Natural convection due to surface cooling in sloping water bodies with vegetation

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/372674289 Natural convection due to surface cooling in sloping water bodies with vegetation ArticleinJournal of Hydraulic Research · July 2023 DOI: 10.1080/00221686.2023.2222094 CITATIONS 3 READS 81 2 authors: Vassilios Papaioannou Centre for Research and Technology Hellas 36 PUBLICATIONS193 CITATIONS SEE PROFILE Panagiotis Prinos Aristotle University of Thessaloniki 194 PUBLICATIONS2,199 CITATIONS SEE PROFILE All content following this page was uploaded by Vassilios Papaioannou on 15 September 2023. The user has requested enhancement of the downloaded file. Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=tjhr20 Journal of Hydraulic Research ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/tjhr20 Natural convection due to surface cooling in sloping water bodies with vegetation Vassilios Papaioannou & Panagiotis Prinos To cite this article: Vassilios Papaioannou & Panagiotis Prinos (2023) Natural convection due to surface cooling in sloping water bodies with vegetation, Journal of Hydraulic Research, 61:3, 382-395, DOI: 10.1080/00221686.2023.2222094 To link to this article: https://doi.org/10.1080/00221686.2023.2222094 Published online: 26 Jul 2023. Submit your article to this journal Article views: 5 View related articles View Crossmark data Journal of Hydraulic Research Vol. 61, No. 3 (2023), pp. 382–395 https://doi.org/10.1080/00221686.2023.2222094 © 2023 International Association for Hydro-Environment Engineering and Research Research paper Natural convection due to surface cooling in sloping water bodies with vegetation VASSILIOS PAPAIOANNOU ,PhD Student, Hydraulics Laboratory, Department of Civil Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece Email: [email protected] PANAGIOTIS PRINOS , Professor, Hydraulics Laboratory, Department of Civil Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece Email: [email protected] (author for correspondence) ABSTRACT Natural convection induced by surface cooling in sloping water bodies with vegetation is investigated numerically. The sloping water body consists of a vegetated region with a bottom slope equal to 0.1 and a deep region with a horizontal bottom. The volume-averaged Navier–Stokes equations together with the volume-averaged energy equation are solved numerically in the vegetated region. Submerged vegetation has an equivalent porosity of 0.85. The vegetation length is either equal to the total or half the sloping region. A differential cooling is applied at the top free surface with a varying heat loss rate between the two regions. The non-vegetated sloping water body is also considered for validation purposes. The results indicate that, when cooling is reduced in the vegetated region (a) there is a time delay for the establishment of the quasi-steady regime and (b) the exchange flow rate and the gravity current’s velocity decreases with increasing vegetation length. When cooling is completely blocked, different circulation patterns are developed. Keywords: Circulation; cooling; natural convection; thermal siphon; vegetation 1 Introduction Natural convection in sloping water bodies (lakes, reservoirs, wetlands) can occur when surface waters are heated or cooled at the same rate (Bouffard & Wüest, 2019; Horsch & Stefan, 1988; Lei & Patterson, 2005; Mao et al., 2010; Ulloa et al., 2022). Uniform cooling along the free surface of the water body and the increasing water depth of the sloping water body result in a more rapid cooling of the shallow waters than that of the deep waters. Hence, the generated horizontal temperature density gradient can drive an offshore–onshore exchange flow (large-scale overturning circulation), also known as a “thermal siphon” (Monismith et al., 1990). The latter increases the water exchange between nearshore and offshore waters, which in turn affects the ecological characteristics of the water body (MacIntyre & Melack, 1995). Natural convection can also occur when there is a nonuniform (differential) heating or cooling along