Steady flow in a frictionless homogenous ocean

2020 ◽  
Vol 78 (4) ◽  
pp. 219-226
Author(s):  
N. P. Fofonoff
Keyword(s):  
Mathematical Model ◽  
Steady Flow ◽  
High Velocity ◽  
Vertical Component ◽  
Relative Vorticity ◽  
Horizontal Flow ◽  
Constant Depth ◽  
Absolute Vorticity ◽  
Dynamic Constraint

A mathematical model is developed to study the free (frictionless) steady horizontal flow which can occur in a homogeneous ocean of constant depth. The flow satisfies the dynamic constraint that the vertical component of absolute vorticity is constant along a streamline. The conclusion is reached that in an enclosed ocean a free steady circulation cannot have any slow broad eastward currents. The eastward currents must occur as narrow streams of high velocity and high relative vorticity. Intensified currents are present along the eastern and western coasts. The theory which is developed for the homogeneous ocean of constant depth can be applied to the two-layer ocean if the horizontal divergence of flow is negligible. If the horizontal divergence is not negligible, then the intensification of poleward currents is more pronounced and that of equatorward currents less pronounced as compared with the homogeneous ocean.

scholarly journals Mathematical model of steady flow in a helium loop

2019 ◽  
Vol 20 (7) ◽  
pp. 704
Author(s):  
František Világi ◽  
Branislav Knížat ◽  
Marek Mlkvik ◽  
František Urban ◽  
Róbert Olšiak ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Steady Flow ◽  
Gaseous Medium ◽  
Natural Circulation ◽  
Variable Density ◽  
Experimental Facility ◽  
Flowing Medium ◽  
Current State ◽  
Natural Circulation Loop

The article describes the application of a mathematical model to a natural circulation loop. A set of measurements were conducted at the experimental facility. The pressure and velocity relations were observed during the steady flow of helium. The main goal was to create a numerical model of flow capable of determining the velocity of flowing medium. The model describes the flow of highly compressed gaseous medium with variable density in direct pipelines with local resistances. At the current state, the temperature values along the loop are taken as input to the model. The article also includes the evaluation of local resistances in DHR and GFR, which significantly affects the resulting accuracy. The results from a numerical model are compared with experiments.

scholarly journals Observations of an Inertial Peak in the Intrinsic Wind Spectrum Shifted by Rotation in the Antarctic Vortex

2012 ◽  
Vol 69 (12) ◽  
pp. 3800-3811 ◽  
Author(s):  
L. J. Gelinas ◽  
R. L. Walterscheid ◽  
C. R. Mechoso ◽  
G. Schubert
Keyword(s):  
Solid Body ◽  
Wave Spectrum ◽  
Polar Vortex ◽  
Relative Vorticity ◽  
Body Rotation ◽  
Background Flow ◽  
Absolute Vorticity ◽  
Solid Body Rotation ◽  
The Absolute ◽  
The Antarctic

Abstract Spectral analyses of time series of zonal winds derived from locations of balloons drifting in the Southern Hemisphere polar vortex during the Vorcore campaign of the Stratéole program reveal a peak with a frequency near 0.10 h−1, more than 25% higher than the inertial frequency at locations along the trajectories. Using balloon data and values of relative vorticity evaluated from the Modern Era Retrospective-Analyses for Research and Applications (MERRA), the authors find that the spectral peak near 0.10 h−1 can be interpreted as being due to inertial waves propagating inside the Antarctic polar vortex. In support of this claim, the authors examine the way in which the low-frequency part of the gravity wave spectrum sampled by the balloons is shifted because of effects of the background flow vorticity. Locally, the background flow can be expressed as the sum of solid-body rotation and shear. This study demonstrates that while pure solid-body rotation gives an effective inertial frequency equal to the absolute vorticity, the latter gives an effective inertial frequency that varies, depending on the direction of wave propagation, between limits defined by the absolute vorticity plus or minus half of the background relative vorticity.

scholarly journals LOCAL SCOUR CHARACTERISTICS OF GROINS AT TIDAL WATERWAYS AND THEIR SIMULATION

