Hubbry Logo
Wake (physics)Wake (physics)Main
Open search
Wake (physics)
Community hub
Wake (physics)
logo
8 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Wake (physics)
Wake (physics)
Wake (physics)
View on Wikipedia
from Wikipedia
Kelvin wake pattern generated by a small boat.

In fluid dynamics, a wake may either be:

  • the region of recirculating flow immediately behind a moving or stationary blunt body, caused by viscosity, which may be accompanied by flow separation and turbulence, or
  • the wave pattern on the water surface downstream of an object in a flow, or produced by a moving object (e.g. a ship), caused by density differences of the fluids above and below the free surface and gravity (or surface tension).

Viscosity

[edit]
Visualisation of the Kármán vortex street in the wake behind a circular cylinder in air; the flow is made visible through release of oil vapour in the air near the cylinder.

The wake is the region of disturbed flow (often turbulent) downstream of a solid body moving through a fluid, caused by the flow of the fluid around the body.

For a blunt body in subsonic external flow, for example the Apollo or Orion capsules during descent and landing, the wake is massively separated and behind the body is a reverse flow region where the flow is moving toward the body. This phenomenon is often observed in wind tunnel testing of aircraft, and is especially important when parachute systems are involved, because unless the parachute lines extend the canopy beyond the reverse flow region, the chute can fail to inflate and thus collapse. Parachutes deployed into wakes suffer dynamic pressure deficits which reduce their expected drag forces. High-fidelity computational fluid dynamics simulations are often undertaken to model wake flows, although such modeling has uncertainties associated with turbulence modeling (for example RANS versus LES implementations), in addition to unsteady flow effects. Example applications include rocket stage separation and aircraft store separation.

Density differences

[edit]

In incompressible fluids (liquids) such as water, a bow wake is created when a watercraft moves through the medium; as the medium cannot be compressed, it must be displaced instead, resulting in a wave. As with all wave forms, it spreads outward from the source until its energy is overcome or lost, usually by friction or dispersion.

The non-dimensional parameter of interest is the Froude number.

Wave cloud pattern in the wake of the Île Amsterdam (lower left, at the "tip" of the triangular formation of clouds) in the southern Indian Ocean
Cloud wakes from the Juan Fernández Islands
Wake patterns in cloud cover over Possession Island, East Island, Ile aux Cochons, Île des Pingouins

Kelvin wake pattern

[edit]
This section is an excerpt from Kelvin wake pattern.[edit]
Fr = 0.5
Fr = 1
Fr = 2
Kelvin wake simulation for Gaussian distortion (shown besides the wake) at various Froude numbers

Waterfowl and boats moving across the surface of water produce a wake pattern, first explained mathematically by Lord Kelvin and known today as the Kelvin wake pattern.[1]

This pattern consists of two wake lines that form the arms of a chevron, V, with the source of the wake at the vertex of the V. For sufficiently slow motion, each wake line is offset from the path of the wake source by around arcsin(1/3) = 19.47° and is made up of feathery wavelets angled at roughly 53° to the path.

Other effects

[edit]

The above describes an ideal wake, where the body's means of propulsion has no other effect on the water. In practice the wave pattern between the V-shaped wavefronts is usually mixed with the effects of propeller backwash and eddying behind the boat's (usually square-ended) stern.

The Kelvin angle is also derived for the case of deep water in which the fluid is not flowing in different speed or directions as a function of depth ("shear"). In cases where the water (or fluid) has shear, the results may be more complicated.[2] Also, the deep water model neglects surface tension, which implies that the wave source is large compared to capillary length.

Recreation

[edit]

"No wake zones" may prohibit wakes in marinas, near moorings and within some distance of shore[3] in order to facilitate recreation by other boats and reduce the damage wakes cause. Powered narrowboats on British canals are not permitted to create a breaking wash (a wake large enough to create a breaking wave) along the banks, as this erodes them. This rule normally restricts these vessels to 4 knots (4.6 mph; 7.4 km/h) or less.

