Mechanics of thermohaline interleaving: beyond the empirical flux laws

2011 ◽  
Vol 675 ◽  
pp. 117-140 ◽  
Author(s):  
TIMOUR RADKO
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Field Measurements ◽  
Navier Stokes ◽  
Homogeneous Field ◽  
Spontaneous Generation ◽  
Navier Stokes Equations ◽  
Salt Fingers ◽  
Stratified Ocean

An analytical theory is developed which illustrates the dynamics of the spontaneous generation of thermohaline intrusions in the stratified ocean with density compensated lateral temperature and salinity gradients. Intrusions in the model are driven by the interaction with the initially homogeneous field of salt fingers, whose amplitude and spatial orientation is weakly modulated by the long wavelength perturbations introduced into the system. The asymptotic multiscale analysis makes it possible to identify intrusive instabilities resulting from the positive feedback of salt fingers on large-scale perturbations and analyse the resulting patterns. The novelty of the proposed analysis is related to our ability to avoid using empirical double-diffusive flux laws – an approach taken by earlier models. Instead, we base our analytical explorations directly on the governing (Navier–Stokes) equations of motion. The model predictions of the growth rates and preferred slopes of intrusions are in general agreement with the laboratory and field measurements.

Numerical Investigation of the Coulter Principle in a Microfluidic Device

2013 ◽  
Author(s):  
Muheng Zhang ◽  
Yongsheng Lian
Keyword(s):  
Electric Field ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Working Mechanism ◽  
Navier Stokes Equations ◽  
Sheath Flow ◽  
Coulter Counters ◽  
Pass Through ◽  
Cell Motion

Coulter counters are analytical microfluidic instrument used to measure the size and concentration of biological cells or colloid particles suspended in electrolyte. The underlying working mechanism of Coulter counters is the Coulter principle which relies on the fact that when low-conductive cells pass through an electric field these cells cause disturbances in the measurement (current or voltage). Useful information about these cells can be obtained by analyzing these disturbances if an accurate correlation between the measured disturbances and cell characteristics. In this paper we use computational fluid dynamics method to investigate this correlation. The flow field is described by solving the Navier-Stokes equations, the electric field is represented by a Laplace’s equation in which the conductivity is calculated from the Navier-Stokes equations, and the cell motion is calculated by solving the equations of motion. The accuracy of the code is validated by comparing with analytical solutions. The study is based on a coplanar Coulter counter with three inlets that consist of two sheath flow inlet and one conductive flow inlet. The effects of diffusivity, cell size, sheath flow rate, and cell geometry are discussed in details. The impacts of electrode size, gap between electrodes and electrode location on the measured distribution are also studied.

3D modelling of the flow distribution in the delta of Lake Øyeren, Norway

2010 ◽  
Vol 41 (2) ◽  
pp. 92-103 ◽  
Author(s):  
Peggy Zinke ◽  
Nils Reidar Bøe Olsen ◽  
Jim Bogen ◽  
Nils Rüther
Keyword(s):  
Water Level ◽  
Cross Sections ◽  
Stokes Equations ◽  
Morphological Changes ◽  
Flow Distribution ◽  
Field Measurements ◽  
Navier Stokes ◽  
Error Sources ◽  
Navier Stokes Equations ◽  
Water Level Measurements

A 3D numerical model was used to compute the discharge distribution in the channel branches of Lake Øyeren's delta in Norway. The model solved the Navier–Stokes equations with the k–ɛ turbulence model on a 3D unstructured grid. The bathymetry dataset for the modelling had to be combined from different data sources. The results for three different flow situations in 1996 and 1997 showed a relative accuracy of the computed discharges within the range of 0 to±20% compared with field measurements taken by an ADCP at 13 cross sections of the distributary channels. The factors introducing the most error in the computed results are believed to be uncertainties concerning the bathymetry. A comparison between the computational results of the older morphology data from 1985–1990 and the model morphology from 1995–2004 indicated that morphological changes in this period had already had consequences for the flow distribution in some channels. Other important error sources were the inevitable use of averaged water level gradients because of unavailable water level measurements within the delta.