2011 ◽  
Vol 1 (32) ◽  
pp. 66
Author(s):  
Xiping Dou ◽  
Xinzhou Zhang ◽  
Xiao-dong Zhao ◽  
Xiangming Wang
Keyword(s):  
Mathematical Model ◽  
Sediment Transport ◽  
Steady Flow ◽  
Tidal Current ◽  
River Regulation ◽  
Local Scour ◽  
Hydraulic Structures ◽  
Scour Depth ◽  
Channel Regulation ◽  
Tidal Rivers

For the channel regulation in tidal rivers, groins are often used as typical hydraulic structures. Precisely predicting the local scour depth at the groin head is the key for the project of river regulation. The local scour of groins for tidal rivers is significantly different from that for the undirectional steady flow of general rivers. In the present paper, a three-dimendional (3D) mathematical model for turbulence and sediment transport are establishmented. The local scour near the groin under the actions of tidal current and steady flow are simulated by established 3D turbulence and sediment transport numerical model.The differences of the scour development and the scour pattern near the groin under these two actions are compared.

Theoretical Model and Application of Nodal Analysis in Layered Water Flooding Regime - Take Bi-Layer Reservoir as an Example

2014 ◽  
Vol 522-524 ◽  
pp. 1552-1557
Author(s):  
Lei Wang ◽  
Guo Wei Qin ◽  
Rui Wang ◽  
Wen Bo Xu ◽  
Rui Gao ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Theoretical Model ◽  
Optimum Condition ◽  
Water Flooding ◽  
Horizontal Flow ◽  
Vertical Flow ◽  
Nodal Analysis ◽  
Flooding Regime ◽  
Set Up ◽  
Inflow Performance

A bi-layer mathematical model of nodal analysis under the condition of separate layer injection-production has been set up on the study of inflow performance relationship between injectors and producers, horizontal flow, vertical flow, choke flow etc., according to nodal analysis principle. In theory, this method can be used to determine reasonable working system of injectors and producers, and can be optimized the allocation and injection allocation, and can also be made water flooding regime in its optimum condition.

scholarly journals Vortical and Internal Wave Shear and Strain

2014 ◽  
Vol 44 (8) ◽  
pp. 2070-2092 ◽  
Author(s):  
Robert Pinkel
Keyword(s):  
Internal Wave ◽  
Frequency Spectrum ◽  
Strain Field ◽  
Spectral Gap ◽  
Vertical Component ◽  
Low Frequency ◽  
Relative Vorticity ◽  
Buoyancy Frequency ◽  
Linear Filter ◽  
Aspect Ratios

Abstract Depth–time records of isopycnal vertical strain have been collected from intensive CTD profiling programs on the research platform (R/P) Floating Instrument Platform (FLIP). The associated vertical wavenumber frequency spectrum of strain, when viewed in an isopycnal-following frame, displays a clear spectral gap at low vertical wavenumber, separating the quasigeostrophic (vortical) strain field and the superinertial internal wave continuum. This gap enables both model and linear-filter-based methods for separating the submesoscale and internal wave strain fields. These fields are examined independently in six field programs spanning the period 1983–2002. Vortical and internal wave strain variances are often comparable in the upper thermocline, of order 0.2. However, vortical strain tends to decrease with increasing depth (decreasing buoyancy frequency as ~(N2)1/2, while internal wave strain variance increases as ~(N2)−1/2, exceeding vortical variance by a factor of 5–10 at depths below 500 m. In contrast to strain, the low-frequency spectral gap in the shear spectrum is largely obscured by Doppler-smeared near-inertial motions. The vertical wavenumber spectrum of anticyclonic shear exceeds the cyclonic shear and strain spectra at all scales greater than 10 m. The frequency spectrum of anticyclonic shear exceeds that of both cyclonic shear and strain to frequencies of 0.5 cph, emphasizing the importance of lateral Doppler shifting of near-inertial shear. The limited Doppler shifting of the vortical strain field implies surprisingly small submesoscale aspect ratios: kH/kz ~ 0.001, Burger numbers Br = kH N/kzf ~ 0.1. Submesoscale potential vorticity is dominated by vertical straining rather than the vertical component of relative vorticity. The inferred rms fluctuation of fluid vorticity is far less for the vortical field than for the internal wavefield.

