Recent Advances in Free Surface Flows
Gautam Biswas and Kirti Chandra Sahu
1 Background
A free surface is an interface between liquid and gas [1]. A free-surface exhibits
the surface tension force which is a consequence of the cohesive force acting at the
interface. In many under-graduate books, free-surface flow is also termed as openchannel flow [2, 3]. In a moving air–water system, as the values of the density of
water and air are approximately 998 kg m
−3 and 1.2 kg m
−3 , respectively, the inertia
due to the air phase is much smaller than that of the water phase. Thus, one can think
that water moves independently, or freely, with respect to the air phase. In other
words, an air–water interface is free and the only coupling between the phases is due
to the air pressure that exerts on the liquid surface. implest examples of free-surface
flows are the waves created by throwing a small stone in a still-water surface and
patterns formed at water surface due to air current. Although, we see these flows
in our everyday life, understanding the associated physics is quite complicated [4].
If the free surface of a liquid is disturbed, waves are produced due to the interplay
between gravity that acts to bring the disturbed surface back to its horizontal position
and the momentum that causes the waves to overshoot. Due to this the free surface
oscillates and the waves spread to the neighbouring regions. The surface tension
force plays an important role to stabilize these waves/instabilities.
Free surface flows are encountered in a wide range of industrial applications and
natural phenomena, such as jets, cavities, bubble columns, seepage of groundwater,
ice melting, gravity waves, clouds and raindrops, to name a few (see for instance,
G. Biswas (B)
Department of Mechanical Engineering, Indian Institute of Technology Kanpur,
Kanpur 208016, UP, India
e-mail: gtm@iitk.ac.in
K. C. Sahu
Department of Chemical Engineering, Indian Institute of Technology Hyderabad,
Sangareddy 502285, Telangana, India
e-mail: ksahu@che.iith.ac.in
© Springer Nature Singapore Pte Ltd. 2021
U. S. Dixit and S. K. Dwivedy (eds.), Mechanical Sciences,
https://doi.org/10.1007/978-981-15-5712-5_6
121
Gautam Biswas and Kirti Chandra Sahu
1 Background
A free surface is an interface between liquid and gas [1]. A free-surface exhibits
the surface tension force which is a consequence of the cohesive force acting at the
interface. In many under-graduate books, free-surface flow is also termed as openchannel flow [2, 3]. In a moving air–water system, as the values of the density of
water and air are approximately 998 kg m
−3 and 1.2 kg m
−3 , respectively, the inertia
due to the air phase is much smaller than that of the water phase. Thus, one can think
that water moves independently, or freely, with respect to the air phase. In other
words, an air–water interface is free and the only coupling between the phases is due
to the air pressure that exerts on the liquid surface. implest examples of free-surface
flows are the waves created by throwing a small stone in a still-water surface and
patterns formed at water surface due to air current. Although, we see these flows
in our everyday life, understanding the associated physics is quite complicated [4].
If the free surface of a liquid is disturbed, waves are produced due to the interplay
between gravity that acts to bring the disturbed surface back to its horizontal position
and the momentum that causes the waves to overshoot. Due to this the free surface
oscillates and the waves spread to the neighbouring regions. The surface tension
force plays an important role to stabilize these waves/instabilities.
Free surface flows are encountered in a wide range of industrial applications and
natural phenomena, such as jets, cavities, bubble columns, seepage of groundwater,
ice melting, gravity waves, clouds and raindrops, to name a few (see for instance,
G. Biswas (B)
Department of Mechanical Engineering, Indian Institute of Technology Kanpur,
Kanpur 208016, UP, India
e-mail: gtm@iitk.ac.in
K. C. Sahu
Department of Chemical Engineering, Indian Institute of Technology Hyderabad,
Sangareddy 502285, Telangana, India
e-mail: ksahu@che.iith.ac.in
© Springer Nature Singapore Pte Ltd. 2021
U. S. Dixit and S. K. Dwivedy (eds.), Mechanical Sciences,
https://doi.org/10.1007/978-981-15-5712-5_6
121