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

Numerical Modelling of Circulation in Lake Sperillen, Norway

2000 ◽  
Vol 31 (1) ◽  
pp. 57-72 ◽  
Author(s):  
N. R. B. Olsen ◽  
D. K. Lysne
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Field Measurements ◽  
Navier Stokes ◽  
Water Current ◽  
Simple Method ◽  
Vertical Temperature Profile ◽  
Navier Stokes Equations ◽  
Good Agreement

A three-dimensional numerical model was used to model water circulation and spatial variation of temperature in Lake Sperillen in Norway. A winter situation was simulated, with thermal stratification and ice cover. The numerical model solved the Navier-Stokes equations on a 3D unstructured non-orthogonal grid with hexahedral cells. The SIMPLE method was used for the pressure coupling and the k-ε model was used to model turbulence, with a modification for density stratification due to the vertical temperature profile. The results were compared with field measurements of the temperature in the lake, indicating the location of the water current. Reasonably good agreement was found.

Rayleigh number scaling in numerical convection

1996 ◽  
Vol 310 ◽  
pp. 139-179 ◽  
Author(s):  
Robert M. Kerr
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Large Scale ◽  
Stokes Equations ◽  
Good Evidence ◽  
Navier Stokes ◽  
Fixed Temperature ◽  
Navier Stokes Equations ◽  
Local Boundary ◽  
Velocity Boundary Layer

Using direct simulations of the incompressible Navier-Stokes equations with rigid upper and lower boundaries at fixed temperature and periodic sidewalls, scaling with respect to Rayleigh number is determined. At large aspect ratio (6:6:1) on meshes up to 288 × 288 × 96, a single scaling regime consistent with the properties of ‘hard’ convective turbulence is found for Pr = 0.7 between Ra = 5 × 104 and Ra = 2 × 107. The properties of this regime include Nu ∼ RaβT with βT = 0.28 ≈ 2/7, exponential temperature distributions in the centre of the cell, and velocity and temperature scales consistent with experimental measurements. Two velocity boundary-layer thicknesses are identified, one outside the thermal boundary layer that scales as Ra−1/7 and the other within it that scales as Ra−3/7. Large-scale shears are not observed; instead, strong local boundary-layer shears are observed in regions between incoming plumes and an outgoing network of buoyant sheets. At the highest Rayleigh number, there is a decade where the energy spectra are close to k−5/3 and temperature variance spectra are noticeably less steep. It is argued that taken together this is good evidence for ‘hard’ turbulence, even if individually each of these properties might have alternative explanations.

Heat Pollution by Large Buildings and the Effects upon Astrometric Observations

1991 ◽  
Vol 112 ◽  
pp. 326-326
Author(s):  
James A. Hughes ◽  
Calvin A. Kodres
Keyword(s):  
Real Estate ◽  
Boundary Conditions ◽  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Real Estate Development ◽  
Atmospheric Effects ◽  
Navier Stokes Equations ◽  
Naval Observatory ◽  
The U.S

ABSTRACTRecent, large scale, real estate development near the U.S. Naval Observatory has led to an investigation of the systematic atmospheric effects which heat from large buildings can cause. Results show that non-negligible slopes of the atmospheric layers can be induced which cause a surprisingly large anomalous refraction. The Navier-Stokes equations were numerically integrated using the appropriate boundary conditions and the resulting isopycnic tilts using the appropriate boundary conditions and the resulting isopycnic tilts charted. Rays were then essentially traced through the perturbed atmosphere to determine the magnitude of the anomalous refraction.

scholarly journals Vortex motion of a continuous medium depending on the pressure change

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Alexander Braginsky
Keyword(s):  
Angular Velocity ◽  
Continuous Medium ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Vortex Motion ◽  
Pressure Change ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Least Action ◽  
Force Components

Abstract In this paper, we study the vortex motion of a continuous medium, which is described by forces obtained from the principle of least action. It is shown that in a continuous medium the vortex force components are proportional to the velocity and pressure gradient components. This article gives a description of the 2D vortex motion of air in zones of high and low pressure. If the pressure decreases, the angular velocity of rotation of the continuous medium increases, whereas if the pressure increases, the angular velocity fades. The lifting force is obtained due to the vortex movement of air in the form of a funnel. It is shown that the vortex force contains a vortex term of the Euler hydrodynamic equations with a relative factor equal to the velocity of the continuous medium squared divided by the sound velocity squared. To describe the motion of a continuous medium correctly it is necessary to replace the forces obtained by Euler with the forces obtained from the minimum of action in the equations of motion. It is concluded that vortex motions and turbulence are described by the obtained equations of motion, and not by the Navier–Stokes equations. Most likely, this is related to the Problem of the Millennium description of turbulence announced at the International Congress of Mathematics in 2000.

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