78

These waves are called "roll waves." They are due to an instability in shallow shear flows. The analysis is much too complex for a short answer, but if you google "Roll Wave" you will find more images and links to technical articles. If you are not bothered by a little mathematics you will find a discussion of the cause of the instability starting on ...


57

You are correct if your boat will only travel in a straight line. In real life the motion of the boat will often have a yaw angle, so that it is moving slightly "sideways" relative to the water. For example it is impossible to make a turn and avoid this situation. If the front is too sharp, the result will be that the flow can not "get round ...


37

Gravity can, of course, become turbulent if it is coupled to a turbulent fluid. The interesting question is thus, as John Rennie points out, whether a vacuum solution can be "turbulent". As far as I'm aware this is not known. If turbulence does occur in vacuum gravity, it is remarkably hard to stir up. Even in very extreme situations like colliding black ...


29

Any speculation about what shape might be best is meaningless without specifying the flow conditions. For the keel on a boat, the main one is the Reynolds Number, a parameter that is proportional to the the length multiplied by the speed. In most low-speed applications, a sharp leading-edge is not the best. With any incidence, the flow will tend to separate ...


27

Turbulence is indeed an unsolved problem both in physics and mathematics. Whether it is the "greatest" might be argued but for lack of good metrics probably for a long time. Why it is an unsolved problem from a mathematical point of view read Terry Tao (Fields medal) here. Why it is an unsolved problem from a physical point of view, read Ruelle and Takens ...


20

Thanks to holography, we now know that solutions to the Einstein equation in certain $d+1$ dimensional spaces are equivalent (dual) to solutions of the Navier-Stokes equation in $d$ dimensions. This is the fluid-gravity correspondence. As a result, turbulence can be studied using the Einstein equations, see, for example, http://arxiv.org/abs/1307.7267.


18

I’d like to answer by expanding the analogy made by @Charlie. A theory of everything would be like knowing the rules of chess. We could understand all the rules, the pieces, and their moves and interactions. But there would remain many deep mathematical problems: e.g., what’s the perfect strategy in chess? It seems unlikely that this will be solved in our ...


15

Is this possible; due to some effect of turbulence? Sure. I'd consider that video plausible, at the very least. Can the "suction force" due to a moving vehicle propel an object, faster than the speed of the vehicle itself? If so, from where does the extra kinetic energy of the box come from? First, keep in mind that the box already has enough ...


13

From the Wikipedia article for Reynolds number: In fluid mechanics, the Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions. In addition to measuring the ratio of inertial to viscous ...


11

Reynold's number is defined to be: $$ \text{Re} = \frac{ v D }{ \nu } $$ where $v$ is the characteristic velocity for the flow, $D$ is a characteristic size and $\nu$ is the kinematic viscosity. Now, why should we care? Why is Reynold's number important? Well, the first thing to realize is that the Reynolds number is a dimensionless number. This means ...


9

Basically, the scale of a certain parameter is the order of magnitude of that parameter. Being able to determine the scales of a parameters in a complex system (like turbulence problems) is very useful. For turbulence, the size of the largest eddies is given by the characteristic length scale you are working with, $L$, and the smallest eddy size is given ...


9

Update Recently, there was a talk titled Turbulent gravity in asymptotically AdS spacetimes which may be of interest. In these papers, spacetimes which are anti-de Sitter asymptotically with reflecting boundary conditions are considered, and the notion of turbulence in this case is that small perturbations about these spacetimes exhibit 'turbulent behavior.'...


8

The onset of turbulence in fluids is determined by the Reynolds number $$ \mathrm{Re} = \frac{vL}{\nu}, $$ where $L$ is the characteristic length scale, $v$ the characteristic velocity, and $\nu$ the viscosity. The onset of turbulence in fluids occurs for $\mathrm{Re}$ greater than about 1000 or more, depending on geometry. If we want to see the equivalent ...


8

Can we have unified theory of universe without solving the problem of turbulence? Yes. Because the "unified" in the name refers to the basic interactions, from which in principle everything could be explained. In practice, a hierarchy of models, with effective theories emerging from lower-level ones (think fluids laws from molecules' interactions, ...


8

Dimensionless numbers in fluid dynamics are always a ratio of two quantities. The expression that you share is only a results of that expression. The Reynolds number is defined as the ratio between inertial forces and viscous forces. Both forces can be approximated from the Navier-Stokes equations. The inertial term is: $\rho \vec{u} \cdot \nabla\vec{u}\sim \...