Wakes are occasionally used recreationally. Swimmers, people riding personal watercraft, and aquatic mammals such as dolphins can ride the leading edge of a wake. In the sport of wakeboarding the wake is used as a jump. The wake is also used to propel a surfer in the sport of wakesurfing. In the sport of water polo, the ball carrier can swim while advancing the ball, propelled ahead with the wake created by alternating armstrokes in crawl stroke, a technique known as dribbling. Furthermore, in the sport of canoe marathon, competitors use the wake of fellow kayaks in order to save energy and gain an advantage, through the practice of sitting their boats on the wake of another, so their kayak is propelled by the wash.

See also

[edit]

References

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Wake (physics)

View on Grokipedia
from Grokipedia
In physics, particularly within the field of fluid dynamics, a wake is the region of disturbed flow—often characterized by turbulence and unsteady motion—that forms downstream of a solid body moving relative to a surrounding fluid, such as air or water. This phenomenon results from the fluid's interaction with the body, where viscous effects and pressure gradients cause the flow to separate from the body's surface, leading to a trailing zone of recirculating eddies and reduced velocity compared to the undisturbed upstream flow. Wakes typically form when the —the thin layer of fluid adjacent to the body—experiences an , causing the flow near the surface to reverse direction and detach, creating a separated shear layer that rolls up into vortices. For bluff bodies like cylinders or spheres, this separation is pronounced, producing large-scale structures such as the von Kármán vortex street, a repeating pattern of alternating counter-rotating vortices shed at a characteristic frequency determined by the body's size, flow speed, and fluid properties (governed by the ). In contrast, streamlined bodies minimize separation, resulting in narrower wakes with less turbulence. These dynamics are influenced by the , which dictates the transition from laminar to turbulent flow regimes in the wake. The formation and evolution of wakes have significant implications for drag forces, , and in applications. Wakes contribute substantially to form drag on vehicles, , and marine vessels by converting into through viscous in the eddies, often accounting for a large portion of total resistance at higher speeds. In , wake turbulence behind poses hazards to following planes, while in hydrodynamics, boat wakes can affect and . Understanding wakes is crucial for design optimizations, such as shapes to reduce induced drag or vortex suppression techniques to prevent in structures. Advanced studies also explore wakes in complex scenarios, including stratified fluids or multi-body interactions, to improve efficiency in turbines and systems.

Fundamentals

Definition and Characteristics

In fluid dynamics, a wake refers to the region of disturbed flow downstream of a solid body moving through a fluid, characterized by recirculating or slower-moving fluid relative to the undisturbed free stream, resulting from the body's interaction with the surrounding medium. This disturbance arises as the fluid separates from the body's surface, creating a low-pressure zone that draws fluid back toward the body and generates complex flow patterns. Key characteristics of wakes include velocity deficits, where the local speed is reduced compared to the free-stream velocity, leading to loss and associated the body; pressure variations across the wake due to the separation and recirculation; and the presence of , which manifests as rotational motion and can promote formation. Wakes may exhibit at low Reynolds numbers, with smooth, ordered streamlines, or become turbulent at higher Reynolds numbers (typically Re > ~1000 for bluff bodies), where irregular fluctuations enhance mixing and of the disturbance. In turbulent wakes, the increased often leads to and larger-scale eddies, amplifying the wake's unsteadiness. Wakes occur across various media, such as air, where generate trailing vortices that persist far downstream and pose hazards to following planes; , as seen in wakes that produce surface waves and subsurface ; and gases, exemplified by exhaust plumes that create elongated disturbed regions behind the vehicle due to high-speed ejection and mixing. The spatial extent of a wake follows basic scaling laws: its initial width is proportional to the or characteristic dimension of the body, while the wake and spreading increase with downstream , driven by viscous and entrainment of ambient . In the near wake, close to the body, the disturbance is highly concentrated, but it broadens progressively, with the rate of growth depending on the flow regime and properties.

