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Yes, you are right about the definition, both ways are correct, but not mixed expressions. Thank you.

Cork is the 2nd largest city in Ireland

@@ScienceofFluids is it where wine corks come from?

In fact, cork from Irish means marsh

@@ScienceofFluids y'all name things so funny 😂

thank you

Thank you

I think it should be phi(X), the velocity potential in the field, because the integral is on the surfaces, that is, for different X0.

Yes, it is a lecture. And yes, there are assumptions for the hydrodynamic forces, but it is a very useful and reliable method for getting the forces, and these can be used for industrial design. Or we can say the best method, but not the most complicated one.

@@ScienceofFluids I found your lectures since I have hydrodynamics course based on Newman book. Its hard go go through since almost any equations have so many assumptions and there are just few if any explanations. Some are obvious (like linearization terms) but rest not that much.

@@WojciechowskaAnna yes, that's because the full fluid dynamics is so complicated, the nonlinear 2nd-order partial differential equations, and so far there are no good methods to solve them. However, it is found that the assumptions, such as the potential flow theory, are good enough for many practical problems, as in aerodynamics and in hydrodynamics (wave-structure interactions). otherwise you have to use CFD for solving the problems, very very computational demanding. And also CFD is based on the turbulence models (again the assumptions). so this is the reality for fluid dynamics. you have to simplify the problem, or you can go nowhere.

@@ScienceofFluids i undurstand the need of simplification, I just wish that that there would be more explanations of "why some assumptions can be done". When I go through many boundary conditions - they are usually listed, with little explanation. I am studying it, so most of them are see first time - and I just wish books and lecturures would cover more this subject.

@@WojciechowskaAnna I have published a book in 2022, 'Fundamentals of Wave Energy Conversion', published by Eliva Press. The first few chapters are on potential flows, and I explained why we can use potential flows for our practical problems (I would say I didn't find such explanations in anywhere). Of course, I have talked about the boundary conditions in the book too. if you are interested, I can send you a chapter of the book on potential flows.

Thank you

Thanks a lot 😊

The wavemakers have 3m depth.

@@ScienceofFluids i mean money, how much is this. Thanks.

I would like to see that, but unfortunately 0:44 we can't do that.

@@ScienceofFluids It's a shame it doesn't work. It's relatively simple you need to figure out the Resonance frequency of the full vet by doing a frequency swipe you watch for non lineare Effects then you modulate multiple frequencies into the vet such that the phase velocity exceeded the group velocity such that non linear effect add up. The waves will add up to a single huge wave and that is then the Soliton wave. Also if the depth of the vet decrease in the end like a beach then you will get a even more higher wave aka a tsunami.🌊😉😁

In fluids, there are some cases the fluid compressibility must be included. that's why the compressibility term must be included in the general N-S equation. Thank you.

@@ScienceofFluids Oh, but then why didn't you include the part that you had omitted from the second term. Because even that part was omitted by applying the continuity equation for incompressible flow right?

If you watch my video 'Derivation of the Navier-Stokes equation', you can see how the Laplacian is calculated. Thank you.

I recently saw some developments on the flexible wave energy converters, and I think you can find some useful information from that development. Google search would lead you there.

It would be interesting, but it would be also damaging...

Thank you. it would be interesting in swimming in large waves...

10:43 in the video in the compressibility part of the Stokes's matrix. Might have something to do with the -2/3 factor. My hunch is that is a simmilar assumption as seen with common derivations of pressure, regarding there are 3 directions (x,y,z), of which 1 does not leave the plane.

I think in many books on fluid mechanics you can find the derivations. the books I would recommend are John Anderson's 'fundamentals of Aerodynamics', or Frank White's 'fluid mechanics'.

like a water fountain?

It is the grid number in streamwise direction.

Thank you very much

Thanks for asking. These may be both correct, but depending on how the tensor component is defined. for instance, Tij can be defined as a component in i-direction on a plane of constant y, or in j-direction on a plane of constant x. these two different definitions would cause different expressions as you have seen in different books. Hope this helps.

@@ScienceofFluids Thanks a lot. Explanation is really helpful

the matrix size is dependent on how many motion modes are included. for a single body, there should be 6 DOFs, thus the matrix is 6*6. and for a 2-body system, there should be 12 DOFs, thus the size of matrix is 12*12. I don't know what is the second question, can you specify it more?

@@ScienceofFluids thank you prof. The second question is this: is there any transformation of the body mesh or panels to in order to get the radiation potentials in a 3D case? What i mean is how do we get the parameters for the green function inputs;r and eta as in G(r,eta)? Thanks

I see, but I have no idea how the transformation can be done. However, there are open source software, and you may not need to go for such detailed calculation. I wonder whether you can find something in HAMS (Hydrodynamic Analysis of Marine Structure) and the relevant publications.

@@ScienceofFluids thank you very much prof. I will check hams then

Thanks for suggestions. I will see to add some more information in the description.