Subcritical Flow Explained: Your Ultimate Guide is Here!

Understanding hydraulic engineering requires a grasp of fundamental concepts, and subcritical flow is undeniably one of them. The Froude number, a dimensionless parameter, serves as the key indicator distinguishing this flow regime from others, influencing channel design. Analysis often involves software like HEC-RAS to model these complex hydraulic conditions. In fact, Dr. Ven Te Chow, a prominent figure in hydraulics, significantly contributed to our understanding through comprehensive studies that highlighted the importance of understanding and predicting subcritical flow scenarios.

Image taken from the YouTube channel Civil Engineering RWTH Aachen University , from the video titled Different Types of Flow - Supercritical and Subcritical .

In the realm of open channel hydraulics, the manner in which water flows dictates the behavior of rivers, canals, and engineered waterways. Among the various flow regimes, subcritical flow holds significant importance, shaping the design and management of hydraulic structures and influencing natural riverine processes. Understanding its characteristics is crucial for engineers, environmental scientists, and anyone involved in water resource management.

Defining Subcritical Flow

Subcritical flow, also known as tranquil or streaming flow, is characterized by a flow depth that is greater than the critical depth. This regime signifies that gravitational forces dominate inertial forces within the flow. In simpler terms, the water is flowing relatively slowly and deeply. This contrasts sharply with other flow regimes where inertial forces are more prominent.

The behavior of water in subcritical flow is more predictable and stable, making it a desirable condition in many engineering applications.

Importance of Understanding Flow Regimes

The ability to identify and understand flow regimes in open channels is paramount for effective water resource management. Consider, for instance, the design of irrigation systems. Knowing whether the flow will be subcritical ensures that water is distributed evenly and efficiently across agricultural fields.

Similarly, in river management, understanding flow regimes helps predict flood patterns and design appropriate flood control measures. Ignoring these principles can lead to catastrophic consequences, including infrastructure damage and loss of life. Understanding flow regimes is essential in the design and management of:

• Dams.
• Spillways.
• Culverts.
• Other hydraulic structures.

The Froude Number: A Key Determinant

The flow regime, whether subcritical, critical, or supercritical, is intrinsically linked to the Froude number. This dimensionless number represents the ratio of inertial forces to gravitational forces. In the context of subcritical flow, the Froude number is always less than 1. This indicates that gravitational forces are dominant, leading to the characteristic slow and deep flow. The Froude Number can be defined by the equation:

Where:

• Fr is the Froude number.
• V is the flow velocity.
• g is the acceleration due to gravity.
• D is the flow depth.

Flow depth and velocity are inversely proportional to the Froude number. The relationship between flow depth, velocity, and the Froude number provides a clear framework for understanding and classifying flow behavior.

Purpose and Scope

This article aims to provide a comprehensive overview of subcritical flow, its defining characteristics, and related concepts. We will explore the Froude number's role, the significance of critical depth and specific energy, and contrast subcritical flow with its supercritical counterpart. Furthermore, we will delve into practical applications and the tools used to analyze subcritical flow in real-world scenarios. By the end of this exploration, readers should possess a solid understanding of subcritical flow and its importance in the field of hydraulics and water resource engineering.

The Froude Number: A Key Indicator

Having established the fundamental definition and significance of subcritical flow, a critical tool for its identification and analysis comes into focus: the Froude number. This dimensionless parameter serves as a reliable yardstick for characterizing different flow regimes in open channels, enabling engineers and scientists to predict and manage hydraulic behavior with greater precision.

Defining the Froude Number

The Froude number (Fr) is a dimensionless number that expresses the ratio of inertial forces to gravitational forces acting on a fluid. This ratio is crucial in determining the flow regime, indicating whether the flow is dominated by inertia or gravity.

A high Froude number suggests that inertial forces are dominant, leading to rapid and potentially unstable flow. Conversely, a low Froude number indicates that gravitational forces prevail, resulting in a slower, more stable flow.

Calculating the Froude Number

The Froude number is calculated using the following formula:

Fr = V / √(g * D)

Where:

• V is the mean flow velocity.
• g is the acceleration due to gravity (approximately 9.81 m/s² or 32.2 ft/s²).
• D is the characteristic length scale, typically the hydraulic depth (cross-sectional area of flow divided by the top width).