Historical Development

The study of wakes in physics originated in the 19th century amid naval efforts to optimize ship and reduce drag, where empirical observations of trailing wave patterns informed early hydrodynamic designs. These practical concerns prompted theoretical advancements, culminating in Lord Kelvin's seminal analysis, which mathematically derived the characteristic V-shaped wave pattern formed by a ship moving through deep water at constant speed, assuming and linear wave theory. Kelvin's work, motivated by needs, established foundational principles for dispersive surface waves and remains a cornerstone for understanding far-field wake geometry. The early 20th century shifted focus to viscous effects, with Ludwig Prandtl's 1904 theory introducing the concept of a thin shear layer near solid surfaces where dominates, directly explaining the formation and persistence of wakes behind bluff bodies like or airfoils. Building on this, developed the vortex street model in 1911–1912, describing the periodic shedding of alternating vortices in the wake of a at moderate Reynolds numbers, which quantified unsteady drag and mechanisms through stability . These contributions bridged inviscid and viscous regimes, enabling predictive models for aerodynamic and hydrodynamic wakes. Mid-20th-century progress accelerated through experimental and computational methods, as facilities proliferated post-World War II to study wakes, revealing complex vortex dynamics critical for flight safety. 's research from the 1950s onward, including wake vortex studies in the 1960s–1970s, utilized large-scale tunnels and early numerical simulations to mitigate hazards like trailing vortices from jetliners, informing spacing standards for . Initial (CFD) efforts in the 1960s, leveraging methods on early computers, began simulating wake flows, though limited by grid resolution and closure models. Post-2000 developments marked a in wake theory, with advanced CFD incorporating large eddy simulations and high-fidelity meshes to resolve multi-scale in wakes, enabling accurate predictions for complex geometries like arrays. Interdisciplinary links emerged, applying to analyze deterministic unpredictability in wake instabilities, such as bimodal transitions in square-back body flows. By the 2020s, integration accelerated wake prediction, using data-driven surrogates to approximate CFD outputs for real-time applications, while microscale wake studies for unmanned aerial vehicles (UAVs) in formation flight optimized energy savings by modeling rotor interference and vortex upwash.

Viscous Wakes

Formation Mechanisms

The formation of viscous wakes behind bluff bodies is primarily driven by the effects of fluid viscosity, which generates frictional forces that decelerate fluid particles adjacent to the body surface, thereby creating a thin of reduced velocity. This boundary layer experiences an in the aft region of the body, where rises in the flow direction due to the body's decelerating the external flow. The opposes the momentum in the boundary layer, and when it exceeds the layer's capacity to recover, reverse flow occurs near the wall, leading to boundary layer separation and the onset of the wake as low-velocity fluid is shed into the . Boundary layer dynamics govern the transition from attached flow upstream to separated shear layers that define the wake boundaries. Initially, the adheres to the surface with velocity increasing from zero at the wall () to value at its edge; however, the reduces the layer's momentum, causing the velocity profile to inflect and the wall to approach zero at the separation point. Beyond separation, the flow detaches, forming two free shear layers that bound a region of recirculating fluid, marking the wake's core. For bluff bodies like cylinders, this process often results in periodic from the shear layers, quantified by the St=fDUSt = \frac{f D}{U}, where ff is the shedding frequency, DD is the body's characteristic diameter, and UU is the velocity; typical values range from 0.18 to 0.22 for circular cylinders in subcritical regimes. In viscous wakes, form drag predominates over , stemming from the asymmetric pressure distribution induced by separation: high pressure at the forward contrasts with low pressure in the separated wake region. This pressure imbalance generates a opposing the motion, with the wake acting as a low-pressure cavity. Wake formation mechanisms depend strongly on the Re=UDνRe = \frac{U D}{\nu}, where ν\nu is kinematic , delineating distinct regimes. At low ReRe (e.g., Re<1Re < 1), creeping flow prevails with viscous diffusion dominating, yielding symmetric fore-aft flow and no separation, as in Stokes flow past a sphere where drag is purely viscous. Separation emerges at moderate ReRe (roughly 5–40 for cylinders), forming a steady, symmetric wake with closed recirculating bubbles. In the subcritical regime (high ReRe, 300 to ≈3×10^5), the boundary layer remains laminar and separates early (≈80°–85° from stagnation), producing wide wakes with high drag. Near the critical Reynolds number (≈3×10^5), transition to a turbulent boundary layer delays separation to ≈120°, narrowing the wake and causing a sharp reduction in drag known as the drag crisis. A detailed aspect of viscous wake formation involves the development and stability of separation bubbles, closed zones of recirculating flow immediately downstream of the body where separated shear layers initially converge before diverging. These bubbles form due to the balance between adverse pressure recovery and viscous entrainment, often exhibiting unsteady behavior as instabilities amplify within the shear layers, potentially bursting to initiate shedding or turbulence. Bubble stability is sensitive to ReRe and surface roughness; stable bubbles maintain attached-like flow in transitional regimes, while unstable ones contribute to wake widening and drag escalation, a phenomenon underexplored in early models but critical for predicting onset of unsteadiness. In contrast to inviscid flows lacking separation, viscosity enables bubble persistence, fostering turbulent eddies that evolve the wake downstream.

