Mixing by offshore wind infrastructure: Resolving the density stratified wakes past vertical cylinders

TL;DR

This paper investigates how offshore wind infrastructure perturbs stratified shelf-sea flows by simulating a vertical cylinder wake in a two-layer density field. Using high-resolution DNS/LES with a Schwarz-Spectral-Element approach, it reveals two distinct regimes: a weakly stratified, horizontally dominated wake with downstream vertical mixing, and a strongly stratified wake featuring a large thermocline recirculation and standing internal waves that drive localized mixing near the thermocline. By analyzing time-averaged fields, mean flows, and detailed energy budgets (KE, PE, TKE, SBV), the study elucidates how energy flows from drag into turbulent production, buoyancy flux, and irreversible mixing, with irreversible mixing reaching up to ~10% of the drag power in strong stratification. The findings have important implications for parameterizing infrastructure wakes in regional ocean models and suggest that field-scale mixing is strongly regime-dependent, governed by the interplay of $Re_d$, $Ri_d$, and buoyancy-driven vertical motions. The work also highlights the need to bridge DNS-LES results with field observations to constrain wake-induced mixing in offshore wind developments.

Abstract

This work is focussed on understanding the fundamental fluid dynamics of tidal wakes generated by offshore wind infrastructure in stratified waters, using direct numerical simulations. The tidal flows past the structures are approximated by a uniform quiescent background flow with a two-layer density profile, interacting with a vertically oriented cylinder. Through these simulations we identify the processes through which turbulence generated in the wake of the structures leads to vertical mixing across the thermocline.We identify two fundamentally different flow regimes, dependent on both the stratification strength and the flow Reynolds number. The 'weakly stratified' wake is characterised by a highly energetic wake and a dominance of horizontal shear. As a result, vertical mixing occurs much further downstream than the region of maximum turbulent kinetic energy production. In contrast, the `strongly stratified' wake regime is characterised by a large-scale recirculation region that develops across the thermocline which generates significant vertical shearing. This subsequently leads to time-independent standing waves which account for up to 10% of the total energy budget, and have characteristics similar to 'mode 2' internal solitary waves. The vertical shear introduced near the edges of the thermocline is highly efficient at local mixing, but vertical fluctuations are quickly suppressed as the wake propagates further downstream. We speculate that the emergence of this flow regime may explain discrepancies in previous field observations, which have been unable to detect a coherent wake far downstream of offshore wind infrastructure. Future work should focus on bridging the scale gaps between idealised simulations and the field.

Figures (20)

• Figure 1: Plan view (a) and side view (b) of the fluid domain and inflow conditions.
• Figure 2: Visualisation of instantaneous spanwise velocity (a to f) and temperature (g to l). $\hbox{Re}_d = 500$ for all panels with: $\hbox{Ri}_d = 0.05$ in panels (a, d, g, j); $\hbox{Ri}_d = 0.5$ in panels (b, e, h, k); and $\hbox{Ri}_d = 2.0$ in panels (c, f, i, l). Panels (a) to (c) and (g) to (i) show a $z-$normal slice at $z=0$, and panels (d) to (f) and (j) to (l) show a $y-$normal slice at $y=0$.
• Figure 3: Drag coefficient time series for all simulations over the full data acquisition time (a). Panel (b) shows the power spectral density associated to each drag coefficient time series, with successive cases shifted downward by two orders of magnitude, for clarity. Vertical dashed lines of (b) highlight the dominant vortex shedding frequency ($\omega_\text{peak}$) for case Re500Ri005, and twice this frequency ($2\omega_\text{peak}$).
• Figure 4: Time-averaged temperature (a to c), streamwise velocity (d to f) and vertical velocity (g to i) on a $y-$normal slice at $y=0$. $\hbox{Re}_d = 500$ for all panels with: $\hbox{Ri}_d = 0.05$ in panels (a, d, g); $\hbox{Ri}_d = 0.5$ in panels (b, e, h); and $\hbox{Ri}_d = 2.0$ in panels (c, f, i). Temperature data are presented as a perturbation from the spatially varying background field $\theta_0(x,z)$. Lines represent the thermocline bounds, quantified by the contours $\overline{\theta} = \pm 0.475$.
• Figure 5: Time-averaged spanwise velocity on a $z-$normal slice at $z=0$. $\hbox{Re}_d = 500$ for all panels with: $\hbox{Ri}_d = 0.05$ in panel (a); $\hbox{Ri}_d = 0.5$ in panel (b); and $\hbox{Ri}_d = 2.0$ in panel (c).