Δu represents the diffusion effect of the speed field. Its role in space is usually related to the rate of change in the speed field. Intuitively speaking, the viscous term controls the smoothness of the speed field.
But within the framework of modal space, the viscous term needs to consider not only the gradient of the speed field but also how it interacts with the modal structure.
This involves how transformations in these spaces are mapped to modal space and understanding how these transformations affect the nature of solutions.
Additionally, can we understand modal space as a space resulting from the projection of the speed field, where each mode corresponds to a specific base function or frequency.
In such a space, the complexity of the problem might be simplified because the components within modal space can be seen as a representation or breakdown of the solution.
