ARTICLE

Numerical modeling of bed form induced hyporheic exchange

Du Han Lee • Young Joo Kim • Samhee Lee

Received: 27 December 2013 / Revised: 27 May 2014 / Accepted: 4 June 2014 / Published online: 26 June 2014

� The International Society of Paddy and Water Environment Engineering and Springer Japan 2014

Abstract The hyporheic zone is a region beneath and

alongside a stream, river, or lake bed where shallow

groundwater and surface water mix. Field and experimental

observations, along with modeling studies, indicate that

hyporheic exchange occurs mainly in response to pressure

gradients driven by the geomorphological features of stream

beds. Flow over a pool-riffle sequence creates an irregular

pressure gradient that drives hyporheic exchange. Currently

to analyze the overall flow pattern in different types of pool-

riffle structures, hyporheic exchange flow was analyzed

using a fully coupled hydro-dynamic model. Simulation

results showed that recirculation zones and stagnation points

in the pool-riffle structures dominantly controlled the

upwelling and downwelling patterns. Numerical simulations

were analyzed for the velocity distribution, velocity vectors,

and the streamline and flux of groundwater and surface

water. Upwelling flow was dominated by a pressure gradient

generated by the apex of riffles. Downwelling flow patterns

were affected by the flow pattern formed in pools, which was

related to the geometric shapes of the pools. The mixing

pattern in the groundwater was also affected by the pool

shape. The results will be applicable for river restoration

projects and stream ecology related to hyporheic exchange,

in the prediction and management of upwelling and down-

welling flow induced by bed forms.

Keywords Hyporheic exchange � Pool-riffle structures �Hydro-dynamic model � Bed form

Introduction

The hyporheic zone is a region beneath and alongside a

stream bed, where there is mixing of shallow groundwater

and surface water (Orghidan 1959). Exchanges of water,

nutrients, and organic matters occur in response to varia-

tions in discharge and types of bed form.

Characteristics of the hyporheic zone are regulated by

biogeochemical processes determined by hydrologic flows

(Brunke and Gonser 1997; Hester and Gooseff 2010).

Surface water containing oxygen and other nutrients enters

the hyporheic zone in a downwelling zone at the head of

the riffle, while hyporheic water rich in minerals returns to

surface water in an upwelling zone at the tail of the riffle

(Franken et al. 2001). Especially, dynamics of nitrate

production and removal can be controlled by residence

time which is determined by upwelling and downwelling

flow in the hyporheic zone (Zarnetske et al. 2011). In

addition, upwelling waters in temperate climates are gen-

erally cooler in summer (Hester et al. 2009), and may

provide thermal refugia for stenothermic fish species. For

example, bull trout spawn in transitional bed forms that

feature strong localized downwelling and high inter-gravel

flow rates within stream reaches influenced by upwelling

(Baxter and Hauer 2000). Furthermore, simulation studies

indicate that the presence of redds induces hyporheic cir-

culation nested within, caused by pool-riffle topography,

and that subsequent spawning-related changes in hyporheic

velocities and dissolved oxygen content could create con-

ditions suitable for incubation in locations (Tonina and

Buffington 2009).

D. H. Lee (&) � Y. J. Kim � S. Lee

Korea Institute of Construction Technology, Daehwa-Dong 283,

Goyangdae-Ro Ilsanseo-Gu, Goyang-Si, Gyeonggi-Do 411-712,

Korea

e-mail: dhlee@kict.re.kr

Y. J. Kim

e-mail: yjee@kict.re.kr

S. Lee

e-mail: samhee.lee@kict.re.kr

123

Paddy Water Environ (2014) 12(Supp. 1):S89–S97

DOI 10.1007/s10333-014-0449-8

Hyporheic exchange (or Darcy flux) in the hyporheic

zone is an ecological hot spot caused by head gradients

created by head loss due to form drag as stream flows over

bed forms such as ripples and dunes (Thibodeaux and

Boyle 1987; Tonina and Buffington 2009). For example,

groundwater flow in porous media is dominated by a

pressure gradient determined by the hydrostatic pressure

related to the surface water level, and dynamic pressure

related to the surface water velocity. Although the surface

water levels at the front and back sides of a riffle are

equivalent, geometric differences, such as the presence of a

pool-riffle structure, produce a difference in velocity that

creates a pressure gradient via a difference in dynamic

pressure (Hester and Doyle 2008; Angermann et al. 2012).