Investigation in the Effect of Gravity on the Droplet Removal in the Flow Channel of PEMFC

2011 ◽  
Vol 314-316 ◽  
pp. 1487-1491
Author(s):  
Zhong Min Wan ◽  
Jun Hua Wan ◽  
Jing Liu ◽  
Xi Chen ◽  
Ka Lin Su
Keyword(s):  
Mathematical Model ◽  
Tilt Angle ◽  
Flow Channel ◽  
Force Balance ◽  
Horizontal Flow ◽  
Apparent Effect ◽  
Airflow Velocity ◽  
Small Droplet ◽  
Working Temperature ◽  
Operation Pressure

Dealing with a droplet on the flow channel of PEMFC, a mathematical model based on the force balance of the flow force, gravity and hysteresis tension is derived to address the expressions of the critical airflow velocity and the droplet radii. The results show that in the horizontal flow channel, the critical airflow velocity is hardly affected by the working temperature but decreasing with the increasing of operation pressure. The droplet removal capability can be enhance by increasing the tilt angle of the cell. For a small droplet, the operation pressure has an apparent effect on the airflow velocity, while for a droplet in the spontaneous departure area, this effect can be neglected.

Observations of vertical propagation of near-inertial Waves in a complex vorticity field during the EURAC4A-OA campaign in the tropical western North Atlantic

2021 ◽  
Author(s):  
Daniel Rudloff ◽  
Johannes Karstensen ◽  
Tim Fischer ◽  
Florian Schütte ◽  
Arne Bendinger ◽  
...  
Keyword(s):  
North Atlantic ◽  
Velocity Structure ◽  
Mesoscale Eddy ◽  
Vertical Component ◽  
Acoustic Doppler Current Profiler ◽  
Relative Vorticity ◽  
Inertial Waves ◽  
Shear Structures ◽  
Current Profiler ◽  
Using Data

<p>In this study, we investigate the mesoscale flow field and how it enables energy to propagate vertically in form of near-inertial waves. As part of the EURAC4A-OA campaign the research vessels RV Maria S. Merian and NO L’Atalante simultaneously surveyed mesoscale eddy fronts in the western tropical North Atlantic. From velocity profile data, measured by a shipboard Acoustic Doppler Current Profiler (sADCP), we reconstruct eddies in the upper 1000m of the surveyed area, by fitting a Rankine Vortex model. The model derives an idealized velocity structure of the eddy as well as the location of its centre. Multiple occurrences of stacked eddies are identified and often surrounded by current shear structures associated with near-inertial waves. Using data from ship sections, where both research vessels operated less than 1nm apart, the vertical component of the relative vorticity (zeta) is calculated using different methods (single ship, two ships)[Shcherbina et al. 2013]. It is found that in particular zeta outside of the eddy cores is sensitive to the way the vorticity is calculated and may even change sign. Furthermore, the resulting zeta sections and its impact on the ability of near-inertial waves propagating vertically below the mixed layer is discussed.</p>

Study of a Brush-Type Micro-Robot Using Micro Coreless Motor

1999 ◽  
Vol 11 (5) ◽  
pp. 448-453 ◽  
Author(s):  
Kiyoshi Ioi ◽  
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
High Velocity ◽  
Experimental Results ◽  
Centrifugal Forces ◽  
Electric Cable ◽  
Mathematical Mode ◽  
Micro Robot ◽  
Cable Lines

This paper deals with a new brush-Type micro-robot using micro coreless motor. Though many mobile microrobots using PZT elements generally require some highvoltage amplifiers with electric cable lines, making it little difficult for the mobile microrobot to move about on long, thin pipes. The present micro-robot consists of many brush fibers, two coreless motors and an electric cell. The coreless motors with eccentric weights can generate centrifugal forces transmitted to the elastic brush fibers driving the microrobot. A basic mathematical model of the micro mobile robot using centrifugal forces is derived. Simple prototypes are developed, and high velocity is examined by experiments. The validity of the proposed mathematical mode was examined by way of the comparision of simulated and experimental results.

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