TY - JOUR

T1 - Scaling in erosion of landscapes: renormalization group analysis of a model with turbulent mixing

AU - Antonov, N V

AU - Kakin, P I

PY - 2017

Y1 - 2017

N2 - The model of landscape erosion, introduced in (1998 Phys. Rev. Lett. 80 4349, 1998 J. Stat. Phys. 93 477) and modified in (2016 Theor. Math. Phys. in press (arXiv:1602.00432)), is advected by anisotropic velocity field. The field is Gaussian with vanishing correlation time and the pair correlation function of the form $\propto \delta \left(t-{{t}^{\prime}}\right)/k_{\bot}^{d-1+\xi}$ , where ${{k}_{\bot}}=|{{\mathbf{k}}_{\bot}}|$ and ${{\mathbf{k}}_{\bot}}$ is the component of the wave vector, perpendicular to a certain preferred direction—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (1990 Commun. Math. Phys. 131 381). Analogous to the case without advection, the model is multiplicatively renormalizable and has infinitely many coupling constants. The one-loop counterterm is derived in a closed form in terms of the certain function V(h), entering the original stochastic equation, and its derivatives with respect to the height field $h\left(t,\mathbf{x}\right)$ . The full

AB - The model of landscape erosion, introduced in (1998 Phys. Rev. Lett. 80 4349, 1998 J. Stat. Phys. 93 477) and modified in (2016 Theor. Math. Phys. in press (arXiv:1602.00432)), is advected by anisotropic velocity field. The field is Gaussian with vanishing correlation time and the pair correlation function of the form $\propto \delta \left(t-{{t}^{\prime}}\right)/k_{\bot}^{d-1+\xi}$ , where ${{k}_{\bot}}=|{{\mathbf{k}}_{\bot}}|$ and ${{\mathbf{k}}_{\bot}}$ is the component of the wave vector, perpendicular to a certain preferred direction—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (1990 Commun. Math. Phys. 131 381). Analogous to the case without advection, the model is multiplicatively renormalizable and has infinitely many coupling constants. The one-loop counterterm is derived in a closed form in terms of the certain function V(h), entering the original stochastic equation, and its derivatives with respect to the height field $h\left(t,\mathbf{x}\right)$ . The full

M3 - Article

VL - 50

SP - 085002

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

ER -