the free surface of the sloping water body. Such a non-uniform heating or cooling may be due to the existence of aquatic vegetation, usually near the shore, which is able to block (totally or partially) the heating or cooling (Coates & Ferris, 1994; Lightbody et al., 2008; Oldham & Sturman, 2001). The characteristics of the developed horizontal convective currents (Hughes & Griffiths, 2008) are affected by the vegetation porosity ϕand permeability kp. Porosity ϕranges from 0.55 (mangroves) to 0.99 (water lily) as presented by Mazda et al. (1997). The most common values in natural wastewater treatment systems are from 0.7 up to 0.9 (Crites et al., 2006). Such horizontal convective currents have been investigated experimentally and numerically by various researchers (Coates & Ferris, 1994; Coates & Patterson, 1993; Papaioannou & Prinos, 2021; Tsakiri et al., 2016; Zhang & Nepf, 2009) using a non-uniform heating at the top free surface, a water body with horizontal bottom and either a floating or emergent vegetation with complete blockage of the incoming heating (solar radiation). The cooling-driven thermal siphon in a sloping water body has been observed in the field (Fer et al., 2002; Monismith et al., 2006) and is more pronounced when wind and background currents are weak or absent (Doda et al., 2022; Molina et al., 2014). The phenomenon has been investigated experimentally and numerically by several researchers after the pioneering work Received 3 November 2022; accepted 1 June 2023/Currently open for discussion. ISSN 0022-1686 print/ISSN 1814-2079 online http://www.tandfonline.com 382 Journal of Hydraulic Research Vol. 61, No. 3 (2023) Natural convection due to surface cooling in sloping water bodies with vegetation 383 of Horsch and Stefan (1988) and Horsch et al. (1994). They showed that due to the interaction between the surface cooling, induced thermals and the sloping bottom a two-layer exchange flow is formed, which leads to an overturning circulation. Laboratory experiments at small scales have been performed by Sturman et al. (1999), Wells and Sherman (2001) and Bednarz et al. (2008) for investigating several aspects of the phenomenon such as the horizontal exchange flow rate and the time scale needed for flushing the sloping region, the initialization of the gravity currents, the onset of Rayleigh–Bénard convection and the convective flow. Mao et al. (2010), using scaling analysis and numerical simulation, investigated the quasi-steady regime of natural convection induced by surface cooling. They indicated two possible flow scenarios depending on the bottom slope. For relatively large slopes, usually found in perialpine or alpine lakes, three flow regimes have been identified depending on the global Rayleigh number. For a given Rayleigh number, the sloping water body may be composed of one, two or three sub-regions, denoted as conductive, transition and convective zones, with their dynamics to depend on the Rayleigh number and the slope of the water body. Very recently, Ulloa et al. (2022) performed numerical experiments, using a 2D spectral large-eddy simulation (SLES) approach, for testing the theoretical regimes of Mao et al. (2010) and focusing on the transient convective regimes for Ra numbers up to 1020.TheRa number is determined using Ra =gβIoLs4 ρoCpvk2, where g=acceleration due to gravity, β=thermal expansion coefficient, Io=heat loss rate, Ls=length of the sloping region, ρo=water density at a reference temperature To,CP=specific heat of water, v=kinematic viscosity and k=thermal diffusivity. The vegetation presence in water bodies and its effect on cooling and/or heating induced natural convection have been studied by a few researchers (Coates & Ferris, 1994;Lin& Wu, 2014,2015; Lövstedt & Bengtsson, 2008; Molina et al., 2014; Monismith et al., 2006; Oldham & Sturman, 2001; Ulloa et al., 2018). Oldham and Sturman (2001) studied the effect of emergent vegetation on convective circulation, due to cooling, in shallow sloping wetlands using scaling analysis and experiments. They measured bottom convective currents of 1–10 mm s−1approximately