the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Apr 2026
Dynamic Geostrophic Nudging (DGN): A Novel Method for Controlling the Background Flow in Large Eddy Simulation
Abstract. Initializing idealized Large-Eddy Simulations (LES) for wind energy applications presents a persistent control problem, typically characterized by slow convergence due to inertial oscillations and the difficulty of matching target height wind targets. To address this, we present Dynamic Geostrophic Nudging (DGN), a method that couples physical fidelity with computational efficiency. Unlike standard velocity nudging, DGN acts on the forcing terms: it dynamically adjusts the geostrophic wind components based on the flow tendency and the error between the mean velocity and the target value. This mechanism allows the controller to efficiently steer the mean wind toward the target while actively damping inertial oscillations in the boundary layer. We employ a one-dimensional model to perform a parameter sweep and investigate the sensitivity of the control parameters before applying the method to a full three-dimensional LES. The results demonstrate that DGN reduces the spin-up time from the standard 12–24 hours to approximately two hours while maintaining the target wind vector with high accuracy. Furthermore, by arresting the unphysical transient growth of the boundary layer, the method allows for the use of vertically optimized domains, representing a significant advancement in the operational efficiency of precursor generation for wind farm simulations.
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RC1: 'Comment on wes-2026-66', Anonymous Referee #1, 04 May 2026
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The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2026-66/wes-2026-66-RC1-supplement.pdfReplyCitation: https://doi.org/
10.5194/wes-2026-66-RC1 -
RC2: 'Comment on wes-2026-66', Anonymous Referee #2, 03 Jun 2026
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I really enjoyed reading this manuscript. I think the author(s) did an excellent job presenting this topic and addressing all advantages and shortcomings of this study. I believe this study presents an approach that will be an amazing tool and opportunity to reduce computational costs for some of those computationally intensive three-dimensional LES runs.
Citation: https://doi.org/10.5194/wes-2026-66-RC2 -
RC3: 'Comment on wes-2026-66', Anonymous Referee #3, 04 Jun 2026
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The manuscript describes a method reduce the spin-up time of Large-Eddy Simulations (LES) used to describe
the atmospheric boundary layer, with use of LES for wind energy as an important application in mind.
The work carried out may be of interest and may introduce improvements in the methodology for
such simulations. However, there is a major concern in the way the method is introduced. Rather
than a change of method for the spinup, the authors introduce a change in the frame and objectives
of the simulation. The formulation and equations are presented in a confusing and misleading way
unfortunately (see 'Main concern' below). Reconsidering the work and the presentation as a whole
seems necessary to make it possible for the manuscript to state clearly what is at stake.
I therefore advise rejection, but encourage the authors to present their approach and results
under a different angle.Main concern
The authors compare two sets of simulations as if they were comparable, arguing that the
difference comes from the method used to control the spinup and in particular the inertial
oscillations that arise during the spin up of these simulations. In fact they are comparing
simulations that differ in their setup and objective. Hence the comparison is misleading and
the comments and vocabulary used to interpret them is at the very least confusing.Part of the confusion may arise from the fact that throughout the manuscript, the authors
always present the pressure gradient, imposed by the large-scale atmospheric state above
the boundary layer, only though the form of a geostrophic wind (see lines 20-21, 25, 48)).
An insidious effect is that the reader may not realize clearly that modifying the
geostrophic wind consists in modifying the external pressure gradient.The difference is particularly clear in the 1D example, described in Section 3.
These simulations describe a one-dimensional velocity profile in an atmospheric boundary
layer with a constant eddy viscosity. Stationary equilibrium solutions are known (Ekman
spiral).A first set of simulations aims to answer the following question: what wind profile
sets up at equilibrium given a given environmental forcing in the form of an external
pressure gradient force? Here the simulations aim as simulating the response of a
small volume of fluid, near the surface, subject to given environmental conditions
(an external pressure gradient, that is fixed).A second set of simulations aims to answer the following question: what wind profile
sets up at equilibrium so that a target velocity is achieved at a given level (typically
a target wind speed at hub height for wind energy applications)? Here the simulations
aim at having specified wind values at a given level in the interior of the domain,
with the possibility of modifying the boundary conditions (the external pressure
gradient).The first set of simulations is called 'NoNudge', the second set of simulations is
called 'Nudge'. They differ in their aim. A person interested in the development of
the atmospheric boundary layer, given a large-scale atmospheric state (the external
pressure gradient) is interested in the first set. A person interested in the flow
at hub-height, for a given value of the incoming wind, is obvisouly interested in the
second set of simulations.Using a simulation framework corresponding to 'NoNudge' with the aim of having a given
wind speed at a given height leads to a "laborious trial-and-error process to achieve
specific wind conditions at a target height" (line 295). It is rather clear that the
frame proposed here is of interest for LES simulations aiming at wind energy applications.
However, the way the method is presented and the way the simulations are commented
is very problematic:1. the way the method is presented in equations (1) to (7) seems a convoluted way to
present that the tendency for the horizontally averaged wind is simply imposed. In
equation (3), a modification to the external pressure gradient is introduced (Delta G)
so that this tendency is exactly what is targeted (as defined in equation (2)). It
may make sense, for the implementation which involves smoothing and filtering, to write
things out this way. But it should be clearly stated: "We impose the tendency
for the horizontally averaged wind, as defined in equation (2). This is done
by modifying the boundary conditions (external pressure gradient)."2. The way the simulations are commented is very misleading, or even wrong. Examples
are given only from Section 3, which has the advantage of having unambiguous solutions.
The NoNudge simulation (organge curves in Figure 3) gives the answer to the question
of the wind profile that sets up given an external pressure gradient such that the
geostrophic wind aloft is 10 m/s. Very clearly, the simulation gives the right answer
(figure 3). It has the disadvantage of taking time to adjust to it (figure 4).
The Nudge simulation (green curves) gives the right answer to another question (the
profile such that the wind at hub-height is 10 m/s). Statements as in the end of the
caption to Figure 3 ("the NoNudge simulation exhibits a large steady-state error")
are misleading, if not wrong. This is not an "error". The simulation is simply not
designed to yield a given wind at hub-height.
Minor pointsl75 should the authors first write the pressure gradient as a pressure gradient, before switching to its
expression using the geostrophic wind? For a reader not familiar with geostrophic wind, this would be
helpful. Presently, the authors simply assume all readers are familiar, or will go and seek understanding
from cited references. More importantly, writing this as a pressure gradient emphasizes that
this corresponds to a large-scale environmental boundary condition.Citation: https://doi.org/10.5194/wes-2026-66-RC3
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