Sea surface temperature variability off north-west Africa: 1981-1989

A temporal and spatial Empirical Orthogonal Function (EOF) analysis has been performed on monthly maximum sea surface temperature (SST) satellite data over eight years (July 1981-August 1989) to examine the SST patterns of variability off north-west Africa. The first temporal EOF mode (75 per cent) represents the cooling and warming cycle over the region. The temporal amplitudes show an interannual variability with 1982 summer temperatures abnormally much colder, immediately preceding the largest El Nino phenomenon of the century. The second temporal mode (9 per cent) distinguishes a large-scale behaviour of the northern and southern areas of the region, the two areas being out of phase presumably related to the variability of the wind field. The first spatial EOF mode (66 per cent), which resembles the mean of all images, is stronger in fall, with a smaller second maximum at the beginning of spring. The second spatial mode (10 per cent) shows the coastal upwelling region where a seaward extension of upwelled water around 300km offshore is observed off Cape Blanc. All the modes show complex eastern boundary dynamics with different regimes north and south of Cape Blanc. The Cape Blanc vicinity must have some interesting dynamics with a sharp boundary evident in all the modes. Only these two first temporal and spatial EOF modes are significantly above the noise level. The EOF method is efficient in compressing monthly SST satellite imagery off north-west Africa, with a great percentage of the total variance being accounted by only two modes.     

Seasonal and temporal study of the northwest African upwelling system

The upwelling index (UI) obtained from sea surface temperature (SST) images for the period 1987–2006 and remote sensing wind stress were used to analyse the features of the coastal upwelling region off northwest Africa. The seasonal distribution shows a persistent upwelling throughout the year from 20° N to 33° N, seasonal behaviour from 12° N to south of 20° N, and an almost total lack of upwelling throughout the year from 5° N to 12° N. The major centres of active upwelling are located around Cape Ghir, Cape Juby and Cape Blanc. The UI shows an intensification of the upwelling system off northwest Africa during the 20-year period while the alongshore wind stress remains almost stable. During this period, upwelled waters off Cape Blanc have increased their offshore spreading.     

Chlorophyll variability in the northeastern Gulf of Mexico

Changes in chlorophyll concentration distribution in surface waters of the northeastern Gulf of Mexico (NEGOM) were examined using satellite and in situ data collected between November 1997 and August 2000. The patterns of chlorophyll distribution derived from in situ data consistently matched the satellite observations, even though the satellite-derived concentrations in coastal and offshore waters influenced by rivers were overestimated by the standard satellite data processing algorithms. River discharge and wind-driven upwelling were the major factors influencing surface chlorophyll-a variability for inshore regions. High in situ chlorophyll-a concentrations (≥1 mg m^?3) occurred inshore and particularly near major river mouths during the summer seasons of 1998, 1999 and 2000. Plumes of Mississippi River water extended offshore to the southeast of the delta over distances >500 km from the river delta for maximum periods of 14 weeks between May and September every year and could reach the Florida Keys in certain years. The offshore transport of the plume was initiated by eastward or southeastward winds and then by separate anticyclonic eddies located southeast of the Mississippi delta and nearby shelf every year. Chlorophyll concentrations during the winter to spring transition in 1998 off Escambia, Choctawhatchee, Apalachicola and Suwannee Rivers and off Tampa Bay were up to 4 times higher than during the same periods in 1999 and 2000. This was related to higher freshwater discharge during the 1997–1998 winter–spring transition, coinciding with an El Niño–Southern Oscillation event, and to the unusually strong upwelling observed along the coast in spring 1998.     

Validation of ERS-2 SAR offshore wind-speed maps in the North Sea

Wind maps are retrieved from ERS-2 Synthetic Aperture Radar (SAR) scenes by the CMOD-IFR2 and CMOD4 algorithms for 61 cases at the Horns Rev site in the North Sea and compared to meteorological in situ observations from a mast located 14?km offshore. The in situ data are corrected for flow distortion and sea-level changes prior to validating the SAR wind maps. The SAR wind maps are area-averaged by a simple footprint method assuming neutral stability and with three nonlinear weighting footprint methods including correction for stability. From a physical point of view, the latter is more correct. However, between in situ and SAR-derived wind-speed estimates comparison results of the nonlinear footprint values are statistically less correlated (R ²=0.73–0.77) and the standard error (SE) is larger (>1.5?m?s^?1) than results from the simple footprint (R ²=0.78–0.80 and SE=1.3?m?s^?1). The results are found with wind direction determined from wind streaks in the SAR images by Fast Fourier Transform. Using in situ wind direction as input to the CMOD-IFR2 and CMOD4 algorithms yields even better linear regression results, e.g. for the simple footprint method R ²=0.88 and SE=0.9?m?s^?1. SAR wind maps may be useful for mapping of future offshore wind resources.     