and short timescales of convective flushing. Lövstedt and Bengtsson (2008) measured in the field the density-driven currents between reed belts and open water in the shallow lake Krakesjon. They measured a current of approximately 1.0 cm s−1for a net heat flux of 200 W m−2. They also estimated maximum velocities up to 1.5 cm s−1using the lock exchange equation for a net radiation at the free surface being 85% lower within the area with Phragmites australis, than that in the open area with no vegetation. Lin and Wu (2015) investigated numerically, using asymptotic solutions, the effect of vegetation shading (blockage), during daytime heating and night-time cooling, on the exchange flow rates and the general circulation in a sloping water body with a very small slope equal to 10−5. They found a vegetation blockage which causes a minimum horizontal exchange flow rate and divided the flow regime as topographic or vegetation shading dominated. In this, work we investigate natural convection induced by surface cooling in sloping and vegetated waters joined to a deeper and flat basin. The unsteady volume-averaged Navier– Stokes (VANS) equations are solved in conjunction with the unsteady volume-averaged equation in the vegetated region, using the Boussinesq approach (Papaioannou & Prinos, 2021). In the non-vegetated region these equations are simplified to the classical NS and energy equations. The maximum flow depth h is equal to 0.1 m, Lsis equal to 1.0 m and hence the slope So is equal to 0.1. The total length Lof the water body is equal to 2.0 m. Based on these length scales, the value of Soindicates a large bottom slope, after a comparison with the critical Rayleigh number (So>Rac−0.5,Rac≈657.5; Drazin & Reid, 2004) and the scenarios of Mao et al. (2010). The vegetation has a porosity ϕ=0.85. Such a slope is considered as a steep slope found in perialpine or alpine lakes. Fer et al. (2002) provide information about a slope of 0.09 in their study site in Lake Geneva. The vegetation length Lvis either equal to Ls(the whole sloping region is vegetated) or 0.5Ls(the shallow half of the sloping region is vegetated). A differential cooling is applied at the top free surface with a heat loss rate Ioin the deep region and Iv, either equal to 0.85Ioor 0.0, in the vegetated region. With Iv=0.85Iothe emergent vegetation blocks 15% of the incoming cooling, while for Iv=0.0 the vegetation blocks completely the incoming cooling. Special emphasis is given to the following questions: (i) What are the effects of vegetation on the thermal siphon induced by surface cooling in relatively large bottom slopes? How water exchange between nearshore and offshore is affected by the presence of vegetation in the nearshore region? (ii) How important are the vegetation length and shading in the occurrence and intensity of cold downslope gravity currents and the thermal siphon in general? 2 Simulation model set-up 2.1 Conceptual model Figure 1shows a two-dimensional (2D) model of the sloping water body used in this work. The body consists of two distinct regions, (1) a sloping region (So=h/Ls=0.1) with vegetation which has a length Lvequal to Lsor 0.5Ls, (2) a region of uniform water depth (horizontal bottom) with no vegetation. The model dimensions are those used by Bednarz et al. (2009)for comparison purposes characterized by the coexistence of two modes of movement, a downhill current driven by buoyancy and rotating plumes immersed from the surface of the water with a total length L=2.0 m and maximum flow depth h=0.1 m. 384 V. Papaioannou and P. Prinos Journal of Hydraulic Research Vol. 61, No. 3 (2023) Figure 1 Water body geometry and various configurations with vegetation The adopted Cartesian coordinate system starts at the left bottom point of the model (Fig. 1). The water body initially has no vegetation (Fig. 1a), the heat loss rate Io=31.4 W m−2and the Ra number is calculated equal to 7.45 ×1011.Itisused in this work for validation purposes and computational results are compared against those of Bednarz et al. (2009) and Mao et al. (2010). For the (b) and (c) configurations