sedimentation models to estimate flood inundation and sediment transport during extreme flood events under a changing climate.

Extreme flood events are disastrous and can cause serious damages to society. Flood frequency obtained based on historical flow records may also be changing under future climate conditions. The associated flood inundation and environmental transport processes will also be affected. In this study, an integrated numerical modeling framework is proposed to investigate the inundation and sedimentation during multiple flood events (2,5,10, 20, 50, 100, 200-year) under future climate change scenarios in a watershed system in northern California, USA. The proposed modeling framework couples physical models of various spatial resolution: kilometers to several hundred kilometers climatic processes, hillslope scale hydrological processes in a watershed, and centimeters to meters scale hydrodynamic and sediment transport processes in a riverine system. The modeling results show that compared to the flows during historical periods, extreme events become more extreme in the 21st century and higher flows tend to be larger and smaller flows tend to be smaller in the system. Flood inundation in the study area, especially during 200-year events, is projected to increase in the future. More sediment will be trapped as the flow increases and the deposition will also increase in the settling basin. Sediment trap efficiency values are within 37.5-65.4% for the historical conditions, within 32.4-68.8% in the first half of the 21st century, and within 34.9-69.3% in the second half of the 21st century. The results highlight the impact of climate change on extreme flood events, the resulting sedimentation, and reflected the importance of incorporating the coupling of physical models into the adaptive watershed and river system management.

Assessing the impacts of future climate change on the hydroclimatology of the Gediz Basin in Turkey by using dynamically downscaled CMIP5 projections.

The Gediz Basin is a Mediterranean watershed along the Aegean coast of Turkey, in which the most important economic activity is agriculture. Over the last few decades, this basin has been experiencing water-related problems such as water scarcity and competing use of water. This study assesses the impact of future climate change on the availability of water resources in the Gediz Basin during the 21st century by investigating the inflows into the major reservoir in the basin, Demirkopru Reservoir, which is the major source of irrigation water to the basin. The analysis in this study involves setting up a coupled hydro-climate model over the Gediz Basin by coupling the Weather Research and Forecasting (WRF) model to the physically-based Watershed Environmental Hydrology (WEHY) model. First, the WRF model is used to reconstruct the historical climatic variables over the basin by dynamically downscaling the ERA-Interim reanalysis dataset. The calibrated and validated WRF model is then used to dynamically downscale eight different future climate projections over the Gediz Basin to a much finer resolution (6 km), which is more appropriate for the hydrologic modeling of the basin. These climate projections are from four Coupled Model Intercomparison Project Phase 5 (CMIP5) Global Climate Models (GCMs), namely, CCSM4, GFDL-ESM2M, HadGEM2-ES, and MIROC5, under two IPCC (The Intergovernmental Panel on Climate Change) representative concentration pathway scenarios (RCP4.5 and RCP8.5). The outputs from the WRF model are then input into the WEHY model, which is calibrated and validated over the basin, to simulate the hydrological processes within the basin and to obtain the projected future inflows into the Demirkopru Reservoir. Results of the future analysis over the 21st century (2017-2100) are then compared to the historical values (1985-2012) to investigate the impacts of future climate change on the hydroclimatology of the Gediz Basin.

Impact of increased atmospheric moisture on the precipitation depth caused by Hurricane Ivan (2004) over a target area.

In this article, numerical experiments are performed to investigate the effects of increasing atmospheric moisture on the precipitation depth (PD) produced by Hurricane Ivan (2004) over a target area, chosen as the drainage basin of the city of Asheville, NC. Atmospheric moisture was increased indirectly by increasing the sea surface temperature (SST) in the simulation initial conditions, and by letting the regional atmospheric model adjust the atmospheric fields to the SST perturbation. The SST was increased in two ways: 1) using spatially constant increments and 2) using a climate change perturbation field obtained from a climate projection. For each SST scenario, the PD over the target area was maximized by using a physically based storm transposition method. Although the mean PD, that was obtained by averaging over all shifting increments, increased with SST, the maximum PD was obtained for the case of no SST increase. It was found that, in the case of no SST increase, the worst-case tropical cyclone track was significantly different than in the SST increase scenarios. In particular, in this case, the storm spent a longer time in the simulation inner domain, thus spawning a larger PD over the target area.

