arXiv subjects

Daniel Sinambela

Publications and source records attributed to Daniel Sinambela.

7 recordsLinked to original sources

arXiv2026

Small-Amplitude Solitary Waves for $f$-Plane Capillary-Gravity Flows with Arbitrary Vorticity

We study small-amplitude solitary waves for two-dimensional capillary--gravity flows with arbitrary vorticity on the equatorial $f$-plane. The steady free-boundary problem is formulated as a reversible Hamiltonian spatial-dynamics system in which rotation enters through the speed-dependent effective gravity $g_*=g-2\Omega c$. A center-manifold reduction reduces the local bifurcation problem to finite-dimensional Hamiltonian systems governed by the low-frequency spectrum of a Sturm--Liouville problem with an eigenvalue-dependent boundary condition. We identify the Hamiltonian $0^2$, real $1{:}1$, and Hamiltonian--Hopf resonance curves and obtain corresponding families of symmetric solitary waves under standard non-degeneracy assumptions. We also show that the weak-effective-gravity threshold $g_*=0$ is separated from the $0^2$ and local Hamiltonian--Hopf resonances for uniformly non-stagnant laminar flows, and can be approached only in a near-stagnation regime.

math.AP↗

arXiv2026

Generalized Error Bounds in the Recovery of Solitary Wave Profiles

We investigate the robustness of Constantin's explicit reconstruction formula for two-dimensional irrotational solitary water waves. This formula recovers the free-surface profile from the dynamic pressure trace at the bed and depends on both the wave speed and the undisturbed depth. We consider simultaneous perturbations in these three quantities and derive an $L^2$ error estimate for the reconstructed profile. The proof uses the hodograph transform, holomorphic extension arguments, and Paley--Wiener Fourier-decay estimates, yielding stability estimates with sublinear dependence on the perturbation size. We include numerical computations to illustrate the effects of specifically designed perturbations.

math.CA↗

arXiv2024

Asymptotic Stability of the two-dimensional Couette flow for the Stokes-transport equation in a finite channel

We study the Stokes-transport system in a two-dimensional channel with horizontally moving boundaries, which serves as a reduced model for oceanography and sedimentation. The density is transported by the velocity field, satisfying the momentum balance between viscosity, pressure, and gravity effects, described by the Stokes equation at any given time. Due to the presence of moving boundaries, stratified densities with the Couette flow constitute one class of steady states. In this paper, we investigate the asymptotic stability of these steady states. We prove that if the stratified density is close to a constant density and the perturbation belongs to the Gevrey-3 class with compact support away from the boundary, then the velocity will converge to the Couette flow as time approaches infinity. More precisely, we prove that the horizontal perturbed velocity decays as $\frac{1}{\langle t\rangle^3}$ and the vertical perturbed velocity decays as $\frac{1}{\langle t\rangle^4}$.

math.AP↗

arXiv2024

Asymptotic stability of the three-dimensional Couette flow for the Stokes-transport equation

In this paper, we investigate the asymptotic stability of the three-dimensional Couette flow in a stratified fluid governed by the Stokes-transport equation. We observe that a similar lift-up effect to the three-dimensional Navier-Stokes equation near Couette flow destabilizes the system. We find that the inviscid damping type decay due to the Couette flow together with the damping structure caused by the decreasing background density stabilizes the system. More precisely, we prove that if the initial density is close to a linearly decreasing function in the Gevrey-$\frac{1}{s}$ class with $\frac{1}{2}< s\leq 1$, namely, $\|\varrho_{\mathrm{in}}(X,Y,Z)-(-Y)\|_{\mathcal{G}^{s}}\leq ε$, then the perturbed density remains close to $-Y$. Moreover, the associated velocity field converges to Couette flow $(Y, 0, 0)^{\top}$ with a convergence rate of $\frac{1}{\langle t\rangle^3}$.

math.AP↗

arXiv2023

The transition to instability for stable shear flows in inviscid fluids

In this paper, we study the generation of eigenvalues of a stable monotonic shear flow under perturbations in $C^s$ with $s<2$. More precisely, we study the Rayleigh operator $\mathcal{L}_{U_{m,γ}}= U_{m,γ}\partial_x-U''_{m,γ}\partial_xΔ^{-1}$ associated with perturbed shear flow $(U_{m,γ}(y),0)$ in a finite channel $\mathbb{T}_{2π}\times [-1,1]$ where $U_{m,γ}(y)=U(y)+mγ^2\widetildeΓ(y/γ)$ with $U(y)$ being a stable monotonic shear flow and $\big\{mγ^2\widetildeΓ(y/γ)\big\}_{m\geq 0}$ being a family of perturbations parameterized by $m$. We prove that there exists $m_*$ such that for $0\leq m m_*$ which also leads to instability.

math.AP↗

arXiv2022

Existence and stability of interfacial capillary-gravity solitary waves with constant vorticity

In this paper, we consider capillary-gravity waves propagating on the interface separating two fluids of finite depth and constant density. The flow in each layer is assumed to be incompressible and of constant vorticity. We prove the existence of small-amplitude solitary wave solutions to this system in the strong surface tension regime via a spatial dynamics approach. We then use a variant of the classical Grillakis--Shatah--Strauss (GSS) method to study the orbital stability/instability of these waves. We find an explicit function of the parameters (Froude number, Bond number, and the depth and density ratios) that characterizes the stability properties. In particular, conditionally orbitally stable and unstable waves are shown to be possible.

math.AP↗

arXiv2020

Large-amplitude solitary waves in two-layer density stratified water

We present a large-amplitude existence theory for two-dimensional solitary waves propagating through a two layer body of water. The domain of the fluid is bounded below by an impermeable flat ocean floor and above by a free boundary at constant pressure. For any piecewise smooth upstream density distribution and laminar background current, we construct a global curve of solutions. This curve bifurcates from the background current and, following along the curve, we find waves that are arbitrarily close to having horizontal stagnation points. The small-amplitude waves are constructed using a center manifold reduction technique. The large-amplitude theory is obtained through analytical global bifurcation together with refined qualitative properties of the waves.

math.AP↗