the vegetation, with ϕ=0.85 and Iv=0.85Io(the upper part of the emergent vegetation blocks 15% of the incoming cooling), has a length Lv=0.5 m and 1.0 m respectively. For the (d) and (e) configurations the heat loss rate in the vegetated region changes to Iv=0.0 (the incoming cooling is blocked completely by the vegetation). The above cases have been selected based on a reasoning presented below: (a) The non-vegetated sloping water body is considered for validation purposes, since experimental and numerical results are available (Bednarz et al., 2008,2009;Mao et al., 2010). Also, it is used for comparing the results with those of the vegetated cases and identifying the vegetation effects. In this case a uniform cooling is applied at the free surface of the water body with a heat loss rate Io. (b) For the water body with vegetation in the sloping region a differential cooling is applied at the top free surface with a heat loss rate Ioin the deep region and Iv, equal to 0.85Io, in the vegetated region (the upper part of the emergent vegetation blocks 15% of the incoming cooling). The vegetation has a length Lveither equal to Ls (the whole sloping region is vegetated) or 0.5Ls(the shallow half of the sloping region is vegetated). Hence, there is a rather mild non-uniform cooling at the free surface, the shallow vegetated region is cooled slower than that of (a); however, gravity currents are expected to appear at the bottom of the sloping region and large scale circulation patterns to form as those of (a). (c) A strong differential cooling is applied at the top surface with Ioin the deep region and no cooling in the vegetated region (Iv=0.0). In this case the incoming cooling is blocked completely by the vegetation. The vegetation length Lvis either equal to Lsor 0.5Ls. Hence, horizontal convective currents are expected to develop near the free surface, from the vegetated region towards the cooler deep region, which may also produce large scale circulation but of opposite rotation to that of the previous cases. Previous studies (e.g. Lei & Patterson, 2005) have shown that a 2D simulation can adequately reproduce the 3D nature of the flow. The slope Sois kept constant and equal to 0.1 which is considered as a large bottom slope (So>Rac−0.5,Rac≈657.5; Drazin & Reid, 2004) based on the scenarios of Mao et al. (2010). The parameters associated with the flow dynamics are (a) the Prandtl number Pr equal to 7.07 and (b) the Rayleigh number Ra equal to 7.45 ×1011 for the non-vegetated case. Based on the above values, Ra >Rac3and therefore the sloping region is expected to have three sub-regions (1) Region I – indistinct, conductive, (2) Region II – distinct, stable conductive and (3) unstable conductive (Mao et al., 2010). 2.2 Governing equations and numerical procedure For the numerical simulation, the unsteady VANS equations are solved – Eqs (1) and (2) in conjunction with the unsteady VAE equation (Eq. 3) – in the vegetated region, using the Boussinesq approach. In the non-vegetated region these equations are simplified to the classical NS and energy equations. These equations are shown below: ∂Uif ∂xi =0(1) ∂Uif ∂t+Ujf∂Uif ∂xj =−1 ρo ∂Pf ∂xi +∂ ∂xjv∂Uif ∂xj +∂Ujf ∂xi+gβTf−Tof+Fi (2) Journal of Hydraulic Research Vol. 61, No. 3 (2023) Natural convection due to surface cooling in sloping water bodies with vegetation 385 ∂Tf ∂t+Ujf∂Tf ∂xj =∂ ∂xjk∂Tf ∂xj (3) where Ui=velocity in the direction i,P=total pressure, T,To=temperature and initial temperature respectively, and Fi=resistance term due to vegetation. The symbol <> findicates the intrinsic volume average of a parameter A(scalar, vector, or tensor) which is defined as: Af=1 Vf Vf AdV (4) where Vfis the fluid volume contained in a volume V.The latter consists of a horizontal slab, extensive enough to eliminate plant-to-plant variations, but thin enough to preserve the characteristic variation of properties in the vertical dimension. The term Fi, due to vegetation, is given by the Darcy– Forchheimer equation which includes linear and nonlinear forces using porous media characteristics (e.g. vegetation permeability