Laboratory Experiments on Flows Over Bottom Topography

This study examines the impact of small-scale irregular topographic features on the dynamics and evolution of large-scale barotropic flows in the ocean. A multiscale theory is developed, which makes it possible to represent large-scale effects of the bottom roughness without explicitly resolving small-scale variability. The analytical model reveals that the key mechanism of topographic control involves the generation of a small-scale eddy field associated with considerable Reynolds stresses. These eddy stresses are inversely proportional to the large-scale velocity and adversely affect mean circulation patterns. The multiscale model is applied to the problem of topography-induced spin-down of a large circularly symmetric vortex and is validated by corresponding topography-resolving simulations. The small-scale bathymetry chosen for this configuration conforms to the Goff–Jordan statistical spectrum. While the multiscale model formally assumes a substantial separation between the scales of interacting flow components, it is remarkably accurate even when scale separation is virtually non-existent.

Section: Introductionmentioning

confidence: 99%

“…Merryfield & Holloway 1997, 1999; Nikurashin et al. 2014; Sansón & van Heijst 2014; Trossman et al. 2017).…”

Section: Introductionunclassified

Spin-down of a barotropic vortex by irregular small-scale topography

Radko

2022

“…The time step is 1 % of the system's rotation period, so 100 time steps are one 'day'. The scheme has been used in numerous previous studies on vortices over a flat bottom or involving topography effects (Zavala Sansón & van Heijst 2002, 2014.…”

Section: Numerical Simulations Of Vortices Over Topographymentioning

confidence: 99%

Linear stability of monopolar vortices over isolated topography

Gonzalez

Sansón

2023

The linear instability of circular vortices over isolated topography in a homogeneous and inviscid fluid is examined for the shallow-water and quasi-geostrophic models in the $f$ -plane. The eigenvalue problem associated with azimuthal disturbances is derived for arbitrary axisymmetric topographies, either submarine mountains or valleys. Amended Rayleigh and Fjørtoft theorems with topographic effects are given for barotropic instability, obtaining necessary criteria for instability when the potential vorticity gradient is zero somewhere in the domain. The onset of centrifugal instability is also discussed by deriving the Rayleigh circulation theorem with topography. The barotropic instability theorems are applied to a wide family of nonlinear, quasi-geostrophic solutions of circular vortices over axisymmetric topographic features. Flow instability depends mainly on the vortex/topography configuration, as well as on the vortex size in comparison with the width of the topography. It is found that anticyclones/mountains and cyclones/valleys may be unstable. In contrast, cyclone/mountain and anticyclone/valley configurations are stable. These statements are validated with two numerical methods. First, the generalised eigenvalue problem is solved to obtain the wavenumber of the fastest-growing perturbations. Second, the evolution of the vortices is simulated numerically to detect the development of linear perturbations. The numerical results show that for unstable vortices over narrow topographies, the fastest growth rate corresponds to mode $1$ , which subsequently forms asymmetric dipolar structures. Over wide topographies, the fastest perturbations are mainly modes $1$ and $2$ , depending on the topographic features.

“…The structure is isolated because it has zero total circulation: the cyclonic or anticyclonic core is surrounded by an annulus of opposite-sign vorticity. This vortex is often used to model experimental vortices in the laboratory (Kloosterziel & van Heijst 1992;van Heijst & Clercx 2009;Zavala Sansón & van Heijst 2014), and similar structures are also helpful for representing mesoscale oceanic vortices (e.g. Gaube et al 2015).…”

Section: Spatial Structure Of W D and W Amentioning

confidence: 99%

Nonlinear surface Ekman effects on cyclonic and anticyclonic vortices

Zavala Sansón,

García-Martínez,

Sheinbaum

2023

The transfer of momentum between the atmosphere and oceanic motions affected by the Earth's rotation occurs through the thin surface Ekman layer. The exchange depends on the surface wind stress, which produces the Ekman pumping of fluid to the ocean upper layer. The Ekman pumping mainly depends on: (i) the curl of the wind stress and (ii) the advection of vorticity due to the Ekman transport. The wind stress is usually parametrised as a quadratic function of the relative speed between the wind and the ocean currents, providing a feedback mechanism between the two fluids. Under steady and spatially uniform wind conditions over mesoscale vortices, the first mechanism generates vertical motions that induce the vortex decay (top drag), while the second promotes the horizontal advection of vorticity in the Ekman transport direction. This study examines the nonlinear effects of both mechanisms in cyclonic and anticyclonic vortices. The analyses consist of simple analytical approximations and nonlinear numerical simulations of quasi-two-dimensional vortices. When considering only the top drag mechanism, it is found that anticyclones decay faster than cyclones. By considering only the vorticity-advection effect, the vortices acquire horizontal momentum and drift; furthermore, anticyclones are reinforced while cyclones are weakened. The joint action of both mechanisms and the possible consequences on vertical transport properties are also discussed.