This seemingly simple equation encapsulates the dynamic interplay between flow velocity, gravity, and channel geometry, providing a single value that encapsulates the essence of the flow regime.

Froude Number and Flow Regimes

The Froude number serves as a clear indicator of the flow regime:

• Subcritical Flow (Fr < 1): Gravitational forces dominate. The flow is tranquil, with a relatively deep and slow-moving water surface. Disturbances in the flow can propagate upstream.
• Critical Flow (Fr = 1): Inertial and gravitational forces are in equilibrium. The flow is highly sensitive to changes in channel geometry or flow rate.
• Supercritical Flow (Fr > 1): Inertial forces dominate. The flow is rapid and shallow, with a high velocity. Disturbances cannot propagate upstream.

Real-World Applications and Examples

The Froude number is not merely a theoretical construct; it has practical implications across various real-world scenarios:

• River Management: Analyzing the Froude number along a river reach helps to identify areas prone to flooding or erosion. Sections with higher Froude numbers may require stabilization measures to prevent scouring.
• Irrigation Canals: Designing irrigation canals with subcritical flow (Fr < 1) ensures even water distribution to agricultural fields, minimizing losses due to turbulence and ensuring stable flow conditions.
• Spillway Design: Spillways, designed to safely discharge excess water from dams, often incorporate features that induce a hydraulic jump (transition from supercritical to subcritical flow) to dissipate energy and prevent erosion downstream. The Froude number is crucial in designing these features.
• Culvert Design: Ensuring subcritical flow conditions (Fr < 1) in culverts prevents backwater effects and maintains stable flow in upstream channels, crucial for road and infrastructure design.

By calculating and interpreting the Froude number in these and other applications, engineers can effectively manage water resources, design hydraulic structures, and mitigate the risks associated with uncontrolled flow. Its widespread applicability cements its role as a key indicator in the field of open channel hydraulics.

The Froude number provides a clear demarcation between flow regimes. However, to fully grasp the nature of subcritical flow, a deeper understanding of critical depth and specific energy is essential. These concepts are inextricably linked and provide a more complete picture of the energy state of the flow.

Critical Depth and Specific Energy: Defining Flow States

Critical depth and specific energy are fundamental concepts in open-channel hydraulics. They provide critical insights into the flow's behavior and its energy characteristics.

Defining Critical Depth

Critical depth (yc) is defined as the flow depth at which the specific energy is minimum for a given discharge.

In simpler terms, for a certain amount of water flowing through a channel, there's a specific depth where the energy required to maintain that flow is at its lowest. This depth is the critical depth.

When flow is at critical depth, any slight change in energy will significantly alter the flow regime, potentially causing it to transition between subcritical and supercritical.

Understanding Specific Energy

Specific energy (E) represents the energy per unit weight of fluid relative to the channel bottom. It's a crucial parameter in open-channel flow analysis.

It’s the sum of the flow depth and the velocity head:

E = y + (V^2) / (2g)

Where:

y is the flow depth, V is the mean flow velocity, and g is the acceleration due to gravity.

Specific energy helps engineers understand how much energy is available within the flow, and how efficiently that energy is being used to transport water.

The Interplay of Critical Depth, Specific Energy, and Subcritical Flow

In subcritical flow, the flow depth is greater than the critical depth.

This means that the specific energy is higher than the minimum required to pass the given discharge. The water is flowing relatively slowly and deeply. Gravitational forces dominate over inertial forces.

A key characteristic of subcritical flow is that it is sensitive to downstream conditions. Changes downstream, such as a dam or a narrowing of the channel, can affect the flow upstream because the flow has sufficient energy to transmit those changes upstream.

The specific energy curve is a valuable tool for visualizing this relationship.

Visualizing the Specific Energy Curve

The specific energy curve is a graphical representation of the relationship between flow depth and specific energy for a constant discharge.

Key Features of the Specific Energy Curve

• The curve typically has two branches: one representing subcritical flow and the other representing supercritical flow.
• The minimum point on the curve corresponds to the critical depth and the minimum specific energy (Ec).
• For a given specific energy greater than Ec, there are two possible flow depths: one subcritical and one supercritical. These are known as alternate depths.

Using Diagrams for Clarity

Imagine a U-shaped curve. The bottom of the U represents the critical depth and minimum specific energy.

The left side of the U, where the depth is shallow, represents supercritical flow. The right side of the U, where the depth is greater, represents subcritical flow.

