On the Wind-Driven Formation of Plankton Patches in Island Wakes

Abstract

Using a three-dimensional coupled physical–biological model, this paper explores the effect that short-lived wind events lasting a few days in duration have on the creation of phytoplankton blooms in island wakes. Findings show that wind-induced coastal upwelling creates initial nutrient enrichment and phytoplankton growth near the island, whereas an oscillating flow, typical of island wakes, expels patches of upwelled water, including its nutrient and phytoplankton loads, into the ambient ocean. Dependent on the wind direction, a short-lived wind event can create one or more plankton patches with diameters of the order of the island diameter. Phytoplankton continues to grow within floating patches, each forming an individual marine ecosystem. While the ecological features of island wakes are well documented, this study is the first that describes the significance of short-lived, transient wind-driven upwelling in the process.

1. Introduction

Plankton concentrations are spatially heterogeneous and not randomly distributed in the sea [1,2,3,4,5,6,7,8,9]. This spatial heterogeneity is characterized as patches, aggregations, or clusters in which planktonic organisms exhibit higher concentrations than found in the surrounding water. In the oceans, patches form and exist at various horizontal scales, from the microscale (from 0.01 to 1 m) to the mesoscale (from tens to hundreds of kilometers), noting that plankton patches also form in the vertical as “thin layers” or as classical subsurface phytoplankton blooms. Moreover, they can exist at multiple scales simultaneously, with smaller patches comprising larger aggregations [10]. Phytoplankton forms the basis of most marine food webs. Hence, knowledge of the physical processes that influence phytoplankton growth and plankton patchiness is essential for understanding the functioning of marine food webs and key biogeochemical cycles. Despite the importance of plankton patchiness over a range of spatial scales, the understanding of the mechanisms underlying the generation and maintenance of plankton patches is relatively poor [11].

The “island mass effect” summarizes various coupled physical–biogeochemical mechanisms that enhance plankton productivity near an island or groups of islands [12]. Its mechanisms include the interaction of oceanic flows with island topography [13], tidal mixing around islands [14], tidally induced internal waves [15], turbulent mixing in island wakes [16], and other factors such as nutrient intake from island runoff [17], atoll flushing [18], groundwater discharge [19], and human activities that increase nearshore nutrient concentrations above natural levels [20].

Island wakes are flow disturbances in fluids that arise from horizontal flow around an obstacle. Ample studies have focused on physical processes in the wakes of islands and headlands [21,22,23,24,25,26,27,28,29,30,31,32,33,34]. The dynamics of island wakes can be characterized by several nondimensional numbers described in Section 2.1. Lateral friction with the island provides the dominant boundary stress in so-called “deep-water wakes”, whereas bottom drag becomes the dominant source of vorticity generation in “shallow-water wakes” [25]. The present study focuses on deep-water wakes, which are a reasonable approximation for reef islands that have relatively steep reef fronts (see [35]).

Several studies addressed the ecological impacts of island wakes (e.g., [16,36,37,38,39]). According to the recent review in [40], the generation of cyclonic eddies via barotropic or baroclinic instabilities [41,42] and flow divergence [16,43] are deemed common nutrient enrichment mechanisms in the lee of an island. Mesoscale cyclonic eddies are traditionally affiliated with colder and nutrient-enriched waters and anticyclonic eddies with warmer and nutrient-low waters [43,44]. This paradigm has been challenged in recent years with observations of cold-core anticyclonic eddies and warm-core cyclonic eddies in several instances (e.g., [45]). Another mechanism that can lead to the appearance of surface phytoplankton near an island is the passive uplift of water that contains the deep chlorophyll maximum [46].

The classical wind-driven coastal upwelling process has received relatively little attention in the discussion of nutrient-enrichment processes near islands with a few exceptions, such as the coupled physical–biogeochemical model study by [47] that suggests the existence of sporadic wind-driven upwelling events on the northeastern side of the Hawaiian Islands. A recent study [35] used a process-oriented coupled physical–biological model to demonstrate that wind events of few days in duration can trigger significant phytoplankton growth near tropical reef islands >10 km in diameter. Simulated vertically integrated chlorophyll-a (chl-a) levels of ~10 mg/m² agreed well with observational evidence from the authors of [18], who reported elevated chl-a levels of 1–10 mg/m² (often intensified at depth) within 10 km from the coast from 25 in situ surveys across 21 pacific coral reef islands and atolls. This finding has motivated the current work, which explores how short-lived wind events influence phytoplankton production in island wakes, not considered in [35]. The findings of this work suggest that wind-induced upwelling events near islands play a significant role in overall nutrient enrichment and phytoplankton production in island wakes.

