Topographic drag in rapidly rotating fluids
Abstract
Flows over topography in stratified fluids have long been studied in oceanography and atmospheric sciences, where internal gravity waves play a major role in energy dissipation, mixing and angular-momentum transfer. By contrast, the impact of topography in rapidly rotating homogeneous fluids remains poorly understood, despite its potential importance in well-mixed rotating fluid layers (e.g. planetary liquid cores or vigorously convecting subsurface oceans). In particular, predictive scaling laws for the drag generated by finite-amplitude topography are still lacking, even in the simplest case of a uniform steady flow past a topography. Here, we investigate the pressure drag produced by a uniform flow over a three-dimensional periodic topography in a rapidly rotating Cartesian fluid layer using asymptotic analysis and direct numerical simulations. We show that the topography excites inertial waves, which radiate energy into the fluid interior and generate a wave-driven pressure drag upper D D D . In the shallow-slope limit left parenthesis h 0 k much less than 1 right parenthesis ( h 0 k ≪ 1 ) (h0k ≪ 1) , we recover the classical scaling law upper D proportional to h 0 squared k D ∝ h 0 2 k D ∝ h02 k . We then extend this theory to finite-slope topographies left parenthesis h 0 k greater than or equivalent to 1 right parenthesis ( h 0 k ≳ 1 ) (h0k ≳ 1) in the quasi-geostrophic regime left parenthesis upper U 0 k much less than upper Omega right parenthesis ( U 0 k ≪ Ω ) (U0k ≪ varOmega ) , deriving a correction that quantitatively agrees with direct numerical simulations. In the asymptotic steep limit left parenthesis h 0 k much greater than 1 right parenthesis ( h 0 k ≫ 1 ) (h0k ≫ 1) , the drag becomes independent of topographic height and scales as upper D proportional to k Superscript negative 1 D ∝ k − 1 D ∝ k−1 , implying a maximum drag for an optimal slope h 0 k asymptotically equals 3.17 h 0 k ≃ 3.17 h0k ≃ 3.17 . Finally, we show that this prediction quantitatively explains previous laboratory experiments reporting an optimal topographic wavelength for spin-up in a rotating fluid.
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BibTeX
@article{giraud2026topographic,
title = {{Topographic drag in rapidly rotating fluids}},
author = {Vadim Giraud and Jerome Noir and David Cébron and Jérémie Vidal and Remy Monville},
journal = {Journal of Fluid Mechanics},
year = {2026},
month = jul,
doi = {10.1017/jfm.2026.11857},
url = {https://hal.science/hal-05847793v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Topographic drag in rapidly rotating fluids
AU - Vadim Giraud
AU - Jerome Noir
AU - David Cébron
AU - Jérémie Vidal
AU - Remy Monville
PY - 2026
DA - 2026/07/29
JO - Journal of Fluid Mechanics
DO - 10.1017/jfm.2026.11857
UR - https://hal.science/hal-05847793v1
AB - Flows over topography in stratified fluids have long been studied in oceanography and atmospheric sciences, where internal gravity waves play a major role in energy dissipation, mixing and angular-momentum transfer. By contrast, the impact of topography in rapidly rotating homogeneous fluids remains poorly understood, despite its potential importance in well-mixed rotating fluid layers (e.g. planetary liquid cores or vigorously convecting subsurface oceans). In particular, predictive scaling laws for the drag generated by finite-amplitude topography are still lacking, even in the simplest case of a uniform steady flow past a topography. Here, we investigate the pressure drag produced by a uniform flow over a three-dimensional periodic topography in a rapidly rotating Cartesian fluid layer using asymptotic analysis and direct numerical simulations. We show that the topography excites inertial waves, which radiate energy into the fluid interior and generate a wave-driven pressure drag upper D D D . In the shallow-slope limit left parenthesis h 0 k much less than 1 right parenthesis ( h 0 k ≪ 1 ) (h_0k ≪ 1) , we recover the classical scaling law upper D proportional to h 0 squared k D ∝ h 0 2 k D ∝ h_0^2 k . We then extend this theory to finite-slope topographies left parenthesis h 0 k greater than or equivalent to 1 right parenthesis ( h 0 k ≳ 1 ) (h_0k ≳ 1) in the quasi-geostrophic regime left parenthesis upper U 0 k much less than upper Omega right parenthesis ( U 0 k ≪ Ω ) (U_0k ≪ varOmega ) , deriving a correction that quantitatively agrees with direct numerical simulations. In the asymptotic steep limit left parenthesis h 0 k much greater than 1 right parenthesis ( h 0 k ≫ 1 ) (h_0k ≫ 1) , the drag becomes independent of topographic height and scales as upper D proportional to k Superscript negative 1 D ∝ k − 1 D ∝ k^−1 , implying a maximum drag for an optimal slope h 0 k asymptotically equals 3.17 h 0 k ≃ 3.17 h_0k ≃ 3.17 . Finally, we show that this prediction quantitatively explains previous laboratory experiments reporting an optimal topographic wavelength for spin-up in a rotating fluid.
SN - 0022-1120
SN - 1469-7645
ER -