Vertical hyporheic exchange can be induced by diffu-

sion, advection, and turbulent momentum processes. Most

recent studies have focused on the advection mechanism

(Anderson et al. 2005; Tonina and Buffington 2009).

Advection-mediated hyporheic exchange predominantly

involves pressure distribution, which is affected by the

interaction of bed form shapes and flow patterns (Elliott

and Brooks 1997b; Huettel and Webster 2001).

Flow patterns of hyporheic exchange affected by bed

form shapes have not yet been extensively studied exper-

imentally and numerically. Elliott and Brooks (1997a)

studied experimentally the exchange flow characteristics in

riffle scale fixed beds and movable beds. Fox et al. (2014)

analyzed experimentally hyporheic exchange fluxes

induced by dune scaled bed forms. Savant et al. (1987) and

Salehin et al. (2004) analyzed numerical flow patterns of

hyporheic exchange in porous media beds. In these studies,

boundary pressure at the bed was determined from the

experimental results. Cardenas and Wilson (2006, 2007)

modeled the exchange flow in a riffle using a semi-coupled

groundwater and surface water model, supposing that the

surface flow was laminar, and extending the flow model to

a turbulent flow. However, they applied a semi-coupled

model only to a single riffle. A semi-coupled model uses a

hydrostatic water surface profile, thus the hydrodynamic

pressure and changes in the velocity head are neglected. A

laboratory flume study of a riffle-pool sequence showed

that a water surface profile based on only hydrostatic

pressure can be a poor predictor of the spatial patterns of

exchange along the streambed, due to velocity stagnation

and hydrodynamic pressure (Tonina and Buffington 2007).

Water flow over a pool-riffle and the resulting hyporheic

flow can be most accurately modeled using a fully coupled

three-dimensional hydro-dynamic model (Endreny et al. 2011;

Janssen et al. 2012; Trauth et al. 2013; Krause et al. 2014).

Therefore, in this study, a fully coupled three-dimensional

hydro-dynamic model was applied to analyze the relationship

between surface water and ground water flow structures in a

pool-riffle, considering hydrodynamic pressure and velocity

stagnation. In a natural river, a pool-riffle has various geometric

shapes, which can be simplified as the difference in slopes

between the front and back sides of the riffles.

The characteristics of the geometric shapes of the pool-

riffles can greatly affect the hyporheic flow patterns, which

have not been considered in previous studies of pool-riffle

systems (Tonina and Buffington 2007; Endreny et al. 2011;

Trauth et al. 2013). Difference in shapes of the pool-riffles

will make difference in formation of recirculation zones

and stagnation points which greatly affect dynamic pres-

sure distribution and, upwelling and downwelling patterns.

Therefore, in this study, a pool-riffle sequence was ana-

lyzed not only from the view point of recirculation zones,

stagnation points and energy dissipation, but also for the

effect of geometric shapes of the pool-riffle on hyporheic

exchange, by simulating two kinds of pool-riffle shapes.

One was a simplified shape of a pool-riffle normally

observed in a natural river, and the other was a reversal-

shaped pool-riffle. These results will allow a better

understanding for relationship of hyporheic exchange pat-

terns and the geometric shapes of the pool-riffles.

Methodology

Governing equations

For a fully coupled simulation of groundwater and surface

water, a fully three-dimensional computational fluid

dynamic (CFD) model (FLOW 3D) was applied. Mass

continuity and x-direction momentum conservation equa-

tions used are shown below (Hirt and Nichols 1981):

VF

qc2

op

otþ ouAx

oxþ ovAy

oyþ owAz

oz¼ 0 ð1Þ

oui

otþ 1

VF

uAx

ou

oxþ vAy

ou

oyþ wAz

ou

oz

��¼ � 1

qop

oxi

þ fi ð2Þ

fi ¼ wsxi �o

oxðAxsixÞ þ

o

oyðAysiyÞ þ ðAzsizÞ

� �� �1

qVF

ð3Þ

where VF is the fractional volume open to flow, c is the

speed of sound, t is time, Ai(Ax, Ay, and Az) are the frac-

tional areas open to flow, ui denotes the velocity in i-

direction, fi are the viscous acceleration terms, wsxi are the

wall shear stresses, and six, siy, siz are the viscous stresses.

