arXiv subjects

Oliver Bühler

Publications and source records attributed to Oliver Bühler.

8 recordsLinked to original sources

arXiv2026

Frequency spreading of internal wave energy by balanced flows in two dimensions

Interactions between inertia-gravity waves and balanced flows lead to a spectral diffusion of wave action. Prior work has established that this diffusion is weak across constant frequency surfaces in three-dimensional settings, but can be significant in two dimensions with a non-stationary balanced flow. We investigate the two-dimensional setting through numerical simulations that simultaneously evolve a turbulent quasigeostrophic balanced flow and advect rotating shallow water wave packets. In contrast to earlier predictions based on the synthetic flows used by Dong et al. (J. Fluid Mech., 2020, vol. 905, R3), we find that frequency spreading from wave mean-flow interactions is weaker for realistic turbulent flows. We derive a timescale for frequency diffusion and show that frequency spreading with a realistic background flow is an order of magnitude smaller than with the synthetic flow. We narrow the discrepancy between the two- and three-dimensional induced diffusion theories, which suggests other mechanisms are responsible for the broadband frequency spectra seen in the atmosphere and ocean.

physics.flu-dyn↗

arXiv2026

Wave turbulence of inertia--gravity waves: a theory for the oceanic spectrum

We present a derivation using kinetic wave theory of the two-dimensional empirical Garrett--Munk spectrum for ocean internal waves, valid at all frequencies including near-inertial frequencies. This is based directly on the governing equations for a two-dimensional Boussinesq system with constant stratification and rotation. Our results improve on previous work by side-stepping the use of canonical variables, by taking full account of the Coriolis parameter in a non-hydrostatic dispersion relation, by filtering the balanced flow component from the dynamics, by using the conservation laws for energy and two components of pseudomomentum to bring the collision integral into a very simple form, by giving precise convergence conditions for the collision integral, and by finding the unique scale-invariant turbulent wave spectrum that corresponds to turbulent fluxes from small to large wavenumbers. The last step was achieved in the limit of small but nonzero Coriolis parameter. Key results are that any nonzero Coriolis parameter regularizes the singular nature of the non-rotating problem and that the homogeneity properties of the dispersion relation and of the interaction coefficients alone already imply that the spectrum is separable in vertical wavenumber and frequency. Within the restrictions of two-dimensional dynamics, this provides a theoretical framework for internal-wave turbulence consistent with oceanic observations.

physics.flu-dyn↗

arXiv2025

Next-order balanced model captures submesoscale physics and statistics

Using nonlinear simulations in two settings, we demonstrate that QG$^\mathrm{+1}$, a potential-vorticity based next-order-in-Rossby balanced model, captures several aspects of ocean submesoscale physics. In forced-dissipative 3D simulations under baroclinically unstable Eady-type background states, the statistical equilibrium turbulence exhibits long cyclonic tails and a plethora of rapidly-intensifying ageostrophic fronts. Despite that the model requires setting an explicit, small value for the fixed scaling Rossby number, the emergent flows are nevertheless characterized by vorticity and convergence values larger than the local Coriolis frequency, as observed in upper-ocean submesoscale flows. Simulations of QG$^\mathrm{+1}$ under the classic strain-induced frontogenesis set-up show realistic frontal asymmetry and a provable finite time blow-up, quantitatively comparable to simulations of the semigeostrophic equations. The inversions in the QG$^\mathrm{+1}$ model are straightforward linear Poisson problems, allowing for the reconstruction of all flow fields from the PV and surface buoyancy, while avoiding the semigeostrophic coordinate transformation. Taken together, these results suggest QG$^\mathrm{+1}$ might be a useful tool for studying upper-ocean submesoscale dynamics.

physics.flu-dyn↗

arXiv2024

Turbulent spectrum of 2D internal gravity waves

We find the turbulent energy spectrum of weakly interacting 2D internal gravity waves using the full, non-hydrostatic dispersion relation. This spectrum is an exact solution of a regularized kinetic equation, from which the zero-frequency shear modes have been excised by a careful limiting process. This is a new method in wave kinetic theory. The turbulent spectrum agrees with the 2D oceanic Garrett--Munk spectrum for frequencies large compared to the Coriolis frequency and vertical scales small compared to the depth of the ocean. We show that this turbulent spectrum is the unique power law solution to the steady kinetic equation with a non-zero radial flux. Our solution provides an interesting insight into a turbulent energy cascade in an anisotropic system -- like isotropic turbulence it is self-similar in scale, but its angular part is peaked along the curve of vanishing frequency and is self-similar in frequency.

physics.flu-dyn↗

arXiv2023

The role of sign indefinite invariants in shaping turbulent cascades

We highlight a non-canonical yet natural choice of variables for an efficient derivation of a kinetic equation for the energy density in non-isotropic systems, including internal gravity waves on a vertical plane, inertial and Rossby waves. The existence of a second quadratic invariant simplifies the kinetic equation and leads to extra conservation laws for resonant interactions. We analytically determine the scaling of the radial turbulent energy spectrum. Our findings suggest the existence of an inverse energy cascade of internal gravity waves, from small to large scales, in practically relevant scenarios.

physics.flu-dyn↗

arXiv2023

Kinetic equation for weak interaction of directional internal waves

Starting from the two-dimensional Boussinesq equation without rotation, we derive a kinetic equation for weak interaction of internal waves using non-canonical variables. We follow a formalism introduced by P. Ripa in the 80's. The advantage of this formalism is that it describes the system in terms of the natural linear eigenfunctions of eastward and westward propagating internal waves. Using properties of orthogonality of the eigenfunctions with respect to a (pseudo) metric set by the energy we can write non perturbative theory for the interaction of waves given in terms of the expansion amplitudes. The evolution is controlled by a system of equations, with quadratic nonlinearity, which is an exact representation of the original model equations. The dynamics is constrained by the conservation of energy and pseudo-momentum, which can be written simply as a linear combination of the squared absolute value of the amplitudes. The possibility of a generalization of the Fjortoft's argument to internal gravity waves and observation of a non trivial double cascade of energy and pseudo-momentum is discussed.

physics.flu-dyn↗

arXiv2015

On the concentration of near-inertial waves in anticyclones

An overlooked conservation law for near-inertial waves propagating in a steady background flow provides a new perspective on the concentration of these waves in regions of anticyclonic vorticity. The conservation law implies that this concentration is a direct consequence of the decrease in spatial scales experienced by an initially homogeneous wave field. Scaling arguments and numerical simulations of a reduced-gravity model of mixed-layer near-inertial waves confirm this interpretation and elucidate the influence of the strength of the background flow relative to the dispersion.

physics.ao-ph↗

arXiv2012

Steady water waves in the presence of wind

In this paper we develop an existence theory for small amplitude, steady, two-dimensional water waves in the presence of wind in the air above. The presence of the wind is modeled by a Kelvin--Helmholtz type discontinuity across the air--water interface, and a corresponding jump in the circulation of the fluids there. We consider both fluids to be inviscid, with the water region being irrotational and of finite depth. The air region is considered with constant vorticity in the case of infinite depth and with a general vorticity profile in the case of a finite, lidded atmosphere.

math.AP↗