kp): Fi=−ϕv kp Uif−ϕ2Cf kp UifUif(5) where ϕ=vegetation porosity, kp=vegetation permeability (m2) and Cf=dimensionless empirical coefficient. The permeability kpand the dimensionless coefficient Cfare determined by the following Eqs (6) and (7) (Lowe et al., 2008; Tsakiri & Prinos, 2016): kp=d2 50ϕ3 α(1−ϕ)2(6) Cf=b1−ϕ ϕkp d50 (7) where d50 is the grain diameter, αand bare empirical coefficients. When the porous medium consists of cylinders then d50 is equal to 1.5d(dis the diameter of the cylinders; Lowe et al., 2008). The empirical coefficients aand btake different values, depending on the type and the length scale of the porous medium. For example, Losada et al. (2016) obtained values of abetween 1000 and 2000 and bbetween 0.3 and 1.1. For ϕ=0.85, d50 =9.0 mm,α=1000 and b=1.1 the values for Cfand kpare calculated as: Cf=0.484, kp=5.04 ×10−6m2. The boundary conditions are defined as follows: (a) The left tip on Fig. 1is cut off at x=1.6 cm to avoid a singularity, and a side wall is assumed there which has a height of 1.6 mm and is rigid, non-slip and adiabatic. (b) The side wall in the deep region is also assumed to be rigid, non-slip and adiabatic. (c) The bottom of the sloping and the horizontal region is also rigid, non-slip and adiabatic (∂T/∂n=0, ndirection normal to the wall). The water surface is assumed to be stress free and the applied thermal boundary condition is given by −∂T/∂y=−Io/kρoCp. Initially, the water body has a temperature To=293.15 K and is motionless. 2.3 Numerical scheme and mesh dependency tests Fluent 15.0.7 CFD code is applied for the numerical computations using a control volume technique. The extra source term Fi is introduced to the initial equations using User Defined Functions (UDF) based on C++ code. The computational domain is divided into finite control volumes on which the governing equations are integrated. The Gambit program is used for the mesh generation. The segregated solution method is used and the velocity–pressure coupling is achieved with the SIMPLE algorithm. The PRESTO scheme is used for discretizing the pressure equation (continuity equation), while the QUICK scheme is used for the momentum and the energy equations (ANSYS Inc., 2013). The time step is sufficiently small such that the Courant–Friedrichs–Lewy condition for numerical stability is satisfied. For the selected grid (4000 ×200 in the x and ydirections respectively), which was used for all cases, the time step, based on the smallest nearshore cell, is set equal to 0.1 s. The total simulation time is up to 16,000 s which is sufficient for establishing quasi-steady flow for the cases considered. Three different meshes of 2000 ×100, 4000 ×200 and 8000 ×400 were tested for examining the solution dependence on the grid spacing. The grid size in the ydirection was smaller in the vicinity of the top and bottom boundaries while it was uniform in the xdirection. The smallest nearshore cell, adjacent to the top and bottom boundary, was 1.0 mm ×0.016 mm, 0.5 mm ×0.008 mm and 0.25 mm ×0.004 mm for the three meshes while the biggest one, in the deep section of h=0.1 m, was 1.0 mm ×1.4 mm, 0.5 mm ×0.7 mm and 0.25 mm ×0.35 mm. The grid resolution (x,y) for the three meshes was compared with the Batchelor microscale, ηb∼Pr−0/5(ν3/ε)0.25 (=local rate of kinetic energy dissipation) which was calculated after the end of the simulations and its minimum value was found equal to 0.485 mm. The last two meshes have xmax/ηb≤1.0 and ymax/ηb≤1.44 ,which satisfy the criterion [x,y]max/ηb≤ πproposed by Stevens et al. (2010) and also used by Gayen et al. (2014). Figures 2and 3show velocity and temperature profiles respectively, at three verticals along the sloping region of the water body (at x/Ls=0.2, 0.6 and 1.0) in the quasi-steady regime. All profiles are quite similar with the two finer meshes to give closer results for both velocity and temperature. Figure 4 shows the effect of grid size on the temporal evolution of the exchange flow rate Q/k from the initial to the transitional and finally to the quasi-steady regime. The exchange flow rate Q is determined by integrating