Non-Newtonian oscillatory boundary layer, a numerical approach

1986 ◽  
Vol 51 (6) ◽  
pp. 1240-1258 ◽  
Author(s):  
Ondřej Wein ◽  
Václav Sobolík
Keyword(s):  
Numerical Approach ◽  
Stress Fields ◽  
Low Flow ◽  
Flow Index ◽  
Differential Formulation ◽  
Oscillatory Boundary Layer ◽  
Flow Enhancement ◽  
Pseudoplastic Liquid ◽  
Oscillating Plate ◽  
Low Flow Index

Differential schemes have been constructed by using the integro-differential formulation of the equation of motion in stresses. The problem of periodic flow of the purely-viscous non-Newtonian liquid on a harmonically oscillating plate has been solved numerically for extremally high values of the Reynolds number. The velocity and stress fields as well as estimates of the flow enhancement E are given for the quasi-oscillatory regime, Fr → ∞, for the pseudoplastic liquid with the extremally low flow index, n = 0.15.

scholarly journals Hydrological characterization of watersheds in the Blue Nile Basin, Ethiopia

2011 ◽  
Vol 15 (1) ◽  
pp. 11-20 ◽  
Author(s):  
S. G. Gebrehiwot ◽  
U. Ilstedt ◽  
A. I. Gärdenas ◽  
K. Bishop
Keyword(s):  
Land Use ◽  
Soil Type ◽  
Low Flow ◽  
Flow Index ◽  
Nile Basin ◽  
Grazing Land ◽  
Blue Nile ◽  
Low Flows ◽  
Blue Nile Basin ◽  
Low Flow Index

Abstract. Thirty-two watersheds (31–4350 km2), in the Blue Nile Basin, Ethiopia, were hydrologically characterized with data from a study of water and land resources by the US Department of Interior, Bureau of Reclamation (USBR) published in 1964. The USBR document contains data on flow, topography, geology, soil type, and land use for the period 1959 to 1963. The aim of the study was to identify watershed variables best explaining the variation in the hydrological regime, with a special focus on low flows. Moreover, this study aimed to identify variables that may be susceptible to management policies for developing and securing water resources in dry periods. Principal Component Analysis (PCA) and Partial Least Square (PLS) were used to analyze the relationship between five hydrologic response variables (total flow, high flow, low flow, runoff coefficient, low flow index) and 30 potential explanatory watershed variables. The explanatory watershed variables were classified into three groups: land use, climate and topography as well as geology and soil type. Each of the three groups had almost equal influence on the variation in hydrologic variables (R2 values ranging from 0.3 to 0.4). Specific variables from within each of the three groups of explanatory variables were better in explaining the variation. Low flow and low flow index were positively correlated to land use types woodland, dense wet forest and savannah grassland, whereas grazing land and bush land were negatively correlated. We concluded that extra care for preserving low flow should be taken on tuffs/basalts which comprise 52% of the Blue Nile Basin. Land use management plans should recognize that woodland, dense wet forest and savannah grassland can promote higher low flows, while grazing land diminishes low flows.

scholarly journals Smooth regional estimation of low-flow indices: physiographical space based interpolation and top-kriging

2011 ◽  
Vol 15 (3) ◽  
pp. 715-727 ◽  
Author(s):  
S. Castiglioni ◽  
A. Castellarin ◽  
A. Montanari ◽  
J. O. Skøien ◽  
G. Laaha ◽  
...  
Keyword(s):  
Spatial Interpolation ◽  
Central Italy ◽  
Low Flow ◽  
Flow Index ◽  
Ungauged Basins ◽  
Low Flows ◽  
Interpolation Techniques ◽  
Point Data ◽  
Leave One Out ◽  
Low Flow Index

Abstract. Recent studies highlight that spatial interpolation techniques of point data can be effectively applied to the problem of regionalization of hydrometric information. This study compares two innovative interpolation techniques for the prediction of low-flows in ungauged basins. The first one, named Physiographical-Space Based Interpolation (PSBI), performs the spatial interpolation of the desired streamflow index (e.g., annual streamflow, low-flow index, flood quantile, etc.) in the space of catchment descriptors. The second technique, named Topological kriging or Top-kriging, predicts the variable of interest along river networks taking both the area and nested nature of catchments into account. PSBI and Top-kriging are applied for the regionalization of Q355 (i.e., a low-flow index that indicates the streamflow that is equalled or exceeded 355 days in a year, on average) over a broad geographical region in central Italy, which contains 51 gauged catchments. The two techniques are cross-validated through a leave-one-out procedure at all available gauges and applied to a subregion to produce a continuous estimation of Q355 along the river network extracted from a 90m elevation model. The results of the study show that Top-kriging and PSBI present complementary features. Top-kriging outperforms PSBI at larger river branches while PSBI outperforms Top-kriging for headwater catchments. Overall, they have comparable performances (Nash-Sutcliffe efficiencies in cross-validation of 0.89 and 0.83, respectively). Both techniques provide plausible and accurate predictions of Q355 in ungauged basins and represent promising opportunities for regionalization of low-flows.

scholarly journals Which objective function to calibrate rainfall–runoff models for low-flow index simulations?