Parameterization of water component absorption in an inland eutrophic lake and its seasonal variability: a case study in Lake Taihu

Water spectral absorption characteristics of eutrophic lakes are largely different from those of ocean and coastal waters. We therefore studied them with the aim of establishing an analytical model for inland water colour, to be used in remote sensing. Field measurements were carried out on 16 and 17 August 2006 (summer), 5 and 6 November 2006 (winter), and 29 and 30 March 2007 (spring) at 15 stations in northern Lake Taihu (China). Chromophoric dissolved organic matter (CDOM) absorption coefficients (a _CDOM) are higher in summer than in spring and winter, with the ratios of a _CDOM in spring, summer and winter being approximately 1 : 4.0 : 1.2 at both UV‐C and UV‐B. The spectral slope S _CDOM values change with wavelength and season, and covary with CDOM concentration, as shown by regression analysis. For the CDOM absorption spectrum in the wavelength region 500–700 nm (important for water colour remote sensing), a linear method simulates better than an exponential method. Seasonal variations in non‐algal particulate (NAP) absorption (a _NAP) at blue, green and red wavelengths show better consistency, in the order winter>spring>summer. The average S _NAP is 0.0065±0.0009 nm^?1, which is lower than that in other types of waters. Phytoplankton absorption (a _ph) peak height changes with the season, with the pattern summer>winter>spring, and phytoplankton absorption spectra can be expressed with high accuracy by a quadratic model. CDOM absorption contributions in the three seasons are low compared to phytoplankton and NAP.     

Spatio-temporal distribution of chlorophyll-a concentration derived from MODIS satellite remote-sensing and in situ observations in Sanya Bay,China

This study examined satellite chlorophyll-a (chl-a) concentration and in situ observations in Sanya Bay (SYB). In situ observation of chl-a was conducted four times per year at 12 sampling stations in SYB from January 2004 to October 2008. Monthly satellite chl-a was derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) during 2000–2012. This study compared satellite chl-a values to in situ measurements in SYB. The two data sets match well in the whole region except for two estuaries. Results show that the average in situ chl-a was 1.49 mg m^?3 in SYB. Chl-a was relatively higher (>2 mg m^?3) and more variable in coastal areas, with a tendency to decrease offshore (<0.4 mg m^?3). The chl-a level in summer displayed obviously vertical stratification, with higher values at the bottom and lower values at the surface. Analysis of monthly mean chl-a showed that the highest level (>2 mg m^?3) appeared in December, with the lowest in March (<1 mg m^?3). The gradients are ranked winter, autumn, summer and spring. There was higher chl-a in autumn and winter, which may be associated with the stronger wind monsoon then. Annual mean chl-a from 2000 to 2012 varied from 1.17 to 2.05 mg m^?3, with the minimum in 2001 and the maximum in 2005. The chl-a level presented a roughly increasing tendency from 2000 to 2012, which may be related to the increasing nutrients associated with the development of tourism and fishery.     

Detection of total suspended sediments in the North Sea using AVHRR and ship data

This study reports on a combined investigation between in situ measurements of total suspended sediments, collected by ship, and remotely sensed data provided by the Advanced Very High Resolution Radiometer (AVHRR) during the winter-summer period of 1989. It is meant to be a case study stating the problems inherent to coastal waters and proposing a methodology to understand them. Ship and satellite data are compared in order to detect suspended sediments in case 2 waters in the North Sea through a linear regression analysis. The results show a wide range of coefficient of determination (R²) values. The highest values correspond to summer dates, while the lowest belonged to the winter and spring period. It was found that for the summer dates the relatively still atmospheric and water conditions were suitable for comparison with satellite data providing good values of R². In winter and spring, unsettled sea water conditions complicated the comparison of the data. It can be concluded that the seasonal stratification of the water column during summer time allows a better correlation between in situ and remotely sensed data than the typically well-mixed waters during winter.     

