arXiv subjects

Lihui Guo

Publications and source records attributed to Lihui Guo.

3 recordsLinked to original sources

arXiv2025

Geometry-dependent Ekman layer approximations on curved domains: L^{\infty} convergence

The Ekman boundary layer is a fundamental concept in fluid dynamics that describes fluid motion near boundaries affected by Earth's rotation. Most theoretical studies have simplified their analysis by assuming a planar boundary surface, resulting in limited exploration of structures with general smooth boundary conditions. Investigating the impact of boundary geometry in the Ekman boundary layer is essential, as initially suggested by J.L. Lions and further examined in Masmoudi's study [Comm. Pure Appl. Math. 53 (2000), 432-483] under small amplitude periodic boundary conditions. This paper clarifies how boundary geometry influences flow fields and characterizes its effects on near-boundary layer flow. We construct a class of multi-scale approximate solutions based on the boundary's geometric features and establish their convergence in the L^{\infty} framework. Our findings do not require a small-amplitude assumption, only an upper bound on the Gaussian curvature of the boundary surface. Notably, when the boundary is planar, our approach aligns with existing studies. Additionally, in the vanishing-viscosity limit, we derive a limiting-state system dependent on boundary geometric parameters. These contributions extend the theoretical understanding of boundary-layer interactions to general curved geometries and have possible applications in atmospheric, oceanic, and other geophysical flow contexts.

math-ph↗

arXiv2024

Non-flat Ekman Boundary Layers: Topographic Lift, Generalized Ekman Pumping, and Anisotropic Asymptotic Behavior

The Ekman boundary layer, a fundamental concept in geophysical fluid mechanics, describes the near-boundary fluid motion subject to rotation. Within the singular limit framework of rapid rotation and vanishing viscosity, classical studies of Ekman theory (e.g., Desjardins and Grenier (1999), Masmoudi (2000)) are predominantly restricted to flat or small-amplitude boundary assumptions. The conventional flat-boundary assumption obscures the complex mechanisms induced by topographic curvature; moreover, even small-amplitude perturbations reduce topographic effects to simple linear forcing terms. Consequently, this paper investigates the singular limit behavior of rotating fluids over a non-flat boundary $z=B(x,y)$ of $\mathcal{O}(1)$ amplitude with uniformly bounded slope and curvature. We elucidate how such topography modulates fluid dissipation through two distinct mechanisms: macroscopic topographic forcing and microscopic anisotropic pumping. First, using multi-scale asymptotic analysis, we construct a class of approximate solutions that explicitly depend on the boundary's geometric characteristics, yielding a two-dimensional limit system fundamentally distinct from classical models. A key innovation of this system is the introduction of a generalized velocity field defined via the topographic metric tensor. This formulation not only generalizes the traditional isotropic linear damping to anisotropic geometric damping but also couples rotational effects to macroscopic vertical acceleration. Furthermore, using energy methods, we establish the $L^2$ convergence of these variable-thickness approximate solutions to the weak solutions of the original three-dimensional system. Finally, we analyze the multiple mechanisms governing rotating fluid motion over large-amplitude topography using a representative class of boundary geometries.

math.AP↗

arXiv2016

The Vanishing Pressure Limits of Riemann Solutions to the Chaplygin Euler Equations

The Riemann solutions to Chaplygin Euler equations with a scaled pressure are considered. When the pressure vanishes, there are three cases. The Riemann solution containing two shock waves converges to the delta shock wave solution of the transport equations. During this process, both the strength and propagation speed of the delta shock are investigated in detail. We find that there is something different from that for polytropic or isothermal gas. The Riemann solution containing two rarefaction waves tends to the two contact discontinuity solution to the transport equations as the pressure goes to zero. The intermediate state between the two contact discontinuities is a vacuum state. The Riemann solution containing one rarefaction wave and one shock wave tends to the contact discontinuity solution to transport equations as the pressure vanishes.

math.AP↗