the flow rate Q(x), at a given x 386 V. Papaioannou and P. Prinos Journal of Hydraulic Research Vol. 61, No. 3 (2023) Figure 2 Effect of grid size on u/ (k/Ls) at three verticals along the sloping region Figure 3 Effect of grid size on T/(IoLs/κ) at three verticals along the sloping region Figure 4 Effect of grid size on temporal evolution of Q/k location, along the horizontal direction x. Hence: Q=1 LL 0 Q(x)dx where Q(x)=1 2h 0 |Ux|dy (8) For the three meshes tested it is shown that the two finer ones give smaller variability (unsteadiness) than the coarser one. Also, the time scale tb, for a Rayleigh–Bénard type instability to occur, is estimated equal to 207 s (t/ (L2/k)=3.0 ×10−5) for Ra =7.45 ×1011, based on the scale analysis (Mao et al., 2010). The numerical results for the start of the transition period using the three meshes are in satisfactory agreement with tb. Contours of temperature and streamlines using the three meshes were also compared (not shown here for the sake of brevity), which showed that the results with the two finer meshes gave better structured small-scale convection cells, especially in the shallow sloping region, during the transitional regime as well as better descending plumes. Journal of Hydraulic Research Vol. 61, No. 3 (2023) Natural convection due to surface cooling in sloping water bodies with vegetation 387 2.4 Model validation The model was validated for the sloping water body with no vegetation (Fig. 1a). Figure 5shows the temperature difference ΔT(=T–To), made dimensionless with IoLs/κ,at three characteristic times t∗(=t/ (Ls2/k)) 0.057 ×10−3(400 s), 0.258 ×10−3(1800 s), and 1.146 ×10−3(8000 s). At t∗equal to 0.057 ×10−3(400 s) transitional stage flow characteristics are observed with sinking cold-water plumes descending over the local water depth and quick cooling of the shallow region near the shoreline t∗=0.057 ×10−3(400 s)). As time increases, t∗=0.258 ×10−3(1800 s), cold undercurrents (gravity currents) are created gradually above the sloping bottom. The gravity currents slowly move towards the deeper region. The currents reach the vertical adiabatic end wall, and the flow enters a quasi-steady state with the average horizontal flow rate remaining almost constant. Later, (t∗=1.146 ×10−3(8000 s)) a relatively stable bottom current is observed along the bottom, while the return flow is very unstable as the free surface is being cooled continuously and sinking plumes burst intermittently from the near surface flow. An enlarged view of the isotherms in the near-shore region, at the quasi-steady state, is shown in Fig. 6,forRa =7.45 ×1011, where the isotherms transform from vertical lines into curved lines with increasing offshore distance. Three distinct subregions separated approximately at x0∼Ra−0.25So−1.5Lsand x1∼Ra−0.25Rac0.75Lsare shown clearly, (a) a nearshore region dominated by conduction up to x0=0.028 m (0.034 m from the above relationship), (b) a central region dominated by stable convection between x0=0.028 m and x1=0.137 m (0.034 m and 0.142 m from the above relationships) (and (c) a deep region dominated by unstable convection. The agreement is satisfactory. The above findings are supported by the streamlines (ψ/ρoLsk) shown in Fig. 7at the same times. Initially, at the transitional stage (t∗=0.057 ×10−3(400 s)) the descending cold plumes are responsible for the development of local quasiisotropic convective cells in the region with the horizontal bottom and in the deep section of the sloping region, which start to expand towards the shallow part of the sloping region. With the development of the cold gravity currents a large-scale overturning circulation appears with a bottom layer flowing towards the deep region and a surface layer towards the near-shore in the quasi-steady regime (t∗equal to 1.146 ×10−3(8000 s)). 