UAS imaging-based decision tools for arid winter wheat and irrigated potato production management

Small unmanned aerial systems (UAS) are gaining global attention for rapid image-based decision making in agricultural production. In this study, the aim was to evaluate UAS-based imagery for rapid assessment of wheat winter survival and spring stand in winter wheat production and crop necrosis in potato production. Both are critical aspects of field (arid) and row (irrigated) crop farming practices. Aerial images from 97 hard and 352 soft single nucleotide polymorphism winter wheat plots, and 32 potato field plots (with 1 and 2 years of green manure applications) were acquired using a multi-band imaging sensor integrated with UAS. The UAS-based imagery was useful in evaluating winter wheat plant winter survival and spring stand, with Pearson correlation coefficient (r) in the range 0.60–0.82 between imagery and ground reference data. Similarly, the image-based potato field necrosis assessment showed a strong relationship with ground reference data (r = 0.93 and 0.88 for 1 and 2 years of green manure application, respectively). Overall, UAS imagery provided quantifiable, timely, and unbiased field data with high spatial resolution (about 2.3 cm/pixel for images acquired at 100 m altitude) that can aid in field and row crop production decision making.     

Thermal fronts of the southern South China Sea from satellite and in situ data

The major goal of this study was to find match-ups between thermal fronts mapped from satellite sea surface temperature (SST) imagery and from in situ data in the southern South China Sea (SSCS), using 11 ship surveys conducted by the South China Sea Institute of Oceanology (SCSIO) between 1987 and 1999. Fronts were automatically detected by the Cayula–Cornillon multi-image edge detection algorithm (CCA) applied to satellite-derived maps of the Advanced Very High Resolution Radiometer (AVHRR) SST obtained from the Pathfinder project (8364 twice-daily global fields with 9 km resolution between 1985 and 1996). Twice-daily near-instant frontal maps were composited without any averaging or smoothing to produce individual monthly frontal maps covering the period from January 1985 through December 1996 (144 maps in total). Although the SSCS is a tropical sea with little SST difference between water masses, the CCA turned out to be an effective tool for front mapping in the SSCS. Out of the 11 ship surveys analysed in this study, four surveys produced satisfactory match-ups. The percentage of match-ups is considered reasonably high given that (1) ship surveys were not optimized to cross fronts, therefore most in situ sections missed fronts; (2) satellite measurements of SST with AVHRR are hampered by cloudiness, therefore satellite-derived frontal maps might miss some fronts masked by persistent cloudiness. Fronts are more distinct in winter, when cross-frontal SST gradients are enhanced. From oceanographic vertical sections and horizontal maps, fronts are much sharper in the subsurface layer (represented here by 50 m level). Nonetheless, the CCA successfully detected SST fronts with a cross-frontal step as small as 1°C.     

Long-term trends of total ozone content over mid-latitudes of the Northern Hemisphere

Dynamic climatic normals and long-term trends of total ozone in the mid-latitudes of the Northern hemisphere (30°N–60°N) have been determined using data from satellite observations for the period of 1978–2017. The annual course of total ozone is shown as changing over the various regions during the period of observations. The specific features of alteration in the state of the ozone layer are discussed depending on latitude and longitude. Thus, a general increase in total ozone in winter, an increase in spring (with the exception of the northern latitudes of Europe, Asia, and Pacific), and a continuing decrease in summer (with the exception of the northern latitudes of America) during the last 17 years is revealed. The long-term trends of total ozone for different regions and latitude zones (30°N–40°N, 40°N–50°N, and 50°N–60°N) are given depending on season.     

Augmenting satellite precipitation estimation with lightning information

We have used lightning information to augment the precipitation estimation from remotely sensed imagery using an artificial neural network cloud classification system (PERSIANN-CCS). Co-located lightning data are used to segregate cloud patches, segmented from Geostationary Operational Environmental Satellite (GOES)-12 infrared (IR) data, into either electrified patches (ECPs) or nonelectrified patches (NECPs). A set of features is extracted separately for the ECPs and NECPs. Features for the ECPs include a new feature corresponding to the number of flashes that occur within a 15 minute window around the time of the nominal scan of the satellite IR images of the cloud patches. The cloud patches are classified and clustered using a self-organizing maps (SOM) neural network. Then, brightness temperature and rain rate (T–R) relationships are derived for different clusters. Rain rates are estimated for the cloud patches based on their representative (T–R) relationship. The equitable threat scores (ETS) of the daily and hourly precipitation estimates at a range of rain rate thresholds show that incorporating lightning information can improve categorical precipitation estimation in the winter and fall seasons. In the winter, the ETS improvement is almost 15% for the daily and 12% for the hourly rainfall estimates (at thresholds below 15 mm hour^?1). During the same period, there is also a drop in the false alarm ratio (FAR) and a corresponding increase in the probability of detection (POD) at most threshold levels. During the summer and spring seasons, no categorical significant improvements have been noted, except for the BIAS scores for the hourly rainfall estimates at higher thresholds (above 5 mm hour^?1) in the summer months. A quantitative evaluation in terms of the root mean squared error (RMSE) and correlation coefficient (CORR) shows that the incorporation of lightning data does improve rainfall estimation over all seasons with the most improvement (around 11–13% CORR improvement) occurring during the winter. We speculate that during the winter, more of the ice processes are packed into a thinner stratiform layer with lower cloud tops and freezing levels. Hence, more of the ice contributes to precipitation on the ground. We also expect that information from lightning, related to the ice microphysics processes, provides surrogate information about the rain rate.     

