Abstract:An analytical model is developed which explores the impact of irregular sea-floor roughness on large-scale oceanic flows. The previously reported asymptotic ‘sandpaper’ theory of flow-topography interaction represents relatively swift currents and exhibits singular behaviour in the weak flow limit. The present investigation systematically spans a wider parameter space and identifies the principal dissimilarities in the topographic regulation of slow and fast currents. The fast flows are controlled by the Reyno… Show more
“…Building on earlier works (Radko 2022 a , b ), Radko (2023) extends his sandpaper theory for flow–topography interaction, which previously only included the high-Reynolds-number (fast-flow) regime, to also account for slow flows. He then provides an analytical form that bridges the two asymptotic limits, resulting in a holistic model spanning slow-to fast-flow regimes.…”
Section: Overviewmentioning
confidence: 99%
“…mesoscales and larger). Figure 1.( a ) A schematic diagram, representing the topography employed in the sandpaper model of Radko (2023). ( b ) An enlarged view of the solution over a small part of the domain, showing the dominant impacts of topography on the flow in the fast-flow (top row) and slow-flow (bottom row) regimes.…”
Section: Overviewmentioning
confidence: 99%
“…( b ) An enlarged view of the solution over a small part of the domain, showing the dominant impacts of topography on the flow in the fast-flow (top row) and slow-flow (bottom row) regimes. Adapted from Radko (2023). …”
Section: Overviewmentioning
confidence: 99%
“…The shortcoming of the fast-flow regime of Radko (2022 a , b ) was that once the flow speeds were reduced (), the topographic forcing would blow up. While this was dealt with by an ad hoc constraining of the forcing in the earlier works, in Radko (2023) this issue is addressed by introducing a slow-flow limit and a bridge between the two. In the slow-flow regime corresponding to , where , Radko shows that the leading-order balance lies between vortex stretching/squeezing due to advection of large-scale flow into deeper/shallower regions and the frictional spin-down of vortical motions (see figure 1 b , bottom row).…”
Section: Overviewmentioning
confidence: 99%
“…Parameterizations of such subgrid-scale processes in ESMs are in their infancy, and hence reliable turbulence closure models for flow–topography interactions are much needed. Radko (2023) provides a useful step forward in this direction.…”
While large-scale seafloor features (e.g. continental slopes, mid-ocean ridges) help shape the broad patterns of ocean circulation, small-scale rough topography (e.g. seamounts, abyssal hills) can also impact the large-scale dynamics in two significant ways. First, they impact the momentum budget through flow steering, flow blocking and drag force, non-local momentum transfer via the generation of radiating internal waves and momentum dissipation by topographically induced turbulence. Second, they impact the density budget. Turbulence induced by flow–topography interactions facilitates ocean overturning circulation by upwelling dense, deep waters which form in polar oceans and sink to the abyss. Rough topography and its associated dynamics are of subgrid scale in Earth systems models (ESMs) and need parameterization for the foreseeable future. A parameterization of the intertwined impacts of flow–topography interactions on momentum and density budgets is currently non-existent, although its importance is well established. Radko (J. Fluid Mech., vol. 961, 2023, A24) provides a novel analytical model for representing the impact of rough seafloor on larger-scale flows, spanning slow to fast flow-speed regimes in homogeneous and multilayer models. The proposed ‘closure’ is in remarkable agreement with high-resolution numerical simulations and provides a crucial step forward in parameterizing the impact of rough topography in coarse-resolution ocean models. Extending the model to the full Navier–Stokes equations, linking it to the density budget and considering more realistic ocean topography are three critical future steps towards implementing Radko's theory in operational ESMs.