3 Analysis of results In the following paragraphs the vegetation effects on the flow development and flow regimes are investigated for the water body with vegetated sloping region. Figures 8and 9show the isotherms and the streamlines respectively for vegetation in the sloping region, with Iv=0.85Ioand Lvequal to 0.5Ls. Both contours are similar to those of the non-vegetated case (Figs 5and 7); however, the flow development is rather slower than that of Fig. 5due to the mild non-uniform cooling of the free surface and the short vegetation length near the shoreline. For example, at t∗=0.258 ×10−3(1800 s), the bottom cold currents in the sloping region have not started to develop yet due to the lower cooling rates in the vegetated region. At t∗=0.573 ×10−3(4000 s) the currents have reached the section in which the slope changes, while at t∗=1.146 ×10−3 Figure 5 Contours of T/(IoLs/κ) for the non-vegetated case Figure 6 Enlarged view of contours of T/(IoLs/κ)forx<0.50 m in the quasi-steady regime 388 V. Papaioannou and P. Prinos Journal of Hydraulic Research Vol. 61, No. 3 (2023) Figure 7 Streamlines (ψ/ρoLsk) for the non-vegetated case. The dashed lines show clockwise and the solid ones anticlockwise rotation Figure 8 Contours of T/(IoLs/κ)forLv=0.5Lsand Iv=0.85Io (8000 s) the currents have reached the deep side wall and the quasi-steady regime is about to start. At t∗=1.146 ×10−3 (8000 s) and 1.283 ×10−3(9000 s) the streamlines are very similar indicating the establishment of this regime. With the increase of Lvfrom 0.5Lsto Lsthe whole sloping region is vegetated, and the flow development is further delayed. Figures 10 and 11 show the isotherms and the streamlines at various times respectively. In this case the flow development and the approach to quasi-steady state are further delayed. At t∗=0.057 ×10−3(400 s) sinking plumes are well developed in the deep section reaching almost the bottom, while in the sloping region the thermal boundary layer remains stable (no sinking plumes) due to the lower Ivand the vegetation porosity. Sinking plumes are well developed in the most part of the sloping region at t∗=0.258 ×10−3(1800 s), while in the deep region such plumes are further developed. The quasi-isotropic convective cells, developed earlier in the deep region, start to extend horizontally slowly while the ones in the sloping region are transformed to an overturning circulation due to the temperature difference between the nearshore and the deep parts of the sloping region. The cold gravity currents form and start to move slowly, due to vegetation, towards the deep region at t∗=0.716 ×10−3(5000 s). A large-scale overturning circulation occupies most of the sloping region and half of the Journal of Hydraulic Research Vol. 61, No. 3 (2023) Natural convection due to surface cooling in sloping water bodies with vegetation 395 Oceanography,33(5), 1068–1083. https://doi.org/10.4319/lo. 1988.33.5.1068 Horsch, G. M., Stefan, H. G., & Gavali, S. (1994). Numerical simulation of cooling-induced convective currents on a littoral slope. International Journal for Numerical Methods in Fluids,19(2), 105–134. https://doi.org/10.1002/fld.165019 0203 Hughes, G. O., & Griffiths, R. W. (2008). Horizontal convection. Annual Review of Fluid Mechanics,40(1), 185–208. https://doi.org/10.1146/annurev.fluid.40.111406.102148 Lei, C., & Patterson, J. C. (2005). Unsteady natural convection in a triangular enclosure induced by surface cooling. International Journal of Heat and Fluid Flow,26(2), 307–321. https://doi.org/10.1016/j.ijheatfluidflow.2004.08.010 Lightbody, A., Avener, M., & Nepf, H. (2008). Observations of short-circuiting flow paths within a free-surface wetland in Augusta, Georgia. Limnology and Oceanography,53(3), 1040–1053. https://doi.org/10.4319/lo.2008.53.3.1040 Lin, Y., & Wu, C. (2014). The role of rooted emergent vegetation on periodically thermal-driven flow over a sloping bottom. Environmental Fluid Mechanics,14(6), 1303–1334. https://doi.org/10.1007/s10652-014-9336-5 Lin, Y., & Wu, C. (2015). Effects of a sharp change of emergent vegetation distributions on thermally driven flow over a slope. Environmental Fluid Mechanics,15(4), 771–791. https://doi.org/10.1007/s10652-014-9382-z Losada, J. I., Lara, L. J., & del Jesus, M. (2016). Modelling the interaction of water waves with porous coastal structures. Journal of Waterway, Port, Coastal and Ocean Engineering, 