2017 ◽  
Vol 62 (7) ◽  
pp. 1149-1166 ◽  
Author(s):  
Florine Garcia ◽  
Nathalie Folton ◽  
Ludovic Oudin
Keyword(s):  
Objective Function ◽  
Low Flow ◽  
Flow Index ◽  
Rainfall Runoff ◽  
Low Flow Index

A Principal Component Regression Method for Estimating Low Flow Index

2010 ◽  
Vol 24 (11) ◽  
pp. 2553-2566 ◽  
Author(s):  
Saeid Eslamian ◽  
Mehdi Ghasemizadeh ◽  
Monireh Biabanaki ◽  
Mansoor Talebizadeh
Keyword(s):  
Principal Component Regression ◽  
Principal Component ◽  
Regression Method ◽  
Low Flow ◽  
Flow Index ◽  
Low Flow Index

Non-Newtonian oscillatory layer flow, approximate solution

1979 ◽  
Vol 44 (10) ◽  
pp. 2908-2914 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Approximate Solution ◽  
Galerkin Method ◽  
Horizontal Plane ◽  
Oscillatory Flow ◽  
Oscillatory Boundary Layer ◽  
Layer Flow ◽  
Pseudoplastic Liquid ◽  
The Galerkin Method

The problem of the oscillatory flow of pseudoplastic liquid in vicinity of the infinitely long horizontal plane is formulated in stresses. For Re i.e. for conditions of oscillatory boundary layer the problem is solved approximately by the Galerkin method.

scholarly journals Multiple causes of nonstationarity in the Weihe annual low-flow series

2018 ◽  
Vol 22 (2) ◽  
pp. 1525-1542 ◽  
Author(s):  
Bin Xiong ◽  
Lihua Xiong ◽  
Jie Chen ◽  
Chong-Yu Xu ◽  
Lingqi Li
Keyword(s):  
Frequency Analysis ◽  
Driving Forces ◽  
Potential Evapotranspiration ◽  
Aridity Index ◽  
Base Flow ◽  
Low Flow ◽  
Distribution Model ◽  
Flow Index ◽  
Explanatory Variables ◽  
Distribution Parameters

Abstract. Under the background of global climate change and local anthropogenic activities, multiple driving forces have introduced various nonstationary components into low-flow series. This has led to a high demand on low-flow frequency analysis that considers nonstationary conditions for modeling. In this study, through a nonstationary frequency analysis framework with the generalized linear model (GLM) to consider time-varying distribution parameters, the multiple explanatory variables were incorporated to explain the variation in low-flow distribution parameters. These variables are comprised of the three indices of human activities (HAs; i.e., population, POP; irrigation area, IAR; and gross domestic product, GDP) and the eight measuring indices of the climate and catchment conditions (i.e., total precipitation P, mean frequency of precipitation events λ, temperature T, potential evapotranspiration (EP), climate aridity index AIEP, base-flow index (BFI), recession constant K and the recession-related aridity index AIK). This framework was applied to model the annual minimum flow series of both Huaxian and Xianyang gauging stations in the Weihe River, China (also known as the Wei He River). The results from stepwise regression for the optimal explanatory variables show that the variables related to irrigation, recession, temperature and precipitation play an important role in modeling. Specifically, analysis of annual minimum 30-day flow in Huaxian shows that the nonstationary distribution model with any one of all explanatory variables is better than the one without explanatory variables, the nonstationary gamma distribution model with four optimal variables is the best model and AIK is of the highest relative importance among these four variables, followed by IAR, BFI and AIEP. We conclude that the incorporation of multiple indices related to low-flow generation permits tracing various driving forces. The established link in nonstationary analysis will be beneficial to analyze future occurrences of low-flow extremes in similar areas.

scholarly journals A method for low-flow estimation at ungauged sites: a case study in Wallonia (Belgium)

2013 ◽  
Vol 17 (4) ◽  
pp. 1319-1330 ◽  
Author(s):  
M. Grandry ◽  
S. Gailliez ◽  
C. Sohier ◽  
A. Verstraete ◽  
A. Degré
Keyword(s):  
Return Period ◽  
Management Practice ◽  
Global Model ◽  
Low Flow ◽  
Quality Analysis ◽  
Flow Index ◽  
Physical Parameters ◽  
Integrated Water Management ◽  
Explanatory Variables ◽  
Ungauged Sites

Abstract. Well-integrated water management can notably require estimating low flows at any point of a river. Depending on the management practice, it can be needed for various return periods. This is seldom addressed in the literature. This paper shows the development of a full analysis chain including quality analysis of gauging stations, low-flow frequency analysis, and building of a global model to assess low-flow indices on the basis of catchment physical parameters. The most common distributions that fit low-flow data in Wallonia were two-parameter lognormal and gamma. The recession coefficient and percolation were the most explanatory variables, regardless of the return period. The determination coefficients of the models ranged from 0.51 to 0.67 for calibration and from 0.61 to 0.80 for validation. The regression coefficients were found to be linked to the return period. This was used to design a complete equation that gives the low-flow index based on physical parameters and the desired return period (in a 5 to 50 yr range). The interest of regionalisation and the development of regional models are also discussed. Four homogeneous regions are identified, but to date the global model remains more robust due to the limited number of 20-yr-long gauging stations. This should be reconsidered in the future when enough data will be available.

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