Related papers: Stokes drift should not be added to ocean general …
Predicting particle transport in complex flows is traditionally achieved by solving the Navier-Stokes equations. While various numerical and experimental methods exist, they typically require deep physical insights and incur high…
We propose a simple model for the phenomenon of Eulerian spontaneous stochasticity in turbulence. This model is solved rigorously, proving that infinitesimal small-scale noise in otherwise a deterministic multi-scale system yields a…
The variance and spectra of wall-normal velocities are investigated for direct numerical simulations of turbulent flow in a channel, pipe, and zero-pressure-gradient boundary layer across a decade of friction Reynolds numbers. Spectra along…
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for…
Stokes flow equations, used to model creeping flow, are a commonly used simplification of the Navier--Stokes equations. The simplification is valid for flows where the inertial forces are negligible compared to the viscous forces. In…
It has been shown in \cite{Tong:2022gpg} that shallow water in the Euler description admits a dual gauge theory formulation. We show in the Lagrange description this gauge symmetry is a manifestation of the 2 dimensional area-preserving…
In this paper, we revisit the global well-posedness of the classical viscous surface waves in the absence of surface tension effect with the reference domain being the horizontal infinite slab, for which the first complete proof was given…
Ocean eddies play an important role in the transport and mixing processes of the ocean due to their ability to transport material, heat, salt, and other tracers across large distances. They exhibit at least two timescales; an Eulerian…
We report on a comparison of high-resolution numerical simulations of Lagrangian particles advected by incompressible turbulent hydro- and magnetohydrodynamic (MHD) flows. Numerical simulations were performed with up to $1024^3$ collocation…
A dynamic procedure for the Lagrangian Averaged Navier-Stokes-$\alpha$ (LANS-$\alpha$) equations is developed where the variation in the parameter $\alpha$ in the direction of anisotropy is determined in a self-consistent way from data…
Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that…
We propose a Navier-Stokes-driven analysis of the mean and fluctuating wall shear stress (WSS) applied to turbulent channel flow data from direct numerical simulations at friction Reynolds numbers up to $Re_\tau\approx 2000$. Starting from…
Previous studies focused primarily on wind stress being proportional to wind velocity relative to the ocean velocity, which induces a curl in wind stress with polarity opposite to the ocean mesoscale vorticity, resulting in net negative…
The aim of this paper is to derive the averaged governing equations for non-degenerated oscillatory flows, in which the magnitudes of mean velocity and oscillating velocity are similar. We derive the averaged equations for a scalar passive…
A fundamental aspect of turbulence theory is related to the identification of realizable phase-space statistical descriptions able to reproduce in some suitable sense the stochastic fluid equations of a turbulent fluid. In particular, a…
We show that in free surface flows, a uniform, streamwise current over small-amplitude wavy bottom topography generates cross-stream drift velocity. This drift mechanism, referred to as the current-bathymetry interaction induced drift…
We derive the general solution of the unsteady Stokes equations for an unbounded fluid in spherical polar coordinates, in both time and frequency domains. The solution is an expansion in vector spherical harmonics and given as a sum of a…
Ocean flows are routinely inferred from low-resolution satellite altimetry measurements of sea surface height assuming a geostrophic balance. Recent nonlinear dynamical systems techniques have revealed that surface currents derived from…
In recent literature several derivations of incompressible Navier-Stokes type equations that model the dynamics of an evolving fluidic surface have been presented. These derivations differ in the physical principles used in the modeling…
Gyres are central features of large-scale ocean circulation and are involved in transporting tracers such as heat, nutrients, and carbon-dioxide within and across ocean basins. Traditionally, the gyre circulation is thought to be driven by…