2. Theoretical Background and Methodology

2.1. Theoretical Background

The dynamics of island wakes can be characterized using several nondimensional numbers. The Reynolds number (Re) is defined by

Re = UD⁄υ

(1)

where U is the unperturbed upstream velocity, D is the island diameter, and υ is the ambient kinematic viscosity. In hydrodynamic modeling applications, ambient kinetic viscosity in the formulation of the Reynolds number is typically expressed by the scale-dependent turbulent viscosity A_h [37], that is

Re = UD⁄A_h

(2)

The value of Re determines the transition between laminar and turbulent flows. Relatively low values of 1 < Re < 40 lead to a laminar separation with the formation of two steady vortices and a return flow (see [35]). This zone, referred to as the retention zone, operates as trap for floating particles [23]. Under nonrotating and uniform-density conditions, higher values of 40 < Re < 1000 lead to the formation of periodic vortices, known as the “von Kármán vortex street”. For Re > 1000, the separated flow becomes increasingly turbulent and temporally irregular.

The relative influence of rotation, i.e., the Coriolis force, is characterized by the Rossby number (Ro), given by

Ro = U⁄(fD)

(3)

where f is the Coriolis parameter. Previous laboratory and numerical studies show that increasing the rotation rate tends to inhibit the shedding of vortices (see [41]).

The relative influence of density stratification can be expressed by a baroclinic Froude number (Fr) that is defined by

Fr = U⁄c

(4)

where c is the phase speed of internal wave modes. For instance, for a linearly stratified fluid layer of thickness H and a vertical density gradient ∂ρ/∂z, this phase speed is given by

c = M H

(5)

where M² = −g/ρ_o∂ρ/∂z is the stability frequency; g = 9.81 m/s² is acceleration due to gravity; and ρ_o = 1026 kg/m³ is the mean density. On the other hand, a two-layer fluid with a density difference of Δρ and an upper layer thickness of h relates to a phase speed (squared) of (e.g., [48])

c² = (Δρ/ρ_o) gh(H − h)/H

(6)

noting that a relatively thin upper layer (h << H) yields the approximation

c² ≈ (Δρ/ρ_o) gh

(7)

Under the influence of both rotation and density stratification, the baroclinic instability process leads to island wakes that shed cyclonic and anticyclonic eddies (i.e., circular geostrophic flow patterns) of sizes of the order of the internal Rossby radius of deformation:

r = c/f

(8)

The squared ratio between the Rossby and Froude numbers gives the Burger number (Bu); that is, Bu = (Ro/Fr)² = (r/D)². Another scale of relevance to the dynamics of island wakes is the aspect ratio (δ) between the depth of the surface mixed layer, h, and the island diameter, D, which is given by δ = h/D. Typical scales for the oceanic situation are U~0.1–0.5 m/s, D~10–30 km, h~100 m, f~1 × 10⁻⁴ s⁻¹, Δρ~1–5 kg/m³, and A_h~5–20 m²/s. The magnitude of A_h is based on the effective diffusivity theory [49,50] under the assumptions of a turbulent Prandtl number of unity and a characteristic turbulent length scale of the order of D. This relates to nondimensional numbers of Re~50–3000 (likely to induce vortex shedding), Fr~0.05–0.5 (subcritical regime), Bu~0.05–2 (related to r~5–25 km), and δ~0.005.

2.2. Model Description

This study applies the same model equations as described in [35]. Only key model features are summarized here. The physical model is a conventional sigma-coordinate model, COHERENS [51], that is applied with a horizontal resolution of 1 km and 20 vertical layers to a model domain that extends 300 km in the x-direction and 100 km in the y-direction (Figure 1). The x-axis points eastward for the identification of wind and flow directions. The island is simplified as a circular vertical cylinder with a diameter varying between 10 km and 30 km.

Initially, the ocean’s density field is horizontally uniform. The initial density profile exhibits a strong pycnocline below a depth of 50 m (Figure 2), characterized by a stability frequency of M = 0.0183 s⁻¹. The presence of strong stratification hinders the development of deeper flows. This allowed us to limit the total depth of the model domain of 100 m, which significantly reduces the CPU time required by model simulations. The Coriolis parameter is set to f = +0.5 × 10⁻⁴ s⁻¹, corresponding to a geographical latitude of 20° N.

Horizontal turbulence is parameterized using the Smagorinsky closure scheme [52]. Eddy diffusivity is assumed to be the same as eddy diffusivity. Vertical turbulence is parameterized with the classical k-ε turbulence closure scheme, using standard parameter settings (see [51]). Bottom friction is disabled, and a semi-slip boundary condition (see [53]) is used for the calculation of lateral friction.