Investigation of Intense Precipitation from Tropical Cyclones during the 21st Century by Dynamical Downscaling of CCSM4 RCP 4.5.

In this article, a dynamical downscaling (DD) procedure is proposed to downscale tropical cyclones (TCs) from a general circulation model, with the goal of investigating inland intense precipitation from these storms in the future. This DD procedure is sequential as it is performed from the large scale to the small scale within a one-way nesting modeling framework with the Weather Research and Forecasting (WRF) model. Furthermore, it involves a two-step validation process to ensure that the model produces realistic TCs, both in terms of their general properties and in terms of their intense precipitation statistics. In addition, this procedure makes use of several algorithms such as for the detection and tracking of TCs, with the objective of automatizing the DD process as much as possible so that this approach could be used to downscale massively many climate projections with several sets of model options. The DD approach was applied to the Community Climate System Model (CCSM) version 4 using Representative Concentration Pathway (RCP) 4.5 during the period 2005⁻2100, and the resulting TCs and their intense precipitation were examined.

Physically based storm transposition of four Atlantic tropical cyclones.

In this article, a method for the storm transposition of tropical cyclones is presented. This method is physically based as it uses a regional atmospheric model to reconstruct the precipitation depth field from a tropical cyclone, thus crucially conserving the mass, momentum and energy in the system. In this physically based storm transposition method, the tropical cyclone vortex in the simulation initial conditions is first shifted spatially. More precisely, the tropical cyclone at the simulation start date is first separated from its background environment, then shifted, and finally recombined with the background environment. Afterwards, the regional atmospheric model is run as usual to simulate the shifted tropical cyclone and its precipitation depth field. The storm transposition method was then applied to four hurricanes which spawned torrential precipitation in the United States: Hurricanes Floyd (1999), Frances (2004), Ivan (2004), and Isaac (2012), in order to maximize the 72-h precipitation depth over the drainage basin of the city of Asheville, NC. It was observed that the precipitation depth fields changed in both structure and intensity after the physically based storm transposition. Besides, the tropical cyclone tracks were generally very sensitive to changes in the initial conditions, which is expected for a storm system whose dynamics is strongly nonlinear. In particular, it was found that a small change in the location of the initial tropical cyclone vortex may result in a very different track, allowing the tropical cyclone's precipitation depth field to move over the target area.

Numerical reconstruction of the intense precipitation and moisture transport fields for six tropical cyclones affecting the eastern United States.

Tropical cyclones (TCs) are intense atmospheric vortices that form over the warm tropical oceans. They are recognized for their ability to generate intense precipitation that may in turn create disastrous floods. This article first assesses the suitability of a regional atmospheric model, the Weather Research and Forecasting (WRF) model, to simulate the intense precipitation depth (PD) fields of six North Atlantic TCs that affected the eastern United States during 2002-2016. Due to the strong nonlinearity involved in tropical cyclones' dynamics and thermodynamics, which causes tropical cyclones' tracks to be very sensitive to the different modeling choices, placing the PD fields in the observed locations was challenging. This involved trying several simulation start dates and combinations of the WRF model's parameterization schemes for each storm simulated. Model performance was evaluated by comparing the simulated PD fields with the observed PD fields obtained from the NCEP Stage IV precipitation dataset. In addition to qualitative comparisons, three quantitative metrics were used to quantify the WRF model performance in simulating a PD field's location, structure and intensity. The sensitivity of the simulation results to the choice of the parameterization schemes was then illustrated using Hurricane Gustav (2008). Eventually, the most satisfactory simulations were used to investigate the mechanisms responsible for the generation of intense precipitation in these TCs. More specifically, the vertically integrated vapor transport field and its divergence were calculated using the model outputs, and it was found that horizontal moisture convergence played a central role in the generation of intense precipitation in these TCs.