Collapse of micrometer-sized cavitation bubbles near a rigid boundary

The interaction of cavitation bubbles with a rigid boundary and its dependence on the distance between bubble and boundary is investigated experimentally. Individual cavitation bubbles, with a maximum radius of 150?μm, are generated by using pulsed high-intensity focused ultrasound. Observations are made with high-speed photography with framing rates of up to 200?million frames per second and exposure time of 5?ns, and the spatial resolution is in the order of a few micrometers. The significant parameter of this study is the non-dimensional stand-off parameter, γ, defined as the distance between the ultrasound focus and the rigid boundary scaled by the maximum bubble radius. Both the velocity of the liquid jet developed during bubble collapse and the maximum pressure of the shock wave emitted during bubble rebound show a minimum for γ?≈?1 and a constant value for γ?>?3. The maximum jet velocity is slightly smaller than the corresponding values obtained in the case of millimeter-sized bubbles and ranges from 80?m/s (at γ?≈?1) to 130?m/s (for γ?>?3). No jet formation was observed for γ?>?3. The shock wave pressure, measured at a distance of 5?mm from the emission center, ranges from 0.2?MPa (at γ?≈?1) to 0.65?MPa (for γ?>?3). These values are an order of magnitude smaller than those obtained in the case of millimeter-sized bubbles. The shock wave duration is almost independent of γ at a value of about 75?ns. For large γ values (γ?>?3), a large percentage of the bubble energy (up to 60?%) is transformed into the mechanical energy of the shock wave emitted during bubble rebound but, for γ?≈?1, the conversion efficiency decreases to 30?%. Independent of the relative distance between bubble and rigid boundary, the shock pressure decays proportionally to r ^?1 with increasing distance r from the emission center. The results are discussed with respect to cavitation damage and collateral effects in pulsed high-intensity focused ultrasound surgery.     

Annual and seasonal variations in tropospheric ozone concentrations around Varanasi

This study examines the annual, seasonal and diurnal variations in the ambient concentrations of ozone at a suburban site of Varanasi, India, during 2002–2006. Prominent seasonal variations in ozone concentrations were recorded. Ozone concentrations were higher during the warmer months. Daytime 12‐hourly mean monthly ozone concentrations varied from 45.18 to 62.35 ppb during summer, from 28.55 to 44.25 ppb during winter and from 24 to 43.85 ppb during the rainy season from 2002 to 2006. Distinct diurnal variations in ozone concentrations were also observed. Daytime maxima in ozone concentration were recorded between 1200 and 1400 h, whereas morning and evening hours showed lower concentrations of ozone. Ozone concentrations in the atmosphere depended on several meteorological factors. Monthly average ozone concentration was significantly correlated with maximum temperature (p<0.001) and mean monthly temperature (p<0.05), maximum relative humidity (p<0.001), minimum relative humidity (p<0.001) and mean monthly relative humidity (p<0.001), and sunshine hours (p<0.001). Ozone concentrations in the ambient air have shown an increase in the past decade that was more in the winter and rainy seasons than in the summer. This study suggests that ozone concentrations around Varanasi were sufficiently high to cause significant damage to agricultural production. The present work can be extended to a regional level by incorporating modelling studies using recent remote sensing tools.     

State operators on GMV algebras

Flaminio and Montagna recently introduced state MVMV algebras as MVMV algebras with an internal state in the form of a unary operation. Di Nola and Dvurečenskij further presented a stronger variation of state MVMV algebras called state-morphism MVMV algebras. In the paper we present state GMVGMV algebras and state-morphism GMVGMV algebras which are non-commutative generalizations of the mentioned algebras.     