By plotting flow conditions on this curve, engineers can quickly determine the flow regime and assess the energy state of the flow.

The Froude number provides a clear demarcation between flow regimes. However, to fully grasp the nature of subcritical flow, a deeper understanding of critical depth and specific energy is essential. These concepts are inextricably linked and provide a more complete picture of the energy state of the flow. Understanding these relationships sets the stage for a comparative analysis, distinguishing subcritical flow from its energetic counterpart: supercritical flow.

Subcritical vs. Supercritical Flow: A Comparative Analysis

While subcritical flow is characterized by its tranquil, gravity-dominated nature, supercritical flow represents the opposite end of the spectrum. It's a realm of rapid, shallow streams where inertia reigns supreme. To truly appreciate subcritical flow, it's crucial to understand how it differs from its more energetic sibling.

Defining Supercritical Flow

Supercritical flow is defined as a flow regime in open channels where the flow depth is less than the critical depth. This seemingly simple definition has profound implications for the behavior of the water and the design of hydraulic structures.

In essence, supercritical flow is characterized by high velocity and shallow depth. The water moves with considerable kinetic energy.

Contrasting Flow Characteristics

The contrast between subcritical and supercritical flow extends beyond just depth. Several key characteristics differentiate these two flow regimes:

• Depth and Velocity: As previously noted, subcritical flow has a greater depth and lower velocity compared to supercritical flow. The inverse relationship is fundamental.

• Froude Number: The Froude number (Fr) serves as a definitive indicator. In subcritical flow, Fr < 1, indicating gravity's dominance. Conversely, in supercritical flow, Fr > 1, highlighting the power of inertial forces.

• Energy: The energy dynamics also differ significantly. Supercritical flow possesses higher specific energy, reflecting its greater kinetic energy. Any disruption will send waves of energy moving downstream.

Implications for Channel Design

The choice between designing for subcritical or supercritical flow has significant implications for channel construction and the selection of appropriate hydraulic structures.

• Subcritical Flow Design: Channels designed for subcritical flow tend to be wider and deeper. They are better suited for navigation and irrigation. Structures need to be designed to withstand the hydrostatic pressure associated with the flow depth.

• Supercritical Flow Design: Supercritical flow channels are often narrower and steeper, designed to efficiently convey water at high velocities. These designs must account for the erosive potential of the fast-flowing water and the impact forces of any obstructions.

Supercritical flow requires robust structures able to resist erosion and dissipate energy.

The Hydraulic Jump: A Critical Transition

A crucial phenomenon linking supercritical and subcritical flow is the hydraulic jump. This occurs when a high-velocity supercritical flow abruptly transitions to a slower, deeper subcritical flow.

The hydraulic jump is characterized by significant energy dissipation. This process involves turbulence, and a marked increase in water depth.

The hydraulic jump is a complex phenomenon with important implications for energy dissipation and flow control in hydraulic structures. It's a powerful example of how flow regimes can change dynamically in open-channel systems.

The contrast between subcritical and supercritical flow is striking. However, nature rarely presents such stark distinctions without a transitional phase. That transition often manifests as a hydraulic jump, a fascinating phenomenon that bridges the gap between these two flow regimes. Understanding hydraulic jumps is crucial for comprehending the dynamics of open channel flow and for designing safe and efficient hydraulic structures.

Hydraulic Jumps: The Transition to Subcritical Flow

A hydraulic jump is a localized phenomenon in open channel flow. It's characterized by a sudden and dramatic increase in water depth, accompanied by significant energy dissipation. This occurs as supercritical flow abruptly transitions into subcritical flow.

Defining the Hydraulic Jump

Specifically, a hydraulic jump is a rapid transition from a high-velocity, shallow flow (supercritical) to a low-velocity, deeper flow (subcritical). This transition isn't gradual; instead, it manifests as a distinct, turbulent surge of water.

Think of it as a waterfall turned on its side, where the flow rapidly decelerates and rises in elevation.

Conditions for Formation

Hydraulic jumps don't just appear spontaneously. They require specific conditions to form. The primary requirement is the presence of supercritical flow encountering conditions that force it to slow down and increase in depth.

This can occur due to:

• An obstruction in the channel.
• A change in channel slope.
• The meeting of supercritical flow with a downstream subcritical flow.

