scholarly journals Diffusion and the formation of vorticity staircases in randomly strained two-dimensional vortices

2009 ◽  
Vol 638 ◽  
pp. 49-72 ◽  
Author(s):  
MATTHEW R. TURNER ◽  
ANDREW P. BASSOM ◽  
ANDREW D. GILBERT
Keyword(s):  
Diffusion Equation ◽  
Surf Zone ◽  
Spatial Scales ◽  
Effective Diffusion ◽  
Effective Diffusivity ◽  
Angular Frequency ◽  
Asymptotic Model ◽  
Two Dimensional ◽  
Fine Scale ◽  
Long Time

The spreading and diffusion of two-dimensional vortices subject to weak external random strain fields is examined. The response to such a field of given angular frequency depends on the profile of the vortex and can be calculated numerically. An effective diffusivity can be determined as a function of radius and may be used to evolve the profile over a long time scale, using a diffusion equation that is both nonlinear and non-local. This equation, containing an additional smoothing parameter, is simulated starting with a Gaussian vortex. Fine scale steps in the vorticity profile develop at the periphery of the vortex and these form a vorticity staircase. The effective diffusivity is high in the steps where the vorticity gradient is low: between the steps are barriers characterized by low effective diffusivity and high vorticity gradient. The steps then merge before the vorticity is finally swept out and this leaves a vortex with a compact core and a sharp edge. There is also an increase in the effective diffusion within an encircling surf zone.In order to understand the properties of the evolution of the Gaussian vortex, an asymptotic model first proposed by Balmforth, Llewellyn Smith & Young (J. Fluid Mech., vol. 426, 2001, p. 95) is employed. The model is based on a vorticity distribution that consists of a compact vortex core surrounded by a skirt of relatively weak vorticity. Again simulations show the formation of fine scale vorticity steps within the skirt, followed by merger. The diffusion equation we develop has a tendency to generate vorticity steps on arbitrarily fine scales; these are limited in our numerical simulations by smoothing the effective diffusivity over small spatial scales.

Path-integral methods for turbulent diffusion

1982 ◽  
Vol 123 ◽  
pp. 59-68 ◽  
Author(s):  
I. T. Drummond
Keyword(s):  
Path Integral ◽  
Effective Diffusion ◽  
Effective Diffusivity ◽  
Passive Scalar ◽  
Path Integral Representation ◽  
Integral Methods ◽  
Long Time ◽  
Negative Effect ◽  
Diffusion Function ◽  
Markovian Limit

We derive a path-integral representation for the effective diffusion function of a passive scalar field. We use it to calculate the long-time effective diffusivity in Gaussian turbulence in the near-Markovian limit. Our results confirm the negative effect of vorticity predicted by previous discussions. They also demonstrate that the helicity of the turbulence when present may be as important an influence as the vorticity.

On the spreading of a turbulent spot in the absence of a pressure gradient

1982 ◽  
Vol 123 ◽  
pp. 69-90 ◽  
Author(s):  
I. Wygnanski ◽  
M. Zilberman ◽  
Joseph H. Haritonidis
Keyword(s):  
Scalar Field ◽  
Effective Diffusion ◽  
Effective Diffusivity ◽  
Passive Scalar ◽  
Turbulent Spot ◽  
Path Integral Representation ◽  
Long Time ◽  
Negative Effect ◽  
Diffusion Function ◽  
Markovian Limit

We derive a path-integral representation for the effective diffusion function of a passive scalar field. We use it to calculate the long-time effective diffusivity in Gaussian turbulence in the near-Markovian limit. Our results confirm the negative effect of vorticity predicted by previous discussions. They also demonstrate that the helicity of the turbulence when present may be as important an influence as the vorticity.

scholarly journals Analysis of the long-time asymptotic behaviour of the solution of a two-dimensional reaction-diffusion equation

2015 ◽  
Vol 4 (2) ◽  
pp. 332
Author(s):  
Joel Ndam
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Asymptotic Behaviour ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Variable Diffusion Coefficient ◽  
Long Time ◽  
Variable Diffusion