The physical model is directly coupled to a nitrogen–phytoplankton (NP) model which, for simplicity, ignores effects due to zooplankton grazing and bacterial nutrient recycling. Initially, the surface mixed layer is devoid of nitrogen, and the the dissolved nitrate concentration increases below the surface mixed layer linearly to a maximum of 10 μM at a depth of 75 m, with constant values underneath (Figure 2).

The conservation equations for the dissolved nitrogen concentration (N) and phytoplankton concentration (P) are given by

∂N⁄∂t + Adv(N) = Diff(N) − (μ*N)/(K_N + N) P

(9)

∂P⁄∂t + Adv(P) = Diff(P) + [(μ*N)/(K_N + N) − λ] P

(10)

where t is time, Adv(.) and Diff(.) are three-dimensional advection and diffusion operators, K_N the half-saturation constant of the phytoplankton’s uptake of nitrogen, taken as 1.0 μM, μ* is the largest possible phytoplankton growth rate under saturated nutrient conditions (i.e., N >> K_N), and λ is the mortality rate, set to 0.05 day⁻¹.

The growth rate μ* is calculated using a prescribed day–night cycle of radiance (see [35]). The resultant daily averaged net growth rate <μ*−λ> attains a maximum value of 0.5 day⁻¹ at a depth of 10 m and becomes negative at depths > 45 m (Figure 3a). This vertical profile allows us to calculate the minimum amount of dissolved nitrogen, N_min, required to facilitate phytoplankton growth (Figure 3b). Phytoplankton growth can only occur at depths < 45 m, and the lowest values of Nmin < 0.14 μM are found in the upper 20 m of the water column. The nutrient-related multiplier in the equation for phytoplankton growth rate in (10) is given by ε = N/(K_N + N). For instance, N = 0.2 μM corresponds to ε = 0.17. This reduces the maximum growth rate, <μ*>, at a 10 m depth to 0.09 day⁻¹ and the maximum net growth rate (<μ* − λ>) to 0.04 day⁻¹. On the other hand, N = 1 μM (ε = 0.5) yields a fivefold higher maximum net growth rate of 0.2 day⁻¹.

Chl-a values in units of mg/m³ are calculated from predicted phytoplankton concentrations in units μM-N on the basis of an average C:chl-a ratio of 50:1 (see [54]) and a Redfield ratio of C:N of 106:16. Results are presented as vertically integrated chl-a concentrations (mg/m²) for comparison with the values reported in [18]. All experiments commenced with a small, initially uniform ambient chl-a concentration of 0.1 mg/m³.

The initial density, nitrogen and phytoplankton distributions were selected based on the following conditions: (1) a small but continuous upward diffusion of nitrogen should not induce significant phytoplankton growth throughout the model domain during simulations; and (2) transient wind-induced upwelling can induce localized nutrient enrichment near the island. These conditions avoid situations in which either wind-induced mixing induces widespread phytoplankton blooms in the presence of a shallower nutricline or where wind events remain without effect for a deeper nutricline.

2.3. Forcing and Boundary Conditions

The simulations are completed in two phases. The first setup phase focuses on the establishment of island wakes without wind effects over 30 days of simulation based on the initial conditions described in Section 2.2. Advective–diffusive variations in the nutrient field are accounted for, but biological effects are ignored. Starting with small uniform chl-a concentrations of 0.1 mg/m³, the second phase of experiments commences with transient wind forcing and continues for another 20 days of simulation.

The ambient current is created with the use of a sea-level field η*(y) that corresponds to a target geostrophic flow speed U according to the geostrophic balance:

η*(y) = Δη y/L where Δη/L = −f U⁄g

(11)

where L is the width of the model domain (100 km). Δη is linearly adjusted from zero to its final value over 5 days of setup experiments to avoid the formation of unwanted gravity waves. The sea-level field η*(y) is applied to force the model’s sea-level elevation η within 5 grid points from the western, southern, and northern boundaries, using a Rayleigh damping of the form of

∂η/∂t = κ(η* − η)

(12)

where the damping parameter κ linearly increases from zero across the damping zones to a value of 0.5/Δt at the boundaries, where Δt is the numerical time step. The values of nitrogen concentration N are kept unchanged along the upstream (western) boundary in all simulations. Zero-gradient conditions are applied to all variables along all open boundary conditions otherwise.