Evaluation of physical parameterizations for atmospheric river induced precipitation and application to long-term reconstruction based on three reanalysis datasets in Western Oregon.

Dynamically downscaled precipitation is often used for evaluating sub-daily precipitation behavior on a watershed-scale and for the input to hydrological modeling because of its increasing accuracy and spatiotemporal resolution. Despite these advantages, physical parameterizations in regional models and systematic biases due to the dataset used for boundary conditions greatly influence the quality of downscaled precipitation data. The present paper aims to evaluate the performance and the sensitivities of physical parameterizations of the Weather Research and Forecasting (WRF) model to simulate extreme precipitation associated with atmospheric rivers (ARs) over the Willamette watershed in Oregon. Also investigated was whether the optimized WRF configuration for extreme events can be used for long-term reconstruction using different boundary condition datasets. Three reanalysis datasets, the Twentieth Century Reanalysis version 2c (20CRv2c), the European Center for Medium-Range Weather Forecasts (ECMWF) twentieth century reanalysis (ERA20C), and the Climate Forecast System Reanalysis (CFSR), which have different spatial resolutions and dataset periods, were used to simulate precipitation at 4 km resolution. Sensitivity analyses showed that AR precipitation is most sensitive to the microphysics parameterization. Among 13 microphysics schemes investigated, the Goddard and the Stony-Brook University schemes performed the best regardless of the choice of reanalysis. Reconstructed historical precipitation with the optimized configuration showed better accuracies during the wet season than the dry season. With respect to simulations with CFSR, it was found that the optimized configuration for AR precipitation can be used for long-term reconstruction with small biases. However, systematic biases in the reanalysis datasets may still lead to uncertainties in downscaling precipitation in a different season with a single configuration.

Long-term trend analysis on total and extreme precipitation over Shasta Dam watershed.

California's interconnected water system is one of the most advanced water management systems in the world, and understanding of long-term trends in atmospheric and hydrologic behavior has increasingly being seen as vital to its future well-being. Knowledge of such trends is hampered by the lack of long-period observation data and the uncertainty surrounding future projections of atmospheric models. This study examines historical precipitation trends over the Shasta Dam watershed (SDW), which lies upstream of one of the most important components of California's water system, Shasta Dam, using a dynamical downscaling methodology that can produce atmospheric data at fine time-space scales. The Weather Research and Forecasting (WRF) model is employed to reconstruct 159years of long-term hourly precipitation data at 3km spatial resolution over SDW using the 20th Century Reanalysis Version 2c dataset. Trend analysis on this data indicates a significant increase in total precipitation as well as a growing intensity of extreme events such as 1, 6, 12, 24, 48, and 72-hour storms over the period of 1851 to 2010. The turning point of the increasing trend and no significant trend periods is found to be 1940 for annual precipitation and the period of 1950 to 1960 for extreme precipitation using the sequential Mann-Kendall test. Based on these analysis, we find the trends at the regional scale do not necessarily apply to the watershed-scale. The sharp increase in the variability of annual precipitation since 1970s is also detected, which implies an increase in the occurrence of extreme wet and dry conditions. These results inform long-term planning decisions regarding the future of Shasta Dam and California's water system.

Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations.

Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach lies in its ability to consider the underlying flow dynamics through not only from the governing equations under consideration but also from the initial and boundary conditions, hence allowing to obtain perfect self-similarity in different time and space scales. The proposed methodology can be a valuable tool in obtaining self-similar flow dynamics under preferred level of detail, which can be represented by initial and boundary value problems under specific assumptions.

Assessment of the effects of multiple extreme floods on flow and transport processes under competing flood protection and environmental management strategies.