Implementation of the complete CFD model involved

iteratively solving for pressure and velocity at each com-

putational node and time step to simultaneously satisfy the

momentum and continuity equations. Equations (1)–(3)

apply to surface and subsurface dynamics, and were solved

S90 Paddy Water Environ (2014) 12(Supp. 1):S89–S97

123

using the finite-volume/finite difference method from the

commercially available FLOW3D CFD software.

Boundary conditions and material coefficients

Water depth was treated as a free surface boundary, and

fluid interfaces were treated using the volume-of-fluid

(VOF) technique, which only requires computation and

storage of the volume fraction as one additional variable.

Time step size was automatically adjusted to maintain

stability and ensure that fluid fraction advection did not

exceed computational cell volumes. No flow boundary

conditions were specified along the bottom and sides of the

model, and free water surface boundaries were established

at the upstream and downstream ends. Numerical simula-

tion was performed at an upstream water depth of 0.6 m.

Substrate roughness along the bed was set to 0.4 cm to

represent the gravel protrusion length. The porosity of the

porous media component was set to 0.3 on the basis of

substrate characteristics. Porous media drag coefficients

were set to establish a permeability of 3.0 9 10-6 cm2,

representing a gravel hydraulic conductivity near 0.3 cm/s.

Geometry of modeling

Two pool-riffle shapes were considered. One was a normal-

shaped pool-riffle (type 1), which was the simplified shape of a

pool-riffle normally observed in a natural river, modified by

vertical distortion (Rodrıguez et al. 2000) (Fig. 1a). The other

was a reversal-shaped pool-riffle (type 2), which was a reverse

of the shape of the simplified normal pool-riffle type (Fig. 1b).

The bed slope was assumed to 1/300 and, excluding the effect

of the upstream and downstream boundaries, three sequential

pools were constructed in modeling. The whole computa-

tional domain is presented in Fig. 2.

Results and discussion

To analyze the relationship of bed forms and the exchange

flow, results were reported as velocity distributions,

detailed velocity vectors in pool-riffles, and exchange

pattern and flux for the two types of bed forms.

Velocity distributions of ground water and surface

water

Velocity distribution results of the ground water and sur-

face water for the two types of bed forms are presented in

Fig. 3. Total velocity magnitudes of the surface water and

vertical velocity magnitude of the ground water are pre-

sented together.

Near the upstream boundary (left part of the figure),

strong upwelling flow was detected in both cases. How-

ever, strong upwelling flow due to the boundary condition

quickly vanished, and no exchange flow appeared in the

upper part of the first pool. Therefore, the boundary con-

dition had no effect on this simulation.

In the type 1 model’s surface water velocity, recircula-

tion zones, and stagnation points (zero velocity points)

appeared in the lower part of each pool, and stagnation

points were located in the middle of the front side of each

riffle. On the other hand, in the type 2 model’s surface

water velocity, no recirculation point appeared, and the

Fig. 1 Artificial pool-riffle

shapes of type 1 (a) and type 2

(b) models

Fig. 2 A computational domain

(type 1)

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velocity decreased to near zero along the depth in each

pool.

The formation of recirculation zones and stagnation

points in type 1 was due to the geometric feature of the bed

forms, and this flow pattern created more energy loss

compared with type 2. In the type 1 groundwater velocity,

downwelling flows formed in the front sides of the riffles,

and upwelling flows formed in the back sides of the riffles.

The downwelling velocity distribution, size of the recir-

culation zone, and height of stagnation points decreased

along the distance, demonstrating the energy loss in the

flow in type 1. The type 1 bed form induced flow separa-

tion to create the recirculation zone, generating more

consequent energy loss.

In the type 2 groundwater velocity, downwelling flows

were formed in the whole region of the first pool: the front

side of the riffles, and the lower parts of the back side of the

riffles. Excluding the first pool, the downwelling and

upwelling pattern was similar to the pattern of type 1.

Detailed velocity vectors in pool-riffles

Velocity magnitude and vectors were used to analyze the

detailed characteristics of exchange flow (Fig. 4). In type 1,

flow separation and recirculation flow was observed within

the pools, and the riffle stagnation point was formed in the

middle of the front side. Below the stagnation point,

reversal downwelling exchange flow was formed. Over the

stagnation point, upwelling flow was formed. Near the

bottom of pool (in the second and third pools), mixing of

the exchange flow in groundwater was observed. In type 2,

no flow separation and recirculation flow was formed,

despite showing similar characteristics in the upwelling

and downwelling patterns. However, mixing of the

exchange flow in groundwater near the bottom of the pool

showed a more complicated flow pattern in type 2 (Fig. 4b,

c). In this mixing zone, three different flows were mixed

and discharged as a reversal exchange flow.