“…Building on earlier works (Radko 2022 a , b ), Radko (2023) extends his sandpaper theory for flow–topography interaction, which previously only included the high-Reynolds-number (fast-flow) regime, to also account for slow flows. He then provides an analytical form that bridges the two asymptotic limits, resulting in a holistic model spanning slow-to fast-flow regimes.…”
Section: Overviewmentioning
confidence: 99%
“…mesoscales and larger). Figure 1.( a ) A schematic diagram, representing the topography employed in the sandpaper model of Radko (2023). ( b ) An enlarged view of the solution over a small part of the domain, showing the dominant impacts of topography on the flow in the fast-flow (top row) and slow-flow (bottom row) regimes.…”
Section: Overviewmentioning
confidence: 99%
“…( b ) An enlarged view of the solution over a small part of the domain, showing the dominant impacts of topography on the flow in the fast-flow (top row) and slow-flow (bottom row) regimes. Adapted from Radko (2023). …”
Section: Overviewmentioning
confidence: 99%
“…The shortcoming of the fast-flow regime of Radko (2022 a , b ) was that once the flow speeds were reduced (), the topographic forcing would blow up. While this was dealt with by an ad hoc constraining of the forcing in the earlier works, in Radko (2023) this issue is addressed by introducing a slow-flow limit and a bridge between the two. In the slow-flow regime corresponding to , where , Radko shows that the leading-order balance lies between vortex stretching/squeezing due to advection of large-scale flow into deeper/shallower regions and the frictional spin-down of vortical motions (see figure 1 b , bottom row).…”
Section: Overviewmentioning
confidence: 99%
“…Parameterizations of such subgrid-scale processes in ESMs are in their infancy, and hence reliable turbulence closure models for flow–topography interactions are much needed. Radko (2023) provides a useful step forward in this direction.…”
While large-scale seafloor features (e.g. continental slopes, mid-ocean ridges) help shape the broad patterns of ocean circulation, small-scale rough topography (e.g. seamounts, abyssal hills) can also impact the large-scale dynamics in two significant ways. First, they impact the momentum budget through flow steering, flow blocking and drag force, non-local momentum transfer via the generation of radiating internal waves and momentum dissipation by topographically induced turbulence. Second, they impact the density budget. Turbulence induced by flow–topography interactions facilitates ocean overturning circulation by upwelling dense, deep waters which form in polar oceans and sink to the abyss. Rough topography and its associated dynamics are of subgrid scale in Earth systems models (ESMs) and need parameterization for the foreseeable future. A parameterization of the intertwined impacts of flow–topography interactions on momentum and density budgets is currently non-existent, although its importance is well established. Radko (J. Fluid Mech., vol. 961, 2023, A24) provides a novel analytical model for representing the impact of rough seafloor on larger-scale flows, spanning slow to fast flow-speed regimes in homogeneous and multilayer models. The proposed ‘closure’ is in remarkable agreement with high-resolution numerical simulations and provides a crucial step forward in parameterizing the impact of rough topography in coarse-resolution ocean models. Extending the model to the full Navier–Stokes equations, linking it to the density budget and considering more realistic ocean topography are three critical future steps towards implementing Radko's theory in operational ESMs.
Recent studies reveal the dramatic impact of seafloor roughness on the dynamics and stability of broad oceanic flows. These findings motivate the development of parameterizations that concisely represent the effects of small-scale bathymetric patterns in theoretical and coarse-resolution numerical circulation models. The previously reported quasi-geostrophic ‘sandpaper’ theory of flow–topography interaction a priori assumes gentle topographic slopes and weak flows with low Rossby numbers. Since such conditions are often violated in the ocean, we now proceed to formulate a more general model based on shallow-water equations. The new version of the sandpaper model is validated by comparing roughness-resolving and parametric simulations of the flow over a corrugated seamount.
Seafloor roughness profoundly influences the pattern and dynamics of large-scale oceanic flows. However, these kilometre-scale topographic patterns are unresolved by global numerical Earth system models and will remain subgrid for the foreseeable future. To properly represent the effects of small-scale bathymetry in analytical and coarse-resolution numerical models, we develop the stratified ‘sandpaper’ theory of flow–topography interaction. This model, which is based on the multilayer shallow-water framework, extends its barotropic antecedent to stratified flows. The proposed theory is successfully tested on the configuration representing the interaction of a zonal current with a corrugated cross-flow ridge.
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