Extreme floods are regarded as one of the most catastrophic natural hazards and can result in significant morphological changes induced by pronounced sediment erosion and deposition processes over the landscape. However, the effects of extreme floods of different return intervals on the floodplain and river channel morphological evolution with the associated sediment transport processes are not well explored. Furthermore, different basin management action plans, such as engineering structure modifications, may also greatly affect the flood inundation, sediment transport, solute transport and morphological processes within extreme flood events. In this study, a coupled two-dimensional hydrodynamic, sediment transport and morphological model is applied to evaluate the impact of different river and basin management strategies on the flood inundation, sediment transport dynamics and morphological changes within extreme flood events of different magnitudes. The 10-year, 50-year, 100-year and 200-year floods are evaluated for the Lower Cache Creek system in California under existing condition and a potential future modification scenario. Modeling results showed that select locations of flood inundation within the study area tend to experience larger inundation depth and more sediment is likely to be trapped in the study area under potential modification scenario. The proposed two dimensional flow and sediment transport modeling approach implemented with a variety of inflow conditions can provide guidance to decision-makers when considering implementation of potential modification plans, especially as they relate to competing management strategies of large water bodies, such as the modeling area in this study.

Fish-protection devices at unscreened water diversions can reduce entrainment: evidence from behavioural laboratory investigations.

Diversion (i.e. extraction) of water from rivers and estuaries can potentially affect native wildlife populations if operation is not carefully managed. For example, open, unmodified water diversions can act as a source of injury or mortality to resident or migratory fishes from entrainment and impingement, and can cause habitat degradation and fragmentation. Fish-protection devices, such as exclusion screens, louvres or sensory deterrents, can physically or behaviourally deter fish from approaching or being entrained into water diversions. However, empirical assessment of their efficacy is often lacking or is investigated only for particular economically or culturally important fishes, such as salmonids. The Southern population of anadromous green sturgeon (Acipenser medirostris) is listed as threatened in California, and there is a high density of water diversions located within their native range (the Sacramento-San Joaquin watershed). Coupled with their unique physiology and behaviour compared with many other fishes native to California, the green sturgeon is susceptible to entrainment into diversions and is an ideal species with which to study the efficacy of mitigation techniques. Therefore, we investigated juvenile green sturgeon (188-202 days post-hatch) in the presence of several fish-protection devices to assess behaviour and entrainment risk. Using a large experimental flume (∼500 kl), we found that compared with an open diversion pipe (control), the addition of a trash-rack box, louvre box, or perforated cylinder on the pipe inlet all significantly reduced the proportion of fish that were entrained through the pipe (P = 0.03, P = 0.028, and P = 0.028, respectively). Likewise, these devices decreased entrainment risk during a single movement past the pipe by between 60 and 96%. These fish-protection devices should decrease the risk of fish entrainment during water-diversion activities.

Unscreened water-diversion pipes pose an entrainment risk to the threatened green sturgeon, Acipenser medirostris.

Over 3,300 unscreened agricultural water diversion pipes line the levees and riverbanks of the Sacramento River (California) watershed, where the threatened Southern Distinct Population Segment of green sturgeon, Acipenser medirostris, spawn. The number of sturgeon drawn into (entrained) and killed by these pipes is greatly unknown. We examined avoidance behaviors and entrainment susceptibility of juvenile green sturgeon (35±0.6 cm mean fork length) to entrainment in a large (>500-kl) outdoor flume with a 0.46-m-diameter water-diversion pipe. Fish entrainment was generally high (range: 26-61%), likely due to a lack of avoidance behavior prior to entering inescapable inflow conditions. We estimated that up to 52% of green sturgeon could be entrained after passing within 1.5 m of an active water-diversion pipe three times. These data suggest that green sturgeon are vulnerable to unscreened water-diversion pipes, and that additional research is needed to determine the potential impacts of entrainment mortality on declining sturgeon populations. Data under various hydraulic conditions also suggest that entrainment-related mortality could be decreased by extracting water at lower diversion rates over longer periods of time, balancing agricultural needs with green sturgeon conservation.