Exchange characteristics of ground water and surface

water

Figure 5 depicts an experiment performed by Elliott (1990)

for hyporheic exchange in riffle scale. The order of riffle

size in the experiment was 10 cm, therefore, a quantified

comparison with our numerical results is not possible.

Streamlines in ground water were compared with the

results in the type 1 model. The experiment was conducted

to observe the streamlines in the ground water over time.

Riffles were formed with medium and fine sand, with a

length of 0.181 m, a height of 0.028 m, and an average

surface water velocity of 0.132 m/s. The flow pattern in the

ground water was measured by dye injection. In Fig. 5,

arrow marks designate dye location measured in 10 min

interval, and cross and circle marks designate measured

dye location at every 30 and 90 min, respectively.

Numerical results are presented as flux (vertical velocity

at the bed boundary) and streamlines to analyze the char-

acteristics of hyporheic exchange in Figs. 5 and 6. Com-

paring Fig. 6 with Fig. 5, streamlines in the front side of

the riffle showed similar patterns, in which the main

downwelling flow was formed in the middle of the front

side of the riffles and reversal flow was formed in the lower

front side of the riffles.

In Figs. 6 and 7, the characteristics of exchange flow

were described, include the locations of the downwelling

zone, upwelling zone, maximum downwelling point, and

maximum upwelling point. In the bed form of type 1, most

Fig. 3 Velocity distributions of

type 1 (a) and type 2 (b). In

ground water vertical velocity,

positive values indicate

upwelling, while negative

values indicate downwelling

flow. (SW surface water zone,

GW ground water zone)

S92 Paddy Water Environ (2014) 12(Supp. 1):S89–S97

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of the downwelling flow was generated in the front sides of

the riffles, and the locations of the maximum downwelling

points were in the middle of the front sides. Upwelling flow

was formed in the back sides of the riffles, and in the lower

part of the front sides of the riffles, and the maximum

upwelling points were near the tops of the riffles. The

reverse exchange flow (exchange flow from downstream to

upstream) was formed in the lower third of the front sides

of the riffles. Most of the downwelling exchange flow

generated in the front of the riffles was discharged in the

back side of the riffles. Only a small part of the down-

welling flow contributed to permanent groundwater, and

this flow was induced by a strong downwelling velocity (at

the first front side of riffles).

Fig. 4 Velocity vectors in the first (a), second (b), and third (c) pools

Fig. 5 Experimental results in a riffle scale hyporheic exchange

(Elliott 1990)

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In the type 1 bed form, a relatively large loss of energy

was observed due to flow separation and recirculation flow.

This energy loss affected the exchange flow pattern, which

is characterized by the length of the recirculation zone (Lr),

the length of the downwelling zone (Ld), and the location of

the maximum downwelling point (Hmd). The relationship

of these factors is presented as a non-dimensional form

(factors are divided by length of the pool (L)) in Table 1.

The length of the recirculation zone decreased due to

energy loss induced in the type 1 bed form, which con-

tributed to the decreased length of the downwelling zone

and location of the maximum downwelling point (Table 1).

In the bed form of type 2, the downwelling flow was

generated in the lower back side of the riffles and the front

side of the riffles, excluding the first pool. Upwelling flow

was only formed in the upper back side of the riffles, and

the reversal upwelling flow was observed in the middle of

the back side of the riffles. Most of the downwelling flow

was discharged directly in the next upwelling zone. Only a

small part of the downwelling flow contributed to perma-

nent groundwater, and this flow was generated in the first

pool. Some of the downwelling flow generated in the first

pool was discharged in the upwelling zone of the third

pool, which was not observed in the case of type 1, dem-

onstrating that the mixing pattern of the exchange flow in

groundwater was more complicated in type 2. In type 1,

downwelling flow generated in the first pool did not affect

the flow patterns of the second and third pools; In contrast

it did have an effect in the second and third pools in type 2.

