Oceanographic or atmospheric context and physical/mathematical gist of the Reynolds’ (1883) results (Life Sciences Essay)

Oceanographic or atmospheric context and physical/mathematical gist of the Reynolds’ (1883) results
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Oceanographic or atmospheric context and physical/mathematical gist of the Reynolds’ (1883) results
The physical/mathematical gist of the Reynolds’ results
In his paper, Reynolds aimed at explaining the change in character during fluid flow in a pipe from laminar to turbulent, which he had shown in previous experiments that they are dimensionless. As such, Reynolds achieved his aim by decomposing the velocity of the fluid into fluctuating and mean components and then noted the changes in the rates of the average kinetic energy that was generated and dissipated (Reichardt, 2017). The changes in both cases were compared to the Reynolds number. Initially, the findings of the paper were grudgingly accepted by two distinguished referees who had initially raised their little interest in the work and the findings of the paper. As time passed, the Reynolds equations, which are the averaged form of the equations that were an otherwise intermediate stage during Reynolds’ analysis, was recognized as the beginning point in the computation of turbulent flows. In addition, 50 years after Reynolds’ paper, there has a successful refinement of the strategy that he formulated for predicting transition.
The strategy has also found a broad application in different spheres. In some engineering problems, computing resources have experienced continual and rapid growth, and this has resulted in the approaches for the computation of turbulent flow phenomenon becoming increasingly more detailed (Eckhardt, 2009). However, such growth and development in computing power it possible to use Reynolds’ approach as an average strategy for analysis and computations in complex flow systems in an environment or industry in which less comprehensive analyses are used. This implies that Reynolds’ approach is highly likely to remain useful during this century. The approach has found broad applications, and it is used in the understanding flows in an oceanographic and atmospheric system.
Some reasons why you think his findings might be relevant to an oceanographic or atmospheric system that you argue to be important.
Reynolds’ approach can be used in computing velocity and understanding turbulence in oceanographic and atmospheric systems. In such cases, the instantaneous velocity, u, is replaced with its mean value, INCLUDEPICTURE "https://royalsocietypublishing.org/cms/asset/3ff8cd2e-8bda-4d20-8d0b-baaaf6dd25cb/rsta20140231im1.gif" \* MERGEFORMATINET HYPER14HYPER15 , and the turbulent fluctuating velocity, u′, and this results in the continuity equation ∂ui/∂xi=0. In this case, Reynolds noted that the turbulent and the mean velocity fields were solenoidal, implying that and ∂u′i/∂xi=0 (Jackson & Launder, 2007). As such, the two equations can be applied in an oceanographic system to compare the mean and turbulent velocity fields, as well as understanding the nature of turbulence. In addition, Reynolds computed the momentum equation, and his computations yielded the following;
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In this equation, ПЃ represents the density of the fluid density and represents the mean value of the stress that is applied to the fluid, made up of static pressure and viscous contributions (Jackson & Launder, 2007). Today, this equation is referred to as the Reynolds equation and it can applied in computing the stress or pressure that is applied in an oceanographic environment. For instance, the equation can be used in computing the pressure that objects, such as plants and other matter, experience in the ocean, depending on the density of the water and the depth at which the objects are lying.
In addition, Reynolds’ results contain what he referred to as Reynolds stresses, represented by the quantities INCLUDEPICTURE "https://royalsocietypublishing.org/cms/asset/762554b4-11c1-4dd7-abd4-f369afdf5062/rsta20140231im4.gif" \* MERGEFORMATINET 
. This makes the equation usable and applicable in determining the Reynolds stresses in reference to calculable or known quantities. Over this century, researchers have established how the equation can be applied in calculating fluid flow and stress in fluid mechanics...