7

Turbulence is not one of the great unsolved problems in physics. Physics tells us exactly how turbulence emerges as a direct consequence of local mass and momentum conservation. We can create multiparticle computer models such as lattice gas automata that generate turbulence at large length and time scales. We can write down the equations that govern ...


7

The size of the Kolmogorov scale is not universal, it is dependent on the flow phenomena you are looking at. I don't know the details for compressible flows, so I will give you some hints on incompressible flows. From the quotes poem, you can anticipate that everything that is dissipated at the smallest scales, has to be present at larger scale first. ...


7

The Reynolds number, with $\rho$ the density, $u$ the velocity magnitude, $\mu$ the viscosity and $L$ some characteristic length scale (e.g. channel height or pipe diameter) is given by $$\text{Re}=\frac{\rho~u~L}{\mu}.$$ This is a dimensionless relation of the ratio of inertial forces ($\rho u u$) to viscous forces ($\mu\frac{u}{L}$). It therefore signifies ...


7

As mentioned above, indeed, this shape is more aerodynamic when parallel to the vector field (flow direction) in particular. You see this shape often on long distance Kayaks and Canoes that move in relatively straight lines. But this shape is certainly not ideal for changing directions, as the drag will be greater than with your first shape.


7

Think about why race cars follow each other very closely. The reason is that the first car creates a suction behind it. This is actually a huge problem with transport trucks because it is very bad for fuel consumption. On this page you can see one possible solution to the problem, flaps that stick out the back of a truck and reduce the suction effect. ...


7

One real-life application of the Reynolds number (no apostrophe as it is named after Osborne Reynolds) is in the design of small scale simulations of fluid dynamics scenarios, such as wind tunnel and water tank models. The Reynolds number is one of the dimensionless parameters that must be replicated in scale models in order to accurately reproduce the full ...


6

The high speed expression, proportional to $v^2$ is the ram pressure, which is wholly a momentum transfer effect and has nothing to do with viscosity - in contrast with the low flow speed Stokes law you cite above. To understand the ram pressure, which arises particularly for supersonic objects, witness the object is just shoving fluid out of its way, and ...


6

Let's make some assumptions. First, assume the fish is rigid. Second, let's assume he's not flapping. Third, I guess let's assume it's a male fish since I said "he." We'll also assume this is 2D because we're looking for an approximation. I would approximate the fish as an airfoil. NACA airfoils are a pretty good choice because they are analytically defined ...


6

The truck will have in its wake some unknown mass of air almost moving with a speed $v$ comparable to the truck's speed $\bf V$. The pressure behind the truck will be lower than the pressure at the sidewalk because air pressure follows the Bernoulli equation, $$ P_\mathbf{P} = P_\text{road} + \frac{1}{2}\rho v^2, $$ where $\rho \approx 1~$kg/m$^3$ is the ...


6

There are three ways you can proceed in: 1. Homogeneous Flow Model Herein, you would assume single averaged flow quantities and then solve the Navier-Stokes equations as if it were arising from the flow of an averaged liquid. What I mean is that if you had water and steam flowing together, you would take the average density, viscosity and so on. Obviously ...


6

The reason why the aft ends of airplanes are streamlined is to preserve a smooth flow of air. Just as the fore ends of airplanes are streamlined to smoothly cleave the air, so too the aft ends are streamlined to smoothly reintegrate the flows. Turbulence is bad, regardless of where on the aircraft it occurs. (source: answcdn.com) Note that there is ...


6

I think that the explanation is that waves of different size run with different speeds. This makes the faster waves run up to the slower which make them stack up, or constructively interfere.


5

Here's a relevant quote from David C. Wilcox's Turbulence Modeling for CFD. This is discussing the interpretation of $\omega_t$, which here is the specific turbulent dissipation rate*. (also, $k_t$ is the turbulent kinetic energy*) In subsequent development efforts, the interpretation of $\omega$ has behaved a bit like the turbulent fluctuations it is ...


5

From mathematics point of view, it is a surface integral of the scalar quantity |Curl v $|^2$. The physical meaning of it, in the context of fluid dynamics in 2-D or 3-D, is that it has the units $(m/s)^2$ which when multiplied by the density of a fluid represents some form of energy. As for the meaning of the intgral in a D-dimentional space, the problem is ...


5

The problem with the phase space flow in Hamiltonian mechanics is that the flow itself is non-dynamical, that is, the flow is immediately defined for a given Hamiltonian, so there is no independent equation governing its evolution. Thus, Liouville equation is simply a transport of a scalar variable in a given flow. So, dimensional analysis of the flow ...


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