<p>A reaction-diffusion equation in two dimensions is considered. The long-time asymptotic behaviour of the solution of this equation is examined in terms of uniform diffusion as well as density-dependent diffusion. The results show that in both cases, the solution attains a steady state, but does so more slowly with the variable diffusion coefficient when its magnitude d&lt;1.</p>

scholarly journals Quantifying Optically Derived Two-Dimensional Wave-Averaged Currents in the Surf Zone

2021 ◽  
Vol 13 (4) ◽  
pp. 690
Author(s):  
Dylan Anderson ◽  
A. Spicer Bak ◽  
Katherine L. Brodie ◽  
Nicholas Cohn ◽  
Rob A. Holman ◽  
...  
Keyword(s):  
Surf Zone ◽  
Spatial Scales ◽  
Low Cost ◽  
Breaking Waves ◽  
Two Dimensional ◽  
Rip Currents ◽  
Circulation Patterns ◽  
Passive Tracers ◽  
A New Technique ◽  
Incident Waves

Complex two-dimensional nearshore current patterns are generated by feedbacks between sub-aqueous morphology and momentum imparted on the water column by breaking waves, winds, and tides. These non-stationary features, such as rip currents and circulation cells, respond to changing environmental conditions and underlying morphology. However, using fixed instruments to observe nearshore currents is limiting due to the high costs and logistics necessary to achieve adequate spatial sampling resolution. A new technique for processing surf-zone imagery, WAMFlow, quantifies fluid velocities to reveal complex, multi-scale (10 s–1000 s meters) nearshore surface circulation patterns. We apply the concept of a wave-averaged movie (WAM) to measure surf-zone circulation patterns on spatial scales of kilometers in the alongshore and 100 s of meters in the cross-shore. The approach uses a rolling average of 2 Hz optical imagery, removing the dominant optical clutter of incident waves, to leave the residual foam or water turbidity features carried by the flow. These residual features are tracked as quasi-passive tracers in space and time using optical flow, which solves for u and v as a function of image intensity gradients in x, y, and t. Surf zone drifters were deployed over multiple days with varying nearshore circulations to validate the optically derived flow patterns. Root mean square error are reduced to 0.1 m per second after filtering based on image attributes. The optically derived patterns captured longshore currents, rip currents, and gyres within the surf zone. Quantifying nearshore circulation patterns using low-cost image platforms and open-source computer vision algorithms presents the potential to further our understanding of fundamental surf zone dynamics.

scholarly journals Repeated surveying over 6 years reveals that fine-scale habitat variables are key to tropical mountain ant assemblage composition and functional diversity

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mulalo M. Muluvhahothe ◽  
Grant S. Joseph ◽  
Colleen L. Seymour ◽  
Thinandavha C. Munyai ◽  
Stefan H. Foord
Keyword(s):  
Climate Change ◽  
Species Composition ◽  
High Altitude ◽  
Functional Diversity ◽  
Large Scale ◽  
Climate Models ◽  
Spatial Scales ◽  
Abiotic Factors ◽  
Composition Analysis ◽  
Fine Scale

AbstractHigh-altitude-adapted ectotherms can escape competition from dominant species by tolerating low temperatures at cooler elevations, but climate change is eroding such advantages. Studies evaluating broad-scale impacts of global change for high-altitude organisms often overlook the mitigating role of biotic factors. Yet, at fine spatial-scales, vegetation-associated microclimates provide refuges from climatic extremes. Using one of the largest standardised data sets collected to date, we tested how ant species composition and functional diversity (i.e., the range and value of species traits found within assemblages) respond to large-scale abiotic factors (altitude, aspect), and fine-scale factors (vegetation, soil structure) along an elevational gradient in tropical Africa. Altitude emerged as the principal factor explaining species composition. Analysis of nestedness and turnover components of beta diversity indicated that ant assemblages are specific to each elevation, so species are not filtered out but replaced with new species as elevation increases. Similarity of assemblages over time (assessed using beta decay) did not change significantly at low and mid elevations but declined at the highest elevations. Assemblages also differed between northern and southern mountain aspects, although at highest elevations, composition was restricted to a set of species found on both aspects. Functional diversity was not explained by large scale variables like elevation, but by factors associated with elevation that operate at fine scales (i.e., temperature and habitat structure). Our findings highlight the significance of fine-scale variables in predicting organisms’ responses to changing temperature, offering management possibilities that might dilute climate change impacts, and caution when predicting assemblage responses using climate models, alone.

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