Model and Method of Establishing Horizontal Velocity Field in Mainland China

2012 ◽  
pp. 205-213
Author(s):  
Xing Chen ◽  
Pengfei Cheng ◽  
Yingyan Cheng
Keyword(s):  
Velocity Field ◽  
Mainland China ◽  
Horizontal Velocity

scholarly journals Reformulating the full-Stokes ice sheet model for a more efficient computational solution

2012 ◽  
Vol 6 (1) ◽  
pp. 21-34 ◽  
Author(s):  
J. K. Dukowicz
Keyword(s):  
Velocity Field ◽  
Boundary Conditions ◽  
Stokes Problem ◽  
Ice Sheet ◽  
Positive Definite ◽  
Horizontal Velocity ◽  
Attractive Alternative ◽  
Ice Shelf ◽  
Minimization Principle ◽  
The Common

Abstract. The first-order or Blatter-Pattyn ice sheet model, in spite of its approximate nature, is an attractive alternative to the full Stokes model in many applications because of its reduced computational demands. In contrast, the unapproximated Stokes ice sheet model is more difficult to solve and computationally more expensive. This is primarily due to the fact that the Stokes model is indefinite and involves all three velocity components, as well as the pressure, while the Blatter-Pattyn discrete model is positive-definite and involves just the horizontal velocity components. The Stokes model is indefinite because it arises from a constrained minimization principle where the pressure acts as a Lagrange multiplier to enforce incompressibility. To alleviate these problems we reformulate the full Stokes problem into an unconstrained, positive-definite minimization problem, similar to the Blatter-Pattyn model but without any of the approximations. This is accomplished by introducing a divergence-free velocity field that satisfies appropriate boundary conditions as a trial function in the variational formulation, thus dispensing with the need for a pressure. Such a velocity field is obtained by vertically integrating the continuity equation to give the vertical velocity as a function of the horizontal velocity components, as is in fact done in the Blatter-Pattyn model. This leads to a reduced system for just the horizontal velocity components, again just as in the Blatter-Pattyn model, but now without approximation. In the process we obtain a new, reformulated Stokes action principle as well as a novel set of Euler-Lagrange partial differential equations and boundary conditions. The model is also generalized from the common case of an ice sheet in contact with and sliding along the bed to other situations, such as to a floating ice shelf. These results are illustrated and validated using a simple but nontrivial Stokes flow problem involving a sliding ice sheet.

Withdrawal from a reservoir of stratified fluid

1981 ◽  
Vol 376 (1767) ◽  
pp. 499-523
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Vertical Velocity ◽  
Mass Flux ◽  
Laboratory Experiments ◽  
Initial Period ◽  
Horizontal Layer ◽  
Horizontal Velocity ◽  
Viscous Stress ◽  
Similar Flows

A series of laboratory experiments are described in which the following major features of the flow field were observed. Well above the outlet the flow was essentially one of uniform vertical velocity, which is such that the free surface falls at a rate determined by the mass flux through the outlet, the isopycnics remaining horizontal. The small vertical velocity is converted to a considerably larger horizontal velocity in an essentially horizontal layer near the level of the outlet slot. The width of this withdrawal layer was almost constant over a large portion of the tank (except for the region near the outlet), and the velocity field within it was found to be steady after an initial period of establishment. Also the horizontal velocity at a given level in the withdrawal layer was found, to a good approximation, to vary linearly with the distance along the tank, and the velocity distribution, at a given station, was determined principally by the viscous stress, once a representative length had been established. For flows initiated in a uniform tank by suddenly opening a valve in the outlet line, the width of the withdrawal layer seemed to be uniquely determined on a scale, dependent on the flux, that appears to derive from terms that are negligible once the steady flow has been established. By placing suitable obstructions in the tank it was possible to obtain similar flows, but with various widths. We were also able to change the structure of the withdrawal layer by controlling the way the mass flux was brought to its final value, thereby establishing that the width of the withdrawal layer was dependent on its history.

scholarly journals Mapping Small-Scale Horizontal Velocity Field in Panzhinan Waterway by Coastal Acoustic Tomography

Sensors ◽  
2020 ◽  
Vol 20 (19) ◽  
pp. 5717
Author(s):  
Haocai Huang ◽  
Xinyi Xie ◽  
Yong Guo ◽  
Hangzhou Wang
Keyword(s):  
Velocity Field ◽  
Travel Time ◽  
Sound Transmission ◽  
Volume Transport ◽  
Velocity Fields ◽  
Horizontal Velocity ◽  
Least Square ◽  
Small Scale ◽  
Acoustic Tomography ◽  
Mean Square Errors

Mapping small-scale high-precision velocity fields is of great significance to oceanic environment research. Coastal acoustic tomography (CAT) is a frontier technology used to observe large-scale velocity field in the horizontal slice. Nonetheless, it is difficult to observe the velocity field using the CAT in small-scale areas, specifically where the flow field is complex such as ocean ranch and artificial upwelling areas. This paper conducted a sound transmission experiment using four 50 kHz CAT systems in the Panzhinan waterway. Notably, sound transmission based on the round-robin method was recommended for small-scale CAT observation. The travel time between stations, obtained by correlation of raw data, was applied to reconstruct the horizontal velocity fields using Tapered Least Square inversion. The minimum net volume transport was 8.7 m3/s at 12:32, 1.63% of the total inflow volume transport indicating that the observational errors were acceptable. The relative errors of the range-average velocity calculated by differential travel time were 1.54% (path 2) and 0.92% (path 6), respectively. Moreover, the inversion velocity root-mean-square errors (RMSEs) were 0.5163, 0.1494, 0.2103, 0.2804 and 0.2817 m/s for paths 1, 2, 3, 4 and 6, respectively. The feasibility and acceptable accuracy of the CAT method in the small-scale velocity profiling measurement were validated. Furthermore, a three-dimensional (3-D) velocity field mapping should be performed with combined analysis in horizontal and vertical slices.

scholarly journals On the Positive Bias of Peak Horizontal Velocity from an Idealized Doppler Profiler

2005 ◽  
Vol 22 (1) ◽  
pp. 98-104
Author(s):  
David A. Short ◽  
Francis J. Merceret
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Vertical Velocity ◽  
Gumbel Distribution ◽  
Extreme Value Distribution ◽  
Value Distribution ◽  
Horizontal Velocity ◽  
Simple Function ◽  
Type I ◽  
Positive Bias

Abstract In the presence of 3D turbulence, peak horizontal velocity estimates from an idealized Doppler profiler are found to be positively biased due to an incomplete specification of the vertical velocity field. The magnitude of the bias was estimated by assuming that the vertical and horizontal velocities can be separated into average and perturbation values and that the vertical and horizontal velocity perturbations are normally distributed. Under these assumptions, properties of the type-I extreme value distribution for maxima, known as the Gumbel distribution, can be used to obtain an analytical solution of the bias. The bias depends on geometric properties of the profiler configuration, the variance in the horizontal velocity, and the unresolved variance in the vertical velocity. When these variances are normalized by the average horizontal velocity, the bias can be mapped as a simple function of the normalized variances.

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