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Update2:
(I may not be the best person to advise you; I also try to avoid saying things that are completely foolish, but my track record is middling. ;-) Looking at your third model, and the path we've taken to get there, makes me think of a couple of things that are worth bearing in mind: First, it is strongly advisable not to drop simpler terms because they are not significant or even because it leads to a 'better' model (see here: does-it-make-sense-to-add-a-quadratic-term-but-not-the-linear-term-to-a-model, and here: including-the-interaction-but-not-the-main-effects-in-a-model--@whuber's answers especially, for example). Second, as we look at the data, decide on some covariates to try, model them, and then try something else, we are data dredging. This is rather worrying. (To see / understand this better, you may want to read my answer here: algorithms-for-automatic-model-selection.) Doing the things we've been doing here, and running simulations as we discussed in the comments, can help you to work though how you are going to think about what you find in your next experiment / how you plan for it. However, if you decide to draw conclusions / say something about these data on the basis of this, the risk of saying something completely foolish is very high. This is true even for the first iteration where I looked at your top plot and suggested including both variables with squared terms. You are probably on reasonable grounds to suggest there there may be a curvilinear relationship with both variables, but I would be cautious about firmly concluding more. (Note, for example, that although the terms in the last model have lots of stars, the residual standard error is larger and the multiple R-squared is smaller.) If, based on these data and scientific knowledge, you can come up with a couple of possibilities, you can design an experiment with your colleagues explicitly to differentiate amongst those possibilities.

Update2:
(I may not be the best person to advise you; I also try to avoid saying things that are completely foolish, but my track record is middling. ;-) Looking at your third model, and the path we've taken to get there, makes me think of a couple of things that are worth bearing in mind: First, it is strongly advisable not to drop simpler terms because they are not significant or even because it leads to a 'better' model (see here: does-it-make-sense-to-add-a-quadratic-term-but-not-the-linear-term-to-a-model, and here: including-the-interaction-but-not-the-main-effects-in-a-model--@whuber's answers especially, for example). Second, as we look at the data, decide on some covariates to try, model them, and then try something else, we are data dredging. This is rather worrying. (To see / understand this better, you may want to read my answer here: algorithms-for-automatic-model-selection.) Doing the things we've been doing here, and running simulations as we discussed in the comments, can help you to work though how you are going to think about what you find in your next experiment / how you plan for it. However, if you decide to draw conclusions / say something about these data on the basis of this, the risk of saying something completely foolish is very high. This is true even for the first iteration where I looked at your top plot and suggested including both variables with squared terms. You are probably on reasonable grounds to suggest there there may be a curvilinear relationship with both variables, but I would be cautious about firmly concluding more. (Note, for example, that although the terms in the last model have lots of stars, the residual standard error is larger and the multiple R-squared is smaller.) If, based on these data and scientific knowledge, you can come up with a couple of possibilities, you can design an experiment with your colleagues explicitly to differentiate amongst those possibilities.

Update2:
I may not be the best person to advise you; I also try to avoid saying things that are completely foolish, but my track record is middling. Looking at your third model, and the path we've taken to get there, makes me think of a couple of things that are worth bearing in mind: First, it is strongly advisable not to drop simpler terms because they are not significant or even because it leads to a 'better' model (see here: does-it-make-sense-to-add-a-quadratic-term-but-not-the-linear-term-to-a-model, and here: including-the-interaction-but-not-the-main-effects-in-a-model--@whuber's answers especially, for example). Second, as we look at the data, decide on some covariates to try, model them, and then try something else, we are data dredging. This is rather worrying. (To see / understand this better, you may want to read my answer here: algorithms-for-automatic-model-selection.) Doing the things we've been doing here, and running simulations as we discussed in the comments, can help you to work though how you are going to think about what you find in your next experiment / how you plan for it. However, if you decide to draw conclusions / say something about these data on the basis of this, the risk of saying something completely foolish is very high. This is true even for the first iteration where I looked at your top plot and suggested including both variables with squared terms. You are probably on reasonable grounds to suggest there there may be a curvilinear relationship with both variables, but I would be cautious about firmly concluding more. (Note, for example, that although the terms in the last model have lots of stars, the residual standard error is larger and the multiple R-squared is smaller.) If, based on these data and scientific knowledge, you can come up with a couple of possibilities, you can design an experiment with your colleagues explicitly to differentiate amongst those possibilities.