The surface boundary condition for the horizontal current (u,v) is derived by specifying the surface stress (τ_x,τ_y) as a function of horizontal wind velocity components (U_w,V_w), measured at a height of 10 m above sea level, according to the standard bulk formulae:

ρ_oν_T ∂u/∂z = τ_x = ρ_aC_DwUW

(13)

ρ_oν_T ∂v/∂z = τ_y = ρ_aC_DwVW

(14)

where the densities of seawater and air are approximated as ρ_o = 1026 kg/m³ and ρ_a = 1.2 kg/m³, the near-surface vertical eddy viscosity, ν_T, is calculated from the k-ε turbulence closure scheme, C_D is the surface wind drag coefficient, and W = (U_W² + V_W²)^1/2 is the wind speed. For a wind speed of 10 m/s, used in this study, the latter can be approximated using a value of 0.0012 [55].

A short-lived wind event is prescribed during the first 6 days of the second phase of the experiments. The spatially uniform wind field is hereby linearly adjusted from 0 to its final value of 10 m/s over a day, kept constant for the following 4 days, and then linearly phased out over another day. For simplicity, orographic modification of the wind field is ignored. Note that wind events of up to 10 m/s in speed and durations of several days are common in tropical regions (see [35]).

2.4. Experimental Design

The control experiment uses an island with a diameter of D = 20 km. Two scenarios are considered. The first scenario considers an ambient flow speed of U = 5 cm/s, resulting in the formation of a laminar separation with two steady vortices and a return flow. The second scenario considers an ambient flow speed of U = 20 cm/s, creating a periodic von Kármán vortex street. Higher ambient flow speeds yield similar results. Both scenarios are repeated four times each with southerly, easterly, northerly, and westerly wind events. Sensitivity experiments consider variations of the island diameter in the range 10–30 km.

3. Results and Discussion

3.1. First Scenario (U = 5 cm/s)

An ambient flow speed of U = 5 cm/s creates a laminar separation with two steady vortices and a return flow (Figure 4a). The relative vorticity in the vortices remains below planetary vorticity with a ratio of ~0.4. Positive (cyclonic) vorticity is found in the southern half of the retention zone, and negative (anticyclonic) vorticity is found in the northern half. Due to vertical diffusion, the dissolved nitrate concentration N marginally increases in the downstream direction and within the retention zone (Figure 4b), but the nutrient enrichment is to too small to induce any phytoplankton growth in the setup experiment.

In contrast, transient wind forcing creates significant nutrient enrichment of N > 1 μM in vicinity of the island (Figure 5a and Figure 6). The wind forcing creates surface Ekman flows that induce a horizontal divergence of volume transports and, hence, upwelling offshore from a certain section of the island [35]. For instance, a southerly wind creates upwelling (downwelling) on the eastern (western) side of the island (Figure 5), which agrees with the classical Ekman theory. After 3 days, the upwelling process has created a 5 km wide upwelling zone with dissolved nitrogen concentrations exceeding 1 µM, which is sufficient to induce phytoplankton growth. In contrast, wind-induced mixing is insignificant in this experiment, as seen in the transect north of the island (Figure 5b), where N stays below 0.2 µM and phytoplankton growth cannot occur.

The location of the upwelling zone depends on the wind direction (Figure 6a–c), noting that the wind-driven upwelling currents interacts with the ambient flow of the island wake. After 5 days of the wind-forced experiment, each wind-forcing scenario has created a nearshore upwelling zone of elevated nutrient levels, but only southerly and easterly wind events have led to nutrient enrichment within the retention zone (Figure 6a,b).

To this end, each transient wind forcing scenario creates phytoplankton patches with vertically integrated chl-a concentrations of up to 20 mg/m² after 20 days of simulation (Figure 7). For instance, a southerly wind event creates a spiral-shaped patch of the same size as the island that becomes detached from the island to form part of the cyclonic vortex (Figure 7a). In contrast, a northerly wind event creates a phytoplankton patch that becomes entrained by the anticyclonic vortex (Figure 7c). An easterly wind event creates a phytoplankton patch that remains largely attached to the island, but with some leakage of nutrients into both vortices where some phytoplankton growth takes place (Figure 7b). Finally, a westerly wind event creates an elongated phytoplankton patch with vertically integrated chl-a concentrations of ~14 mg/m². Note that, due to the varied wind forcing, the structure of the island wakes differs slightly between the experiments.