Essentially, the downstream conditions must exert enough backwater effect to force the supercritical flow to transition. If the downstream conditions aren't sufficient to force the transition, the supercritical flow will simply continue downstream.

Characteristics of a Hydraulic Jump

The hydraulic jump exhibits several key characteristics that distinguish it from other flow phenomena:

• Energy Dissipation: A significant portion of the flow's kinetic energy is converted into turbulence and heat, resulting in substantial energy loss. This energy dissipation is a key reason why hydraulic jumps are used in engineering applications.

• Turbulence: The jump is intensely turbulent. Air entrainment is common, giving the water a frothy or white appearance. This turbulence contributes to the energy dissipation.

• Increase in Depth: The most visually striking characteristic is the abrupt increase in water depth. The ratio of the depth after the jump to the depth before the jump is a function of the Froude number of the incoming supercritical flow.

Engineering Applications

Because of their energy dissipation properties, hydraulic jumps are strategically employed in various engineering applications:

• Spillway Design: Hydraulic jumps are commonly used at the base of spillways to dissipate excess energy and prevent erosion of the downstream channel bed. By forcing a jump to occur within a designed stilling basin, engineers can protect the channel from the destructive forces of high-velocity water.

• Erosion Control: In irrigation canals and other waterways, hydraulic jumps can be used to reduce flow velocity and prevent erosion of the channel banks.

• Mixing: The intense turbulence associated with hydraulic jumps can be used to promote mixing in water treatment plants or other industrial processes.

Understanding and controlling hydraulic jumps is essential for designing safe and efficient hydraulic structures. By carefully considering the conditions that lead to their formation and the characteristics of the jump itself, engineers can harness their energy dissipation properties to protect infrastructure and manage water resources effectively.

Hydraulic jumps provide a dramatic illustration of energy dissipation and flow regime transition. However, quantifying the flow before or after such a jump, or in stable subcritical reaches, requires different tools. Two prominent formulas for estimating flow velocity in open channels are Manning's Equation and Chézy's Formula. These equations, while distinct in their origins and parameters, offer valuable insights into the behavior of subcritical flow and are essential tools for hydraulic engineers.

Manning's Equation and Chézy's Formula: Calculating Flow Velocity

Understanding Manning's Equation

Manning's Equation is an empirical formula used to estimate the average velocity of a liquid flowing in an open channel under the influence of gravity. It provides a practical way to determine flow velocity based on channel characteristics and roughness.

The equation is expressed as:

V = (k/n) R^(2/3) S^(1/2)

Where:

• V is the average flow velocity (m/s or ft/s).
• k is a conversion factor (1 for metric units, 1.49 for US customary units).
• n is Manning's roughness coefficient (dimensionless).
• R is the hydraulic radius (m or ft).
• S is the channel slope (dimensionless).

Parameters in Manning's Equation

Each parameter in Manning's equation plays a crucial role in determining the flow velocity.

The hydraulic radius (R) is the ratio of the cross-sectional area of flow to the wetted perimeter. It represents the efficiency of the channel in conveying water. A larger hydraulic radius generally indicates a more efficient channel.

The channel slope (S) is the decline of the channel bed over a given distance. A steeper slope results in a higher flow velocity, as gravity exerts a greater force on the water.

Manning's roughness coefficient (n) is an empirical value that represents the roughness of the channel bed and banks. It accounts for the resistance to flow caused by the channel's surface. Values range from 0.01 for very smooth channels to 0.07 or higher for channels with dense vegetation or highly irregular surfaces. Accurate determination of 'n' is often the most challenging aspect of applying Manning's equation.

Chézy's formula is an earlier, more fundamental equation for calculating flow velocity in open channels. It's based on the balance between the driving force of gravity and the resisting force of friction.

The formula is expressed as:

V = C (R S)^(1/2)

Where:

• V is the average flow velocity (m/s or ft/s).
• C is the Chézy coefficient (m^(1/2)/s or ft^(1/2)/s).
• R is the hydraulic radius (m or ft).
• S is the channel slope (dimensionless).

The Chézy coefficient (C) represents the resistance to flow and is related to Manning's roughness coefficient.

Comparing Manning's Equation and Chézy's Formula

While both equations estimate flow velocity, they differ in their approach and the parameters used.