Update2:
(I may not be the best person to advise you; I also try to avoid saying things that are completely foolish, but my track record is middling. ;-) Looking at your third model, and the path we've taken to get there, makes me think of a couple of things that are worth bearing in mind: First, it is strongly advisable not to drop simpler terms because they are not significant or even because it leads to a 'better' model (see here: does-it-make-sense-to-add-a-quadratic-term-but-not-the-linear-term-to-a-model, and here: including-the-interaction-but-not-the-main-effects-in-a-model--@whuber's answers especially, for example). Second, as we look at the data, decide on some covariates to try, model them, and then try something else, we are data dredging. This is rather worrying. (To see / understand this better, you may want to read my answer here: algorithms-for-automatic-model-selection.) Doing the things we've been doing here, and running simulations as we discussed in the comments, can help you to work though how you are going to think about what you find in your next experiment / how you plan for it. However, if you decide to draw conclusions / say something about these data on the basis of this, the risk of saying something completely foolish is very high. This is true even for the first iteration where I looked at your top plot and suggested including both variables with squared terms. You are probably on reasonable grounds to suggest there there may be a curvilinear relationship with both variables, but I would be cautious about firmly concluding more. (Note, for example, that although the terms in the last model have lots of stars, the residual standard error is larger and the multiple R-squared is smaller.) If, based on these data and scientific knowledge, you can come up with a couple of possibilities, you can design an experiment with your colleagues explicitly to differentiate amongst those possibilities.

Update2:
I may not be the best person to advise you; I also try to avoid saying things that are completely foolish, but my track record is middling. Looking at your third model, and the path we've taken to get there, makes me think of a couple of things that are worth bearing in mind: First, it is strongly advisable not to drop simpler terms because they are not significant or even because it leads to a 'better' model (see here: does-it-make-sense-to-add-a-quadratic-term-but-not-the-linear-term-to-a-model, and here: including-the-interaction-but-not-the-main-effects-in-a-model--@whuber's answers especially, for example). Second, as we look at the data, decide on some covariates to try, model them, and then try something else, we are data dredging. This is rather worrying. (To see / understand this better, you may want to read my answer here: algorithms-for-automatic-model-selection.) Doing the things we've been doing here, and running simulations as we discussed in the comments, can help you to work though how you are going to think about what you find in your next experiment / how you plan for it. However, if you decide to draw conclusions / say something about these data on the basis of this, the risk of saying something completely foolish is very high. This is true even for the first iteration where I looked at your top plot and suggested including both variables with squared terms. You are probably on reasonable grounds to suggest there there may be a curvilinear relationship with both variables, but I would be cautious about firmly concluding more. (Note, for example, that although the terms in the last model have lots of stars, the residual standard error is larger and the multiple R-squared is smaller.) If, based on these data and scientific knowledge, you can come up with a couple of possibilities, you can design an experiment with your colleagues explicitly to differentiate amongst those possibilities.

As far as interpreting the final model, the fourth line is an interaction. This does not mean that $J$ is dependent on $Re$ or vice versa (although, they are clearly correlated). Rather, this means that the effect of, say, $J$ on $dcl$ depends on the level of $Re$. This is a difficult and nuanced concept. The way I typically explain it is to imagine if someone asked you a question about the effect of two variables on a third, would you use the term 'depends' or the phrase 'that doesn't matter'? For instance, if someone asked you about the effect of someone taking the birth control pill, you would say something like, 'Well, it depends, if you're a woman, it stops you from ovulating, but if you're a man, it doesn't'. Alternatively, if someone asked about how high a shelf someone can reach if they're 5'8" (173 cm) and being male versus female, you might say, 'that doesn't matter, if you're 5'8" you can reach a shelf that is 7' high whether you're male or female'.