| Autor: |
Antonov, N. V., Babakin, A. A., Gulitskiy, N. M., Kakin, P. I. |
| Rok vydání: |
2024 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
The influence of a random environment on the dynamics of a fluctuating rough surface is investigated using a field theoretic renormalization group. The environment motion is modelled by the stochastic Navier--Stokes equation, which includes both a fluid in thermal equilibrium and a turbulent fluid. The surface is described by the generalized Pavlik's stochastic equation. As a result of fulfilling the renormalizability requirement, the model necessarily involves an infinite number of coupling constants. The one-loop counterterm is derived in an explicit closed form. The corresponding renormalization group equations demonstrate the existence of three two-dimensional surfaces of fixed points in the infinite-dimensional parameter space. If the surfaces contain IR attractive regions, the problem allows for the large-scale, long-time scaling behaviour. For the first surface (advection is irrelevant) the critical dimensions of the height field $\Delta_{h}$, the response field $\Delta_{h'}$ and the frequency $\Delta_{\omega}$ are non-universal through the dependence on the effective couplings. For the other two surfaces (advection is relevant) the dimensions are universal and they are found exactly. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