Estimating NO2 dry deposition using satellite data in eastern China

The spatial and temporal characters of ground-level NO₂ concentration over eastern China were retrieved from the monthly averaged tropospheric NO₂ column densities from Global Ozone Monitoring Experiment (GOME, data used in this study are from April 1996 to December 2002) and Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY, data used in this study are from January 2003 to December 2011) measurements. Together with the NO₂ concentration and the dry deposition velocity maps of eastern China, the fluxes of NO₂ dry deposition were estimated for three specific regions. The results indicated that the surface NO₂ concentration in eastern China increased dramatically from 1996 to 2011, and it showed distinct regional and seasonal variational characteristics. The highest concentration occurred in winter while the lowest occurred in summer. There was also variation in the spatial distribution with the peak value of NO₂ concentration appearing in the plains of north China (R1), the Yangtze River delta (R2), and the Pearl River delta (R3). A sharp increase of NO₂ concentration appeared in R1 and R2, while it was invariant or showed an obvious decrease in R3 during the period of 1996–2011. Furthermore, we compared the NO₂ dry deposition fluxes estimated from the ground-level NO₂ concentration and the dry deposition velocity of NO₂ with the mass concentration of NO₂ dry deposition that, measured from the control experiments and by consulting the published literature, showed a significant correlation (P < 0.001) and had a high R value (R = 0.73). The results also indicated that the NO₂ dry deposition fluxes increased over eastern China, with a maximum value of 8.25 kg N ha^?1 yr^?1 from 1996 to 2011 in R3, while the value was characterized by fluxes of less than 2.27 kg N ha^?1 yr^?1 in R2. When comparing the NO₂ dry deposition over different land covers, the values distinctly peaked over artificial surfaces and evergreen forests, with maximum values of 10.07 and 9.49 kg N ha^?1 yr^?1 in R1, 5.05 and 4.94 kg N ha^?1 yr^?1 in R2, and 20.95 and 23.15 kg N ha^?1 yr^?1 in R3. However, the lowest value of NO₂ dry deposition flux appeared over needleleaf forests, with 0.53, 0.24, and 1.29 kg N ha^?1 yr^?1 for R1, R2, and R3, respectively.     

A ground‐validated NDVI dataset for monitoring vegetation dynamics and mapping phenology in Fennoscandia and the Kola peninsula

An NDVI dataset covering Fennoscandia and the Kola peninsula was created for vegetation and climate studies, using Moderate Resolution Imaging Spectroradiometer 16‐day maximum value composite data from 2000 to 2005. To create the dataset, (1) the influence of the polar night and snow on the NDVI values was removed by replacing NDVI values in winter with a pixel‐specific NDVI value representing the NDVI outside the growing season when the pixel is free of snow; and (2) yearly NDVI time series were modelled for each pixel using a double logistic function defined by six parameters. Estimates of the onset of spring and the end of autumn were then mapped using the modelled dataset and compared with ground observations of the onset of leafing and the end of leaf fall in birch, respectively. Missing and poor‐quality data prevented estimates from being produced for all pixels in the study area. Applying a 5 km×5 km mean filter increased the number of modelled pixels without decreasing the accuracy of the predictions. The comparison shows good agreement between the modelled and observed dates (root mean square error = 12 days, n = 108 for spring; root mean square error = 10 days, n = 26, for autumn). Fennoscandia shows a range in the onset of spring of more than 2 months within a single year and locally the onset of spring varies with up to one month between years. The end of autumn varies by one and a half months across the region. While continued validation with ground data is needed, this new dataset facilitates the detailed monitoring of vegetation activity in Fennoscandia and the Kola peninsula.     

Comparison of total ozone column observations from space-borne Ozone Monitoring Instrument with ground-based Dobson Ozone Spectrophotometer measurements at an urban location in Indo-Gangetic Basin

