Domain size is clearly the dominating issue when it comes to dispersion modeling. prediction of turbulent diffusion coefficient for Eulerian method is difficult task. for this either we need to check previous literature or trial and error to fix the diffusion coefficient ? I am looking for any mathematical relation or thumb rule that helps to fix the diffusion coefficient for a given domain size.
Your question is too vague to say much. Are you dispersing chemicals in a flow chamber, water in an ocean, air in an atmosphere, etc? What is the domain scale and shape? What is the initial state? What is the forcing? Your best plan is to look in the literature for others who have done similar tasks in your own particular field.
This is really a meta-answer that could apply with slight rewording to any vague question
sir i hope i am not offending you.
my question might appear vague but as far as i see, i have mentioned in my question that i am looking for relation relating to domain length scale. like what difference does it make if we have domain length of 1 m x 1 m or 1 km x 1 km or 100 km x 100 km , and yes releasing chemicals in ocean best describes my sample situation.
I know that with changing domain size predominant process causing dispersion vary. But i don't see any dependence on boundary and initial conditions when estimating dispersion coefficient alone what if we never has to encounter the domain boundaries.
Thank you. David .
For this paper. This is for the first time i have come across such relation.
I hope i will find some use.
Hello Aditya Kumar: Dispersion of contaminants in water bodies of general shape is a complicated process that has defied rational analysis till date. Unlike dispersion in open channel type flows, dispersion in lakes and oceans cannot be effectively related to the mean flow characteristics. In addition, dispersion in large water bodies are very much influenced by large-scale circulation in shore zones and by wind and wave induced motions. Thus, the answer to your question in the general case of three dimensional dispersion is quite difficult. Most formulas for dispersion coefficient D are applicable to one dimensional dispersion in straight uniform river channels. Of course dispersion in a river channel is 3 dimensional but because of the smaller velocities in the vertical and lateral directions, it could be considered to be essentially one-dimensional.
Kashefipour and Falconer (2002) proposed the following reliable empirical formula for dispersion in river channels:
D = [7.428 + 1.775(B/H)0.630(U*/U)0.572]HU2/U*
where B = channel width, H = channel depth, U = river velocity, and U* = shear velocity
For turbulent flow U* = (gRS)0.5 where g = acceleration due to gravity, R = hydraulic radius, S = energy slope
For laminar flow (unrealistic for natural flow regimes) U* = U(3/Re)0.5 where Re = Reynolds number