Manning's Equation is more empirical and relies heavily on the Manning's roughness coefficient, which is determined experimentally. It is widely used due to its simplicity and ease of application.

Chézy's formula is more fundamental, based on a theoretical balance of forces. The Chézy coefficient is less intuitive than Manning's n and is often derived from experimental data or related to Manning's n.

The relationship between the Chézy coefficient (C) and Manning's roughness coefficient (n) can be approximated as:

C = (R^(1/6))/n (in metric units)

C = (1.49 * R^(1/6))/n (in US customary units)

This relationship highlights that Chézy's C is not constant but depends on the hydraulic radius, making Manning's equation often preferred for practical applications.

Practical Applications and Examples

Both Manning's Equation and Chézy's Formula are invaluable tools for estimating flow velocity in subcritical flow conditions.

For instance, consider a rectangular concrete channel with a known slope, depth, and width. Using Manning's Equation, an engineer can estimate the flow velocity by selecting an appropriate Manning's roughness coefficient for concrete and calculating the hydraulic radius. This velocity can then be used to determine the discharge capacity of the channel.

Similarly, Chézy's formula can be applied to estimate flow velocity in a natural stream with a known hydraulic radius and slope, provided an appropriate Chézy coefficient can be estimated or derived.

These equations are commonly used in:

• Designing irrigation canals to ensure adequate water delivery.
• Estimating flood discharge in rivers and streams.
• Analyzing the performance of culverts and other hydraulic structures.
• Assessing the impact of channel modifications on flow conditions.

By applying these equations, engineers and hydrologists can gain valuable insights into the behavior of subcritical flow and design hydraulic structures that operate safely and efficiently.

Hydraulic jumps provide a dramatic illustration of energy dissipation and flow regime transition. However, quantifying the flow before or after such a jump, or in stable subcritical reaches, requires different tools. Two prominent formulas for estimating flow velocity in open channels are Manning's Equation and Chézy's Formula. These equations, while distinct in their origins and parameters, offer valuable insights into the behavior of subcritical flow and are essential tools for hydraulic engineers.

Applications in Open Channel Flow: Real-World Examples

The principles of subcritical flow aren't confined to textbooks and laboratory experiments; they are fundamental to understanding and managing water resources in a variety of real-world open channel systems.

From the meandering paths of natural rivers to the precisely engineered structures of irrigation canals and hydraulic control systems, subcritical flow dictates much of the observed behavior and requires careful consideration in design and operation.

Subcritical Flow in Natural Rivers and Streams

In their natural state, most rivers and streams exhibit subcritical flow for the majority of their length. The relatively gentle slopes and wider cross-sections promote flow depths that exceed the critical depth.

This characteristic is crucial for maintaining healthy aquatic ecosystems. Slower flow velocities reduce erosion, allow for sediment deposition, and create diverse habitats for various species.

Understanding the dynamics of subcritical flow in natural waterways is essential for effective river management, including flood control, habitat restoration, and water quality preservation.

Analyzing flow rates, channel geometry, and roughness characteristics allows hydrologists to predict water levels, assess flood risks, and design appropriate mitigation measures.

Engineered Canals and Irrigation Systems

Engineered canals and irrigation systems rely heavily on the principles of subcritical flow to efficiently convey water over long distances. These channels are typically designed with mild slopes and controlled cross-sections to maintain stable, subcritical conditions.

Maintaining subcritical flow in irrigation canals is paramount for minimizing energy losses, preventing erosion, and ensuring a consistent water supply to agricultural fields.

Sudden transitions to supercritical flow can lead to significant energy dissipation and damage to the channel structure.

Therefore, careful hydraulic design, incorporating factors like channel roughness, slope, and cross-sectional geometry, is critical for optimizing the performance and longevity of these systems.

Subcritical Flow in Culverts and Weirs

Culverts and weirs are hydraulic structures designed to control and measure flow in open channels. While these structures can induce complex flow patterns, subcritical flow often prevails upstream and downstream, especially under normal operating conditions.

Culverts, which are typically used to convey water under roads or other obstructions, are designed to minimize flow disruption and maintain subcritical conditions.

Weirs, on the other hand, are specifically designed to create a controlled flow constriction, allowing for accurate measurement of flow rates based on the upstream water depth.

The flow over a weir can transition from subcritical to supercritical and back to subcritical, but the upstream reach is typically designed to maintain subcritical conditions for accurate measurement and stable operation.