142(6), 03116003. https://doi.org/10.1061/(ASCE)WW.1943 -5460.0000361 Lowe, R. J., Shavit, U., Falter, J. L., Koseff, J. R., & Monismith, G. (2008). Modeling flow in coral communities with and without waves: A synthesis of porous media and canopy flow approaches. Limnology and Oceanography,53(6), 2668–2680. https://doi.org/10.4319/lo.2008.53.6.2668 Lövstedt, C., & Bengtsson, L. (2008). Density-driven current between reed belts and open water in a shallow lake. Water Resources Research,44(10), W10413. https://doi.org/10.1029/2008WR006949 MacIntyre, S., & Melack, J. M. (1995). Vertical and horizontal transport in lakes: linking littoral, benthic, and pelagic habitats. Journal of the North American Benthological Society, 14(4), 599–615. https://doi.org/10.2307/1467544 Mao, Y., Lei, C., & Patterson, J. C. (2010). Unsteady near-shore natural convection induced by surface cooling. Journal of Fluid Mechanics,642, 213–233. https://doi.org/10.1017/S00 22112009991765 Mazda, Y., Wolanksi, E., King, B., Sase, A., Ohtsuka, D., & Magi, M. (1997). Drag forces due to vegetation in mangrove swamps. Mangrove and Salt Marshes,1(3), 193–199. https://doi.org/10.1023/A:1009949411068 Molina, L., Pawlak, G., Wells, J. R., Monismith, S. G., & Merrifield, M. A. (2014). Diurnal cross-shore thermal exchange on a tropical forereef. Journal of Geophysical Research: Oceans, 119(9), 6101–6120. https://doi.org/10.1002/2013JC009621 Monismith, S. G., Genin, A., Reidenbach, M. A., Yahel, G., & Koseff, J. R. (2006). Thermally driven exchanges between a coral reef and the adjoining ocean. Journal of Physical Oceanography,36(7), 1332–1347. https://doi.org/10.1175/ JPO2916.1 Monismith, S. G., Imberger, J., & Morisin, M. L. (1990). Convective motions in the sidearm of a small reservoir. Limnology and Oceanography,35(8), 1676–1702. https://doi.org/10.4319/lo.1990.35.8.1676 Oldham, C. E., & Sturman, J. J. (2001). The effect of emergent vegetation on convective flushing in shallow wetlands: Scaling and experiments. Limnology and Oceanography,46(6), 1486–1493. https://doi.org/10.4319/lo.2001.46.6.1486 Papaioannou, V., & Prinos, P. (2021). A macroscopic approach for simulating horizontal convection in a vegetated pond. Environmental Processes,8(1), 199–218. https://doi.org/10.1007/s40710-020-00484-x Prinos, P., & Papaioannou, V. (2022). Surface cooling in water bodies with significant vegetated shallow regions. (Under preparation). Stevens, R. J. A. M., Verzicco, R., & Lohse, D. (2010). Radial boundary layer structure and Nusselt number in Rayleigh– Bénard convection. Journal of Fluid Mechanics,643, 495–507. https://doi.org/10.1017/S0022112009992461 Sturman, J. J., Oldham, C. E., & Ivey, G. N. (1999). Steady convective exchange flows down slopes. Aquatic Sciences,61(3), 260–278. https://doi.org/10.1007/s000270050065 Tsakiri, M., & Prinos, P. (2016). Microscopic numerical simulation of convective currents in aquatic canopies. Procedia Engineering,162(C), 611–618. https://doi.org/10.1016/j.pro eng.2016.11.107 Tsakiri, M., Prinos, P., & Koftis, T. (2016). Numerical simulation of turbulent exchange flow in aquatic canopies. Journal of Hydraulic Research,54(2), 131–144. https://doi.org/10.1080/00221686.2016.1141803 Ulloa, H. N., Davis, K. A., Monismith, S. G., & Pawlak, G. (2018). Temporal variability in thermally driven cross-shore exchange: the role of semidiurnal tides. Journal of Physical Oceanography,48(7), 1513–1531. https://doi.org/10. 1175/JPO-D-17-0257.1 Ulloa, H. N., Ramon, C. L., Doda, T., Wüest, A., & Bouffard, D. (2022). Development of overturning circulation in sloping waterbodies due to surface cooling. Journal of Fluid Mechanics,930, A18. https://doi.org/10.1017/jfm.2021.883 Wells, M. G., & Sherman, B. (2001). Stratification produced by surface cooling in lakes with significant shallow regions. Limnology and Oceanography,46(7), 1747–1759. https://doi.org/10.4319/lo.2001.46.7.1747 Zhang, X., & Nepf, H. M. (2009). Thermally driven exchange flow between open water and aquatic canopy. Journal of Fluid Mechanics,632, 227–243. https://doi.org/10.1017/S00 22112009006491 View publication stats