An ill-posed inverse problem of a wing with locally given velocity data and its analysis

Using locally given vertical velocity data around a wing, an inverse formulation is presented to solve a lifting problem. The inverse problem is expressed by a Fredholm integral equation of the first kind. In this paper, the kernel of the integral equation gives a Hilbert–Schmidt integral operator, and therefore the occurrence of ill-posedness in the sense of stability cannot be avoided in a normal topology. This difficulty is solved by using the regularization method for ill-posed problems. A composition mapping is introduced so that local velocity data can be available for this inverse problem. In this paper, the ill-posed inverse problem of a wing is studied using the Landweber–Friedman's regularization method within the framework of linear potential theory. A numerical example demonstrates that only with locally given velocity data is the regularization method accurate and suitable for the present physical problem of an inverse mathematical formulation. Therefore, the lifting problem can be solved by using a locally given fluid velocity instead of a wing geometry. Received: April 13, 2000 / Accepted: April 20, 2000     

福建外海波能分布评估

采用基于第三代海浪模式的水动力分析程序包MIKE21对2014—2016年福建省外海的波浪时间与空间分布进行计算评估。结果表明,福建外海波能功率密度平均值介于1. 8～8 kWm;由于受到台湾岛的掩护,台湾海峡中部海域波高和波周期较小,其波能密度也较小,为4. 2～4. 8 kWm;台湾海峡北部位于开阔水域波能密度增大到7 kWm;海峡南部波能密度平均值接近8 k Wm。因此,建议波能电站的选址首先锁定台湾海峡北部波高及波能较大的平潭海域,该区域的波能相对较大,水深条件较为理想,时空分布也相对稳定。     

海岸工程设计波要素推算方法探讨——以如东人工岛设计波要素推算为例

以如东人工岛设计波要素推算为例,分别利用历史台风天气图推算法和设计风速推算法推求不同重现期设计波要素并进行对比分析。结果表明,两种方法各有优劣,但历史台风天气图推算法的计算精度比设计风速推算法的精度差,为了安全起见,建议采用设计风速推算法。     

Errors in dynamical fields inferred from oceanographic cruise data: Part I. The impact of observation errors and the sampling distribution

Diagnostic studies of ocean dynamics based on the analysis of oceanographic cruise data are usually quite sensitive to observation errors, to the station distribution and to the synopticity of the sampling. Here we present an error analysis of the first two sources. The third one is evaluated in Part II of this work (J. Mar. Sys. (2005), this issue). For observed variables and those linearly related to them, we use the Optimal Statistical Interpolation (OI) formulation. For variables which are not linearly related to observed variables (e.g., the vertical velocity), we carry out numerical experiments in a consistent way with OI statistics. Best results are obtained when some kind of scale selection or spatial filtering is applied in order to suppress small scales that cannot be properly resolved by the station distribution.The formulation is first applied to a high resolution (SeaSoar) sampling aimed to the recovery of mesoscale features in a region of large spatial variability (noise-to-signal fraction of the order of 0.002). Fractional errors (rms error divided by the standard deviation of the field) are estimated in about 2% for dynamic height and between 4% and 20% for geostrophic vorticity and vertical velocity. For observed variables, observation errors and sampling limitations are shown to contribute in similar amounts to total errors. For derived variables, sampling errors are by far the dominant contribution. For less dense samplings (e.g., equally spaced CTD stations), fractional errors are about 6% for dynamic height and between 15% and 30% for geostrophic vorticity and vertical velocity. For this sampling strategy, errors of all variables are mostly associated with sampling limitations.     

Distribution of suspended sediment in the coastal sea off the Ganges–Brahmaputra River mouth: observation from TM data

Remote sensing technique was applied to estimate suspended sediment concentration (SSC) and to understand transportation, distribution and deposition of suspended sediment in the estuary and throughout the coastal sea, off the Ganges–Brahmaputra River mouth. During low river discharge period, zone of turbidity maximum is inferred in the estuary near the shore. SSC map shows that maximum SSC reaches 1050 mg/l in this period. Magnitude of SSC is mainly owing to resuspension of the bottom surface sediments induced by tidal currents flowing over shallow water depths. The influence of depth on resuspension is farther revealed from the distribution and magnitude of SSC along the head of Swatch of No Ground (SNG) submarine canyon. During high river discharge period, huge river outflow pushed the salt wedge and flashes away the suspended sediments in the coastal sea off the river mouth. Zone of turbidity maximum is inferred in the coastal water approximately within 5–10 m depth of water, where the maximum SSC reaches 1700 mg/l. In this period, huge fluvial input of the suspended sediments including the resuspended bottom sediments and the particles remaining in suspension for longer period of time since their initial entry control mainly the magnitude of SSC. In the estuary near the shore, seasonal variation in the magnitude of SSC is not evident. In the coastal sea (>5 m water depth), seasonal influence in the magnitude of SSC could be concluded from the discrepancy between SSC values of two different seasons. Transportation and deposition of suspended sediments also experiences seasonal variations. At present, suspended sediments are being accumulated on the shallow shelf (between 5 and 10 m water depth) in low discharge period and on the mid-shelf (between 10 and 75 m water depth) during high discharge period. An empirical (exponential) relationship was found between gradual settle down of suspended sediments in the coastal sea and its lateral distance from the turbidity maximum.