Hyporheic exchange flux of type 1 and type 2 were

compared (Fig. 8). As mentioned above, upwelling and

downwelling patterns of type 1 and type 2 were similar,

especially in the locations of upwelling zones and maxi-

mum upwelling points. This means that upwelling flow was

dominated by a pressure gradient generated by the apex of

the riffles. On the other hand, downwelling flow patterns

were somewhat different in type 1 and type 2. The location

of the maximum downwelling flow in type 1 was placed

upstream of type 2, and the magnitude of the vertical

velocity of downwelling flow in type 1 was larger than type

2. However, in both cases, maximum downwelling flow

was observed in the middle of the front side of the riffles.

Conclusions

In general, downwelling flow is generated in the front side

of riffles, while upwelling flow is generated in the back

side. However, actual exchange flow formation is depen-

dent on the velocity distribution in the pool, which is

Fig. 6 Flux at the bed boundary and streamlines of groundwater and surface water (type 1)

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related to the geometric shape of the pool and the riffles.

Thus, in this study, various exchange flow formations for

two kinds of pool-riffle sequences were analyzed using a

fully coupled hydrodynamic model. Comparison of the

type 1 results with previous results (Elliott 1990) enabled

qualitative checking of the reliability of the numerical

modeling. Simulation results showed that downwelling

flow was affected by the flow pattern formed in the pool,

which was related to the geometric shape. The mixing

pattern in the groundwater was also affected by the shape

of the pool. Specific behavior and relationship of exchange

flow induced by bed forms are presented.

Dissolved oxygen, water temperature, and fish spawning

on the surface of ground water are highly affected by

hyporheic flow patterns. According to the results, the level

of dissolved oxygen would be high in the middle of the

front side of riffles in both type 1 and type 2 models, while

low levels of dissolved oxygen would appear in down-

welling zones; however, the areas with low levels of dis-

solved oxygen are different for type 1 and type 2 riffles

(Figs. 6, 7). The maximum value of dissolved oxygen

would be obtained by type 1 riffles, due to the higher

vertical velocity on the surface of the ground water.

Temperature distribution on the surface of the ground

water is related to the area of the upwelling zones, and the

residence time of upwelling flow. The area where tem-

perature distribution is affected by upwelling flow would

be identical with that of upwelling zones, which varied in

type 1 and type 2 models. Fish spawning is affected by

velocity and dissolved oxygen, with the maximum down-

welling points being the most suitable locations for

spawning. Comparing type 1 and type 2 models, the

maximum downwelling points of type 1 would be more

suitable for spawning due to the high level of dissolved

oxygen and low surface water velocity. This low velocity is

due to the presence of recirculation zones.

Fig. 7 Flux at the bed boundary and streamlines of groundwater and surface water (type 2)

Table 1 Length of the recirculation and downwelling zones, and

location of the maximum downwelling point downstream (type 1)

Location Length of

recirculation

zone (Lr)

Length of

downwelling

zone (Ld)

Location of maximum

downwelling point

(Hmd)

First

pool

0.59 0.45 0.45

Second

pool

0.48 0.53 0.46

Third

pool

0.43 0.58 0.48

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These results could be applied to evaluate the effect of

artificially created pool-riffle structures on the formation of

a hyporheic zone (ecological hot spot) in river restoration

projects. Experimental studies are currently underway,

focusing on ecological features created by exchanges of

oxygen, nutrients, and heat energy in the hyporheic zone.

These experimental studies, however, require time and

effort to locate the exact downwelling and upwelling

points. By applying the modeling and flux analysis meth-

odology of this study, spatial distribution of the down-

welling and upwelling zones, as well as the mechanism of

exchange flow could be predicted and analyzed more eas-

ily. Inhabitant suitability and mass exchange pattern could

also be predicted spatially by applying the results of the

flow pattern with the oxygen diffusion coefficient and heat

conductivity.

In this study, the bed material was supposed to be

homogeneous and isotropic, and effects of flow unsteadi-

ness and bed change were neglected. Thus, to apply this

method to natural rivers with non-homogeneous and non-

isotropic bed material, such as mixed bed rivers, further

study is needed. Also, to consider effects of flow

unsteadiness and bed change, application of unsteady

model and sediment model should be considered.

Acknowledgments This study was supported by the Center for

Aquatic Ecosystem Restoration (CAER) of Eco-STAR project from

Ministry of Environment, Republic of Korea (MOE; EW12-07-10).

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