This article presents a comparison analysis of OMIT (Ozone Monitoring Instrument retrieved overpass total ozone column (TOC)), and DOST (Dobson Ozone Spectrophotometer observed TOC) over Delhi during a period from October 2004 to June 2011. Megacity Delhi, located in Indo-Gangetic Basin, is an important site for comparison of ground-based and satellite retrieved TOCs due to significant anthropogenic emissions of ozone precursors, large shift in seasons, and large-scale crop residue burning in the region. DOST and OMIT data show an overall bias of 3.07% and significant correlation with coefficient of determination R² = 0.73. Large seasonal fluctuations in the biases and correlations have been observed ranging from 2.46% (winter) to 3.82% (spring), and R² = 0.84 (winter) to R² = 0.09 (summer), respectively. The large biases are attributed to changes in temperature, cloud cover, pollutants emissions from urban area, and crop-residue burning events. We also find notable variations in correlations between the datasets due to the varying burden of absorbing aerosols from open field crop-residue burning. The R² has changed from 0.67 (for aerosol optical depth, AOD 1.5–3.5) to 0.77 (for AOD 0–0.99). The dependence of the bias on solar zenith angle, cloud fraction, and satellite distance is also discussed. A simple linear regression analysis is applied to check the linkage between DOST and OMIT. The influence of atmospheric air temperature and relative humidity on OMIT at different pressure levels between 1000 and 20 hPa has been discussed.     

The regional impacts of climate change on coastal environments and the aquaculture of Japanese scallops in northeast Asia: case studies from Dalian,China, and Funka Bay,Japan

Climate changes affect coastal environments and aquaculture, threatening food security and economic growth. Japanese scallop (Mizuhopecten yessoensis) culture is economically important for the coastal communities of Dalian, China, and Funka Bay, Japan. In this study, we combined satellite remote-sensing data, in situ observations, and a suitable aquaculture site selection model to explore the interactions between marine environments and climate variability over a recent 10-year period (2003–2012). Our selection of appropriate zones in these two Far Eastern regions and our analyses of climatic event (Arctic Oscillation (AO), winter East Asian monsoon (EAM), and El Niño/La Niña Southern Oscillation (ENSO)) and meteorological (precipitation, temperature, and wind) data allowed us to determine the impacts of climate change on regional coastal environments and prospects for scallop aquaculture. These analyses showed that AO and EAM strongly influenced the aquaculture areas on the Dalian coast through their effects on temperature during winter. We also determined that wind was the main driving force behind regional environmental changes during spring. Conversely, ocean conditions and suitable areas in Funka Bay changed rapidly relative to oceanic and atmospheric circulation. In Funka Bay, areas appropriate for scallop aquaculture and variations in chlorophyll-a concentration (which reflect the availability of algal food for scallops) were strongly correlated with ENSO, precipitation, and air temperature. These correlations demonstrate the influence of oceanic and atmospheric parameters on the productivity of scallop aquaculture in Funka Bay. Adaptation to oceanic and atmospheric changes should be considered when developing plans and management strategies for coastal scallop aquaculture in northeast Asia.     

A simple model to estimate the daily value of the regional maximum evapotranspiration from satellite temperature and albedo images

Abstract

We have tried an adaptation of the radiation model proposed by FAO, applicable in any area, for the estimation of the regional maximum evapotranspiration, ET, from temperature and albedo images obtained from a satellite. This model is based on the relationships

ET_m = k _cET_o

ET_o = A + BR _g + CR _g T_a ^max

where k _c is the crop coefficient, ET_o is the maximum evapotranspiration of the reference crop (green grass), R_g is the global radiation obtained from satellite albedo images, T _a ^max is the maximum temperature of the air obtained from the near-midday satellite temperature and A, B and C are the empirical coefficients characteristic of each zone calculated for different intervals of wind velocity and relative humidity of the air. By applying this model to the Valentian Region (Spain) we have obtained an estimation of the maximum daily evapotranspiration to an accuracy of 20 per cent.     

Direct Numerical Simulation in a Lid-Driven Cubical Cavity at High Reynolds Number by a Chebyshev Spectral Method

Direct numerical simulation of the flow in a lid-driven cubical cavity has been carried out at high Reynolds numbers (based on the maximum velocity on the lid), between 1.2 10⁴ and 2.2 10⁴. An efficient Chebyshev spectral method has been implemented for the solution of the incompressible Navier–Stokes equations in a cubical domain. The Projection-Diffusion method [Leriche and Labrosse (2000, SIAM J. Sci. Comput. 22(4), 1386–1410), Leriche et al. (2005, J. Sci. Comput., in press)] allows to decouple the velocity and pressure computation in very efficient way and the simple geometry allows to use the fast diagonalisation method for inverting the elliptic operators at a low computational cost. The resolution used up to 5.0 million Chebyshev collocation nodes, which enable the detailed representation of all dynamically significant scales of motion. The mean and root-mean-square velocity statistics are briefly presented