Nonlinear does not mean unpredictable. There are many non-linear equations for which we have closed solutions, which means that we can predict the behaviour of any object exhibiting that solution.
The problem you are dancing around is that natural science (whether you call it physics or something else) consists of non-quantified theories. These are verbal descriptions of processes that explain what happens and how, but do not provide quantified predictions. An great example is the theory of evolution. However, the effects of some theories can be quantified using mathematical models. The important thing to understand about mathematical models is that they are based on assumptions. The assumptions are simplifications of what happens in the real world. The reason we use simplifications is that it makes the mathematics tractable, allowing us to find solutions that in turn give us quantifiable predictions. But there is a significant trade-off: the simplifications make the models inaccurate because they stop the model expressing what really happens. The equations that we use in science are thus approximations. They work for particular conditions, but not for all. Refinements of theories often allow us to improve the mathematical model by making fewer simplifications, or less drastic simplifications, but they are simplifications nonetheless.
The only case where this might not be true is in particle physics where we are describing the interactions of elementary particles. But the simplification we have to make in order for the mathematics to be tractable is that we limit the number of particles we consider to an unrealistic number for any large-scale description of the universe. In principal, if we can get a powerful enough computer we should be able to model the behaviour of more particles, not using solutions of equations, but by modelling the possible interactions. This gives us a number of possible outcomes, some of which are more likely than others. This is what we do for weather reports. There is a lot of mathematics that can help in producing these models, but again, the mathematics is a model of how large-scale effects emerge from small-scale interactions. And, being a model, it is not precise (in fact, it is probabilistic). Thus, sometimes the weather forecast turns out to be wrong. That doesn't mean that there was not a model that predicted the weather that actually happened. Rather, it means that there were more models that predicted something else.
And this is what you do with aeroplanes and turbulence. You use models (i.e. approximations) to predict what will happen. Usually, the models are not equations that predict the path of air molecules for all time, but rather they are algorithms that calculate the position of the air molecules at a number of instants and use each instant as the starting point for estimating the next one. Varying initial conditions or various parameters leads to different results (sometimes very different), but we pick as our prediction the result that occurs most frequently (or rather, we pick the large-scale effects that occur most frequently).
And then, in the aeroplane business, you go and test it in a wind tunnel (or perhaps on a real plane flown by a test pilot). Usually the prediction is correct (just as the weather forecast is usually correct), but sometimes it isn't.
Presumably, in the aeroplane business you have to consider the fact that whatever situation you are modelling is likely to occur huge numbers of times over the life of plane. So in some circumstances, results that do not occur in the wind tunnel must also be accounted for.
But none of this means that physics isn't informing us as to what happens. Physics is informing us how to make the transition from one instant to the next in our model.
The scary thing is that you appear not to understand this.