Impact on Flow Conditions

Understanding the effects of structures like culverts and weirs on flow conditions is vital for designing effective and safe hydraulic systems.

These structures alter the channel geometry and flow regime, leading to changes in water depth, velocity, and energy.

By analyzing flow characteristics and considering factors like channel slope, roughness, and structure geometry, engineers can design systems that effectively manage water resources while minimizing environmental impacts.

The ability to accurately predict flow behavior under varying conditions is essential for mitigating flood risks, optimizing water distribution, and protecting aquatic ecosystems.

Applications in Open Channel Flow have highlighted the real-world significance of subcritical flow across various systems. Accurately modeling, measuring, and managing such flow requires a diverse set of tools and techniques, ranging from classical hydraulic instruments to sophisticated numerical simulations.

Tools and Techniques for Analyzing Subcritical Flow

Analyzing subcritical flow in open channels requires a multifaceted approach, utilizing both established measurement techniques and advanced computational tools. This section explores some of the key instruments and methods employed by engineers and scientists to understand and predict subcritical flow behavior.

Venturi Meters: Measuring Flow Rate and Regime Variation

Venturi meters are differential pressure flow meters. They are commonly used for measuring flow rates in pipes and closed conduits. Their application in open channel flow is more nuanced but valuable, especially in constricted sections or engineered channels.

A Venturi meter works by constricting the flow, causing an increase in velocity and a corresponding decrease in pressure. By measuring the pressure difference between the unconstricted and constricted sections, the flow rate can be accurately determined.

In the context of subcritical flow, the geometry of a Venturi meter can induce varying flow regimes. While the upstream section typically maintains subcritical flow, the constricted throat may, under certain conditions, transition to critical or even supercritical flow.

Understanding these localized flow regime changes is crucial for accurate flow measurement and for preventing undesirable phenomena like cavitation. Designers must consider the potential for these transitions and ensure the Venturi meter is appropriately sized and positioned to avoid adverse effects.

Computational Fluid Dynamics (CFD): Simulating Subcritical Flow

Computational Fluid Dynamics (CFD) has emerged as a powerful tool for simulating and analyzing complex flow phenomena, including subcritical flow in open channels. CFD software uses numerical methods to solve the governing equations of fluid flow, such as the Navier-Stokes equations.

This allows engineers to create detailed models of open channel systems and to predict flow velocity, water depth, and other important parameters under various conditions.

Advantages of CFD in Subcritical Flow Analysis

• Detailed Flow Field Information: CFD provides high-resolution information about the entire flow field. It goes beyond point measurements, offering insights into velocity profiles, pressure distributions, and turbulence characteristics.
• Complex Geometries and Boundary Conditions: CFD can handle complex channel geometries and boundary conditions that are difficult or impossible to analyze using traditional methods. This includes irregular channel shapes, vegetation, and obstructions.
• Scenario Testing and Optimization: CFD enables engineers to test different design scenarios and optimize channel geometry for specific performance objectives, such as minimizing flow resistance or preventing erosion.

Considerations When Using CFD

While CFD is a valuable tool, it's essential to recognize its limitations. The accuracy of CFD simulations depends on the quality of the model, the choice of turbulence models, and the computational resources available.

• Validation of CFD results with experimental data is crucial to ensure accuracy and reliability.

United States Geological Survey (USGS): Monitoring and Research

The United States Geological Survey (USGS) plays a vital role in studying water resources and flow characteristics across the United States. The USGS operates a vast network of streamgages that continuously monitor water levels and flow rates in rivers and streams.

Data collected by the USGS is essential for understanding long-term trends in water availability, assessing flood risks, and managing water resources effectively.

USGS Contributions to Subcritical Flow Understanding

• Data Collection and Dissemination: The USGS collects and disseminates vast amounts of data on streamflow, water quality, and groundwater levels.
• Research and Modeling: The USGS conducts research on various aspects of hydrology, including the behavior of subcritical flow in natural channels. This research helps to improve our understanding of river dynamics and to develop better models for predicting flow behavior.
• Collaboration and Partnerships: The USGS collaborates with other federal agencies, state and local governments, and academic institutions to address water resource challenges.

By studying the data gathered from these techniques, we can more efficiently understand river behavior, manage water resources, and design systems in a more sustainable way.

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