The Vectrino Profiler was never designed to measure waves in tanks, but it should be possible if a bit of work does not scare you.
First of all, the DIWASP code (DIrectional WAve SPectra) MATLAB Toolbox developed by MetOcean Solutions Ltd is a good solution for an array of sensors and it can also work for “Triplet” types of sensors (PUV, buoys, etc.). A triplet is three orthogonal measurements of wave-related quantities, whereby the corresponding analysis can be used to infer wave properties.
The Vectrino class of instruments does not have a pressure sensor and therefore the PUV method cannot be used. However, you should be able to “swap out” the P for the W vertical velocity component of orbital velocity. You will just need to make sure you use the correct transfer function for W (defined in any wave mechanics reference book).
This should allow you to estimate the energy density spectra, but be aware that there are upper frequency limits where short waves are not measurable and you will have to limit the energy spectra at this frequency. If you are familiar with wave processing, you can use the energy density spectra to estimate standard, non-directional wave parameters such as height and period.
Directional analysis is also possible using the standard output that you would get from the PUV. If you are in a tank, then wave reflection is expected and this means that you will have to be careful when interpreting the results. More advanced analysis allows you to separate two wave directions at the same frequency, but resolving three or more wave directions is simply not possible with a triplet analysis.
As an aside, I am pretty sure that if you perform a PUV analysis with your data, without P, then you will get an ambiguous directional estimate that indicates the axis where the wave propagated.
Finally, you are going to have to pay special attention to where the measurement volume is relative to the surface (measurement depth) and be aware that if this measurement volume is greater than half a wavelength, then you will get very limited information (signal) for waves of the associated frequency. I suspect your waves are short, and this is going to make it challenging.
So, yes, this is most certainly possible, but you will have to keep attention on the details and the frequency limitations.