I once had a chat with a fellow who designed racing cars. He showed me a report that some of his high priced help had given him. He had hired some very bright CFD specialists, bought some awesomely powerful computers and some very expensive CFD software. Their task was to model the airflow around a racing car - with a view to reducing drag and improving down forces. He had spent a very great deal of money.
He was very pleased with the results. They had managed to predict the drag over the body of the car to within 5%. The flow over the wheels was not quite so easy and they had not got within 25% of the experimental results. I asked what is the proportion of wheel drag to the whole car. It was about 85% of the total.
Some things cannot be solved by maths - however good you are. The design of gas turbine combustors is a classic example. The knowledge is gained by sheer hard graft and laborious collection and processing of data to produce correlations (posh rules of thumb). The correlations can then be used, with healthy scepticism, to 'sort of' predict what might happen if we are lucky.
Some of engineering practice is art. Western education seems to be very much focused on analysis. I blame that Descartes bloke. You can't always make the whole system better by analysing the behaviour of the parts. Synthesis is where it's at - try to understand how the whole thing behaves. Then you will know where you will get the best returns for your efforts.
Micro-analysis of small volumes of flow is about as useful as predicting what the next wave will look like on a storm beaten shoreline. The chances of success are about the same as my winning the lottery tonight and hiring a buxom nurse for my dear old weary Dad.
Turn off your mind, relax and float downstream. Happy Christmas everybody.