3.2. Second Scenario (U = 20 cm/s)

An ambient flow speed of U = 20 cm/s leads to the formation of a periodic von Kármán vortex street that consists of flow undulations with a wavelength of ~100 km (Figure 8a). Here, as Re is increased, the shear layer at the island becomes so narrow that the relative vorticity, ζ = ∂v/∂x − ∂u/∂y, is larger than the Coriolis frequency in the near wake, with a |ζ|/f ratio >2. This situation creates alternating patches of cyclonic and anticyclonic vorticity in which the |ζ|/f ratio decreases to <1. Note that cyclonic (anticyclonic) vorticity patches are located near the southern (northern) crests of flow undulations of the island wake. Slight nutrient enrichment occurs in the retention zone and in the vorticity patches, (Figure 8b), but this enrichment is too small to induce phytoplankton growth in the setup experiment.

Again, it is the wind forcing that initiates significant nutrient enrichment near the island. Flow oscillations in the retention zone discharge this nutrient-enriched water within vorticity patches into the island wake (Figure 9a). To this end, the southerly wind forcing creates a single circular phytoplankton patch of a ~20 km diameter with a vertically integrated phytoplankton concentration of ~20 mg/m² after 15 days of simulation (Figure 9b). The vertical transect across this patch reveals that both nutrient and chl-a anomalies are vertically well mixed throughout the surface mixed layer (Figure 10). The phytoplankton patch contains a total of ~2000 kg of chlorophyll-a. The nutrient excess in this patch is sufficient to sustain phytoplankton growth on timescales of several weeks.

Interestingly, an easterly wind event leads to a series of nutrient and, hence, phytoplankton patches that are contained within cyclonic and anticyclonic vorticity patches (Figure 11). The vertically integrated chl-a concentration within the patches (~10 mg/m²) is smaller than that resulting from a southerly wind event (see Figure 9b). Similar to the U = 5 cm/s experiment (see Figure 7b), the upwelled water becomes discharged on both sides of the retention zone, which leads to more but less concentrated plankton patches. Again, the size of the plankton patches is of the order of the island diameter.

Both northerly and westerly wind events induce a more rapid dispersal of the upwelled water compared to the other wind directions (Figure 12). Here, the nutrient patches are elongated filaments of relatively low nutrient anomalies and reduced phytoplankton growth. Finally, sensitivity experiments demonstrate that larger islands increase the size of the plankton patches (Figure 13).

4. Final Discussion

Previous studies have shown that the island mass effect includes several mechanisms inducing phytoplankton production. In addition to these mechanisms, this study reveals that short-lived wind-driving upwelling events can significantly enhance nutrient enrichment in island wakes. The wind-induced patches of upwelled water, simulated here, form individual floating marine ecosystems in which the phytoplankton biomass continues to increase until effects due to reduced nutrient levels and zooplankton grazing (not included in this work) become dominant. Given the frequent occurrence of relatively strong wind events in the tropics (see [35]), such phytoplankton patches can be expected to form on a regular basis. The resultant series of floating phytoplankton patches established downstream from islands may complement the primary production of coastal upwelling systems (see [56]).

In a real oceanic situation, the upstream geostrophic flow involves cross-stream variations in the density field governed by thermal wind relations (see [41]). Due to vortex stretching, the associated flow perturbations in the island wake are prone to the baroclinic instability mechanism and the formation of mesoscale eddies. We can therefore expect that the wind-induced formation of nutrient/plankton patches, simulated here, operates to precondition further phytoplankton growth generated by baroclinic eddies or other processes, including the generation of sub-mesoscale vortices [57,58].

As shown in [35], the nutrient enrichment due to the island-upwelling process depends on several factors. Without ambient currents, it increases for stronger and longer wind forcing and larger islands (also shown here), and it decreases with stronger static stability of the water column. We can expect a similar functional relationship in the presence of ambient currents. However, the ambient currents considered here were relatively weak (<20 cm/s), and the study of stronger ambient flows remains for the future.

This study only considered single singular islands. It can be anticipated that for different wind directions, the shapes of islands modulate the strength of the upwelling process. It is also possible that the upwelling patches created near multiple islands interact with each other, which also remains to be investigated in the future.

5. Conclusions

Both island wakes and plankton patches have attracted scientific curiosity for many decades. The findings of this study shed new insights into the formation of phytoplankton patches in island wakes. Here, it is demonstrated that short-lived wind events can trigger significant nutrient enrichment near islands, which enhances plankton productivity in the turbulent wake. This indicates that localized short-lived wind events near islands are important agents of phytoplankton production in oceans. This study provides new insights into the functioning of marine food webs and biogeochemical cycles associated with the island mass effect. This new knowledge is important in understanding how global climate change can potentially affect the plankton productivity of tropical oceans, contributing to the improved management of marine resources.