Turbulence and Vortex Dynamics

In the downstream evolution of viscous wakes, vortex shedding manifests as the periodic detachment of coherent vortical structures from the separated shear layers of bluff bodies, such as circular cylinders. This process generates a characteristic pattern known as the Kármán vortex street, consisting of alternating rows of counter-rotating vortices that propagate downstream. The shedding frequency ff is given by f=St⋅U/Df = \mathrm{St} \cdot U / D, where UU is the free-stream velocity, DD is the body diameter, and the Strouhal number St≈0.2\mathrm{St} \approx 0.2 for cylinders over a wide range of Reynolds numbers in the subcritical regime. Wake instabilities drive the transition from ordered vortex shedding to fully developed turbulence, primarily through the Kelvin-Helmholtz mechanism acting on the free shear layers. In these layers, velocity gradients amplify small disturbances into rolling-up vortices, with growth rates peaking at nondimensional frequencies around 0.5 based on the momentum thickness. This instability promotes three-dimensional perturbations, leading to vortex pairing and eventual breakdown into smaller-scale motions as the wake meanders and widens. Turbulent wakes exhibit hierarchical structures characterized by integral length scales on the order of the wake half-width, which grow linearly with downstream distance, governing the energy-containing eddies. Energy cascades from these large-scale vortices through inertial-range scales to viscous dissipation at Kolmogorov microscales, with the cascade rate determined by the mean shear and turbulence intensity. Key components of the Reynolds stress tensor, such as the streamwise-vorticity normal stress ⟨u′2⟩\langle u'^2 \rangle and the shear stress −⟨u′v′⟩-\langle u' v' \rangle, dominate near the centerline and shear layers, respectively, contributing up to 70% of the total turbulent kinetic energy transport in high-Reynolds-number cylinder wakes. Numerical modeling of these dynamics contrasts Large Eddy Simulation (LES), which resolves large-scale vortices and models subgrid-scale dissipation to capture unsteady shedding and instability growth, with Reynolds-Averaged Navier-Stokes (RANS) approaches that average and struggle with anisotropic stresses in separated regions. LES provides superior prediction of wake unsteadiness but incurs higher computational costs, particularly for high-Reynolds-number flows where grid resolution must exceed the Taylor microscale. Recent advances in direct numerical simulation (DNS) for high-Reynolds-number wakes (Re > 10^4) have leveraged to resolve all scales without modeling, revealing finer details of secondary instabilities and production in cylinder wakes up to Re = 1.4 × 10^5. These simulations highlight the persistence of large-scale coherence amid small-scale , informing improved subgrid models for LES.

Inviscid Wakes

Density and Gravity Effects

In fluids exhibiting stratification, such as oceanic environments with thermoclines where increases with depth, the motion of a body generates internal waves that propagate within the fluid layers. These internal waves arise due to forces restoring displaced fluid parcels, with the oscillation governed by the Brunt-Väisälä , defined as N=−gρdρdzN = \sqrt{ -\frac{g}{\rho} \frac{d\rho}{dz} }
Add your contribution